Seminar information archive - Graduate School of Mathematical Sciences: Seminar information -05/16/2012
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2012/05/16
16:40 - 17:40Room #002 (Mathematics building)
Naoya Umezaki (University of Tokyo)
"On uniform bound of the maximal subgroup of the inertia group acting unipotently on $¥ell$-adic cohomology"
For a smooth projective variety over a local field,
the action of the inertia group on the $¥ell$-adic cohomology group is
unipotent if it is restricted to some open subgroup.
In this talk, we give a uniform bound of the index of the maximal open
subgroup satisfying this property.
This bound depends only on the Betti numbers of $X$ and certain Chern
numbers depending on a projective embedding of $X$.
2012/05/15
16:30 - 18:00Room #128 (Mathematics building)
MIZUTANI, Haruya (Research Institute for Mathematical Sciences, Kyoto University)
" Strichartz estimates for Schr\"odinger equations with variable coefficients and unbounded electromagnetic potentials"
In this talk we consider the Cauchy problem for Schr\"odinger equations with variable coefficients and unbounded potentials. Under the assumption that the Hamiltonian is a long-range perturbation of the free Schr\"odinger operator, we construct an outgoing parametrix for the propagator near infinity, and give applications to sharp Strichartz estimates. The basic idea is to combine the standard approximation by using a time dependent modifier, which is not in the semiclassical regime, with the semiclassical approximation of Isozaki-Kitada type. We also show near sharp Strichartz estimates without asymptotic conditions by using local smoothing effects.
2012/05/14
10:30 - 12:00Room #126 (Mathematics building)
Hiroshi KANEKO (Tokyo University of Science)
"Duality in the unit circle and the ring of p-adic intergers and van der Corput series"
2012/05/11
16:30 - 17:30Room #002 (Mathematics building)
SAKASAI Takuya (University of Tokyo)
"Moduli spaces and symplectic derivation Lie algebras"
First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).
14:50 - 16:00Room #006 (Mathematics building)
FUKASAWA, Masaaki (Department of Mathematics, Osaka University)
"Efficient Discretization of Stochastic Integrals"
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html
2012/05/08
16:30 - 18:00Room #056 (Mathematics building)
Tadashi Ishibe (The University of Tokyo, JSPS)
"Infinite examples of non-Garside monoids having fundamental elements"
The Garside group, as a generalization of Artin groups,
is defined as the group of fractions of a Garside monoid.
To understand the elliptic Artin groups, which are the fundamental
groups of the complement of discriminant divisors of the semi-versal
deformation of the simply elliptic singularities E_6~, E_7~ and E_8~,
we need to consider another generalization of Artin groups.
In this talk, we will study the presentations of fundamental groups
of the complement of complexified real affine line arrangements
and consider the associated monoids.
It turns out that, in some cases, they are not Garside monoids.
Nevertheless, we will show that they satisfy the cancellation condition
and carry certain particular elements similar to the fundamental elements
in Artin monoids.
As a result, we will show that the word problem can be solved
and the center of them are determined.
16:30 - 18:00Room #002 (Mathematics building)
Motofumi Hattori (Kanagawa Institute of Technology )
"Pressure Oscillation Problem of MPS time evolution scheme for incompressible Navier-Stokes equation "
http://www.infsup.jp/utnas/
14:40 - 16:10Room #470 (Mathematics building)
Keiichi Sakai (Shishu University)
"Embedding spaces and string topology"
There are several similarities between the topology of embedding spaces and that of (free) loop space.
In this talk I will review the similarities, with a focus on "string topology" for embedding spaces.
2012/05/07
10:30 - 12:00Room #126 (Mathematics building)
Yoshihiko Matsumoto (University of Tokyo)
"The second metric variation of the total $Q$-curvature in conformal geometry"
Branson's $Q$-curvature of even-dimensional compact conformal manifolds integrates to a global conformal invariant called the total $Q$-curvature. While it is topological in two dimensions and is essentially the Weyl action in four dimensions, in the higher dimensional cases its geometric meaning remains mysterious. Graham and Hirachi have shown that the first metric variation of the total $Q$-curvature coincides with the Fefferman-Graham obstruction tensor. In this talk, the second variational formula will be presented, and it will be made explicit especially for conformally Einstein manifolds. The positivity of the second variation will be discussed in connection with the smallest eigenvalue of the Lichnerowicz Laplacian.
15:30 - 17:00Room #122 (Mathematics building)
Atsushi Ito (University of Tokyo)
"Algebro-geometric characterization of Cayley polytopes"
A lattice polytope is called a Cayley polytope if it is "small" in some
sense.
In this talk, I will explain an algebro-geometric characterization of
Cayley polytopes
by considering whether or not the corresponding polarized toric
varieties are covered by lines, planes, etc.
We can apply this characterization to the study of Seshadri constants,
which are invariants measuring the positivity of ample line bundles.
That is, we can obtain an explicit description of a polarized toric
variety whose Seshadri constant is one.
14:30 - 16:00Room #370 (Mathematics building)
Takuma Akimoto (Keio university, Global environmental leaders program)
"Distributional behaviors of time-averaged observables in anomalous diffusions (subdiffusion and superdiffusion)"
In anomalous diffusions attributed to a power-law distribution,
time-averaged observables such as diffusion coefficient and velocity of drift are intrinsically random. Anomalous diffusion is ubiquitous phenomenon not only in material science but also in biological transports, which is characterized by a non-linear growth of the mean square displacement (MSD).
(subdiffusion: sublinear growth, super diffusion: superlinear growth).
It has been known that there are three different mechanisms generating subdiffusion. One of them is a power-law distribution in the trapping-time distribution. Such anomalous diffusion is modeled by the continuous time random walk (CTRW). In CTRW, the time-averaged MSD grows linearly with time whereas the ensemble-averaged MSD does not. Using renewal theory, I show that diffusion coefficients obtained by single trajectories converge in distribution. The distribution is the Mittag-Leffler (or inverse Levy) distribution [1,2].
In superdiffusion, there are three different mechanisms. One stems from positive correlations in random walks; the second from persistent motions in random walks, called Levy walk; the third from very long jumps in random walks, called Levy flight.
If the persistent time distribution obeys a power law with divergent mean in Levy walks, the MSD grows as t^2 whereas the mean of positions is zero. When an external bias is added in Levy walks, the response to bias (velocity of drift) appears in the distribution, which is what we term a distributional response [3]. The distribution is the generalized arcsine distribution.
These distributional behaviors open a new window to dealing with the average (ensemble or time average) in single particle tracking experiments.
[1] Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).
[2] T. Miyaguchi and T. Akimoto, Phys. Rev. E 83, 031926 (2011).
[3] T. Akimoto, Phys. Rev. Lett. 108, 164101 (2012)
2012/05/02
16:30 - 18:00Room #128 (Mathematics building)
Yuhei Suzuki (Univ. Tokyo)
"A measurable group theoretic solution to von Neumann's Problem (after Gaboriau and Lyons)"
2012/05/01
16:30 - 18:00Room #056 (Mathematics building)
Hisashi Kasuya (The University of Tokyo)
"Minimal models, formality and hard Lefschetz property of
solvmanifolds with local systems"
2012/04/27
15:00 - 16:10Room #006 (Mathematics building)
NOMURA, Ryosuke (Graduate school of Mathematical Sciences, Univ. of Tokyo)
"Convergence conditions on step sizes in temporal difference learning"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/02.html
2012/04/25
16:30 - 18:00Room #128 (Mathematics building)
Takuya Takeishi (Univ. Tokyo)
"Bost-Connes system and class field theory"
2012/04/24
16:30 - 18:00Room #002 (Mathematics building)
Hideaki Ishikawa (Semiconductor Leading Edge Technologies, Inc.)
"Quantum mechanics and numerical analysis "
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Dylan Thurston (Columbia University)
"Combinatorial Heegaard Floer homology"
Heegaard Floer homology is a powerful invariant of 3- and 4-manifolds.
In 4 dimensions, Heegaard Floer homology (together with the
Seiberg-Witten and Donaldson equations, which are conjecturally
equivalent), provides essentially the only technique for
distinguishing smooth 4-manifolds. In 3 dimensions, it provides much
geometric information, like the simplest representatives of a given
homology class.
In this talk we will focus on recent progress in making Heegaard Floer
homology more computable, including a complete algorithm for computing
it for knots.
2012/04/23
17:10 - 18:40Room #122 (Mathematics building)
Takehiko Yasuda (Osaka University)
"Motivic integration and wild group actions"
The cohomological McKay correspondence proved by Batyrev is the equality of an orbifold invariant
and a stringy invariant. The former is an invariant of a smooth variety with a finite group action and the latter is
an invariant of its quotient variety. Denef and Loeser gave an alternative proof of it which uses the motivic integration theory developped by themselves.
Then I pushed forward with their study by generalizing the motivic integration to
Deligne-Mumford stacks and reformulating the cohomological McKay correspondence from the viewpoint of
the birational geometry of stacks.
However all of these are about tame group actions (the order of a group is not divisible by the characteristic of the base field),
and the wild (= not tame) case has remained unexplored.
In this talk, I will explain my attempt to examine the simplest situation of the wild case. Namely linear actions of a cyclic group
of order equal to the characteristic of the base field are treated. A remarkable new phenomenon is that the space of generalized
arcs is a fibration over an infinite dimensional space with infinite dimensional fibers, where the base space is the space of
Artin-Schreier extensions of $k((t))$, the field of Laurent series.
10:30 - 12:00Room #126 (Mathematics building)
Hajime Tsuji (Sophia University)
"K\"ahler-Ricci flows on projective families"
2012/04/21
13:30 - 17:00Room #122 (Mathematics building)
Yutaka, Terasawa (Graduate School of Mathematical Sciences, University of Tokyo) 13:30 - 15:00
"Dyadic, classical and martingale harmonic analysis"
Yohei Tsutsui (Waseda University) 15:30 - 17:00
"A_\infty constants between BMO and weighted BMO "
2012/04/20
14:50 - 16:00Room #006 (Mathematics building)
KOIKE, Yuta (Graduate school of Mathematical Sciences, Univ. of Tokyo)
"On the asymptotic mixed normality of the pre-averaged Hayashi-Yoshida
estimator with random and nonsynchronous sampling"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/01.html
2012/04/18
16:40 - 17:40Room #056 (Mathematics building)
Alan Lauder (University of Oxford)
"Explicit constructions of rational points on elliptic curves"
I will present an algorithm for computing certain special
values of p-adic L-functions, and discuss an application to
the efficient construction of rational points on elliptic curves.
16:30 - 18:00Room #128 (Mathematics building)
Koichi Shimada (Univ. Tokyo)
"Classification of Group Actions on Factors (after Masuda)"
2012/04/17
16:30 - 18:00Room #056 (Mathematics building)
Eriko Hironaka (Florida State University)
"Pseudo-Anosov mapping classes with small dilatation"
A mapping class is a homeomorphism of an oriented surface
to itself modulo isotopy. It is pseudo-Anosov if the lengths of essential
simple closed curves under iterations of the map have exponential growth
rate. The growth rate, an algebraic integer of degree bounded with
respect to the topology of the surface, is called the dilatation of the
mapping class. In this talk we will discuss the minimization problem
for dilatations of pseudo-Anosov mapping classes, and give two general
constructions of pseudo-Anosov mapping classes with small dilatation.
2012/04/16
15:30 - 17:00Room #122 (Mathematics building)
Makoto Miura (University of Tokyo)
"Toric degenerations of minuscule Schubert varieties and mirror symmetry"
Minuscule Schubert varieties admit the flat degenerations to projective
Hibi toric varieties, whose combinatorial structure is explicitly
described by finite posets. In this talk, I will explain these toric
degenerations and discuss the mirror symmetry for complete intersection
Calabi-Yau varieties in Gorenstein minuscule Schubert varieties.
10:30 - 12:00Room #126 (Mathematics building)
Yusuke Okuyama (Kyoto Institute of Technology)
"Fekete configuration, quantitative equidistribution and wanderting critical orbits in non-archimedean dynamics
"
2012/04/14
13:30 - 16:00Room #123 (Mathematics building)
Kazutoshi Kariyama (Onomichi city university) 13:30 - 14:30
"Explicit formula for the formal degree of the discrete series representations of GL_m(D). "
Keijyu Souno (Math.-Sci., Tokyo Univ.) 15:00 - 16:00
"Moments of the derivatives of the Riemann zeta function"
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.
2012/04/13
14:50 - 16:00Room #006 (Mathematics building)
KAMATANI, Kengo (Graduate School of Engineering Science, Osaka University)
"Asymptotic properties of MCMC for cumulative link model"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html
2012/04/11
16:30 - 18:00Room #128 (Mathematics building)
Shweta Sharma (Univ. Paris Sud)
"Mathematical Aspects of Fractional Quantum Hall Effect"
17:30 - 18:30Room #056 (Mathematics building)
Damian Rossler (CNRS, Universite de Toulouse)
"Around the Mordell-Lang conjecture in positive characteristic "
Let V be a subvariety of an abelian variety A over C and let G\subseteq A(C) be a subgroup. The classical Mordell-Lang conjecture predicts that if V is of general type and G\otimesQ is finite dimensional, then V\cap G is not Zariski dense in V. This statement contains the Mordell conjecture as well as the Manin-Mumford conjecture (for curves). The positive characteristic analog of the Mordell-Lang conjecture makes sense, when A is supposed to have no subquotient, which is defined over a finite field. This positive characteristic analog was proven in 1996 by E. Hrushovski using model-theoretic methods. We shall discuss the prehistory and context of this proof. We shall also discuss the proof (due to the speaker) of the fact that in positive characteristic, the Manin-Mumford conjecture implies the Mordell-Lang conjecture (whereas this seems far from true in characteristic 0).
2012/04/10
16:30 - 18:00Room #056 (Mathematics building)
Takuya Sakasai (The University of Tokyo)
"On homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra"
We discuss homology of symplectic derivation Lie algebras of
the free associative algebra and the free Lie algebra
with particular stress on their abelianizations (degree 1 part).
Then, by using a theorem of Kontsevich,
we give some applications to rational cohomology of the moduli spaces of
Riemann surfaces and metric graphs.
This is a joint work with Shigeyuki Morita and Masaaki Suzuki.
2012/04/09
15:30 - 17:00Room #122 (Mathematics building)
Kazushi Ueda (Osaka University)
"On mirror symmetry for weighted Calabi-Yau hypersurfaces"
In the talk, I will discuss relation between homological mirror symmetry for weighted projective spaces, their Calabi-Yau hypersurfaces, and weighted homogeneous singularities.
If the time permits, I will also discuss an application to monodromy of hypergeometric functions.
10:30 - 12:00Room #126 (Mathematics building)
Shigeharu TAKAYAMA (University of Tokyo)
"Effective estimate on the number of deformation types of families of canonically polarized manifolds over curves
"
2012/04/04
10:30 - 11:30Room #056 (Mathematics building)
Jens Hoppe (Sogang University / KTH Royal Institute of Technology)
"Multi linear formulation of differential geometry and matrix regularizations"
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations.
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and a large class of explicit examples is provided.
2012/04/03
13:30 - 16:00Room #123 (Mathematics building)
Kazutoshi Kariyama (Onomichi city university) 13:30 - 14:30
"Explicit formula for the formal degree of the discrete series representations of GL_m(D). "
Keijyu Souno (Math.-Sci., Tokyo Univ.) 15:00 - 16:00
"Moments of the derivatives of the Riemann zeta function"
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.
2012/03/23
16:30 - 18:00Room #117 (Mathematics building)
Alex Kumjian (University of Nevada, Reno)
"Higher Rank Graph $C^*$-algebras"
10:30 - 11:30Room #117 (Mathematics building)
R. Penner (Aarhus/Caltech)
"Cell decomposition of homotopy Deligne-Mumford."
A long-standing problem has been to extend the ideal cell decomposition of Riemann's moduli space to its compactification by stable curves. In joint work with Doug LaFountain, we have solved this problem with an explicit generalization of fatgraphs. The solution immediately provides a construction of odd-degree cycles, which are conjectured to be non-trivial, thus addressing yet another long-standing issue.
2012/03/21
10:15 - 12:00Room #123 (Mathematics building)
R. Penner (Aarhus/Caltech)
"Geochemical structure of biological macromolecules"
This first of two lectures will explain the basic combinatorial and geometrical structures of both protein and RNA. It is intended to set the stage of subsequent discussions for an audience with mathematical background.
15:15 - 17:00Room #123 (Mathematics building)
R. Penner (Aarhus/Caltech)
"Moduli space techniques in computational biology
"
Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of
3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.
10:00 - 11:00Room #056 (Mathematics building)
Chiun-Chang Lee (National Taiwan University)
"The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations"
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.
2012/03/16
16:30 - 17:30Room #123 (Mathematics building)
Chun LIU (University of Tokyo / Penn State University)
"On Complex Fluids"
The talk is on the mathematical theories, in particular the energetic variational approaches, of anisotropic complex fluids, such as viscoelastic materials, liquid crystals and ionic fluids in proteins and bio-solutions.
Complex fluids, including mixtures and solutions, are abundant in our daily life. The complicated phenomena and properties exhibited by these materials reflects the coupling and competition between the microscopic interactions and the macroscopic dynamics. We study the underlying energetic variational structures that is common among all these multiscale-multiphysics systems.
In this talk, I will demonstrate the modeling as well as analysis and numerical issues arising from various complex fluids.
2012/03/14
10:30 - 11:30Room #056 (Mathematics building)
Jürgen Saal (Technische Universität Darmstadt)
"Exponential convergence to equilibria for a general model in hydrodynamics"
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system describes the dynamics of charged particles dispersed in an incompressible fluid.
In contrast to existing literature and in view of its physical relevance, we also allow for different diffusion coefficients of the charged species.
In addition, the commonly assumed electro-neutrality condition is not required by our approach.
Our aim is to present results on local and global well-posedness as well as exponential stability of equilibria. The results are obtained jointly with Dieter Bothe and Andre Fischer at the Center of Smart Interfaces at TU Darmstadt.
2012/03/13
15:00 - 16:00Room #050 (Mathematics building)
Aleksandar Ivic (University of Belgrade, the Serbian Academy of Science and Arts)
"Problems and results on Hardy's Z-function"
The title is self-explanatory: G.H. Hardy first used the function
$Z(t)$ to show that there are infinitely many zeta-zeros on the
critical line $\Re s = 1/2$. In recent years there is a revived
interest in this function, with many results and open problems.
14:00 - 15:00Room #154 (Mathematics building)
Tsuyoshi Kajiwara (Okayama University)
"On construction of Lyapunov functions and functionals"
2012/03/09
13:30 - 14:30Room #002 (Mathematics building)
Shintarou Yanagida (Kobe Univ.)
"On Hall algebra of complexes"
The topic of my talk is the Hall algebra of complexes,
which is recently introduced by T. Bridgeland.
I will discuss its properties and relation to
auto-equivalences of derived category.
If I have enough time,
I will also discuss the relation
of this Hall algebra to the so-called Ding-Iohara algebra.
2012/03/07
17:00 - 18:00Room #370 (Mathematics building)
Kazufumi Ito (North Carolina State Univ.)
"Nonsmooth Optimization, Theory and Applications."
We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.
2012/03/06
16:00 - 17:00Room #370 (Mathematics building)
Dietmar Hoemberg (Weierstrass Institute, Berlin)
"On the phase field approach to shape and topology optimization"
Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.
From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.
To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).
We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.
17:00 - 18:00Room #370 (Mathematics building)
Thomas Petzold (Weierstrass Institute, Berlin)
"Finite element simulations of induction hardening of steel parts"
Induction hardening is a modern method for the heat treatment of steel parts.
A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.
The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.
In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.
The finite element method is used to perform numerical simulations in 3D.
This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.
We will give a short overview of edge elements and present numerical simulations of induction hardening.
We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.
2012/02/29
16:00 - 17:00Room #270 (Mathematics building)
Johannes Elschner (Weierstrass Institute, Germany)
"Direct and inverse scattering of elastic waves by diffraction gratings"
The talk presents joint work with Guanghui Hu on the scattering of time-harmonic plane elastic waves by two-dimensional periodic structures. The first part presents existence and uniqueness results for the direct problem , using a variational approach. For the inverse problem, we discuss global uniqueness results with a minimal number of incident pressure or shear waves under the boundary conditions of the third and fourth kind. Generalizations to biperiodic elastic diffraction gratings in 3D are also mentioned. Finally we consider a reconstruction method applied to the inverse Dirichlet problem for the quasi-periodic 2D Navier equation.
2012/02/22
18:00 - 19:00Room #056 (Mathematics building)
Takuro Mochizuki (Research Institute for Mathematical Sciences, Kyoto University)
"Twistor $D$-module and harmonic bundle"
Abstract:
We shall overview the theory of twistor $D$-modules and
harmonic bundles. I am planning to survey the following topics,
motivated by the Hard Lefschetz Theorem for semisimple holonomic
$D$-modules:
1. What is a twistor $D$-module?
2. Local structure of meromorphic flat bundles
3. Wild harmonic bundles from local and global viewpoints
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
15:00 - 16:00Room #270 (Mathematics building)
Bernadette Miara (Université Paris-Est, ESIEE, France)
"Justification of a Shallow Shell Model in Unilateral Contact with an Obstacle"
We consider a three-dimensional elastic shell in unilateral contact with a plane. This lecture aims at justifying the asymptotic limit of the set of equilibrium equations of the structure when the thickness of the shell goes to zero. More precisely, we start with the 3D Signorini problem (with finite thickness) and obtain at the limit an obstacle 2D problem. This problem has already been studied [4] in the Cartesian framework on the basis of the bi-lateral problem [3]. The interest and the difficulty of the approach in the curvilinear framework (more appropriate to handle general shells) is due to the coupling between the tangential and transverse covariant components of the elastic field in the expression of the nonpenetrability conditions.
The procedure is the same as the one used in the asymptotic analysis of 3D bilateral structures [1, 2]: assumptions on the data, (loads and geometry of the middle surface of the shell) and re-scalling of the unknowns (displacement field or stress tensor); the new feature is the special handling of the components coupling.
The main result we obtain is as follows:
i) Under the assumption of regularity of the external volume and surface loads, and of the mapping that defines the middle surface of the shell, we establish that the family of elastic displacements converges strongly as the thickness tends to zero in an appropriate set which is a convex cone.
ii) The limit elastic displacement is a Kirchhoff-Love field given by a variational problem which will be analysed into details. The contact conditions are fully explicited for any finite thickness and at the limit.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.
16:15 - 17:15Room #270 (Mathematics building)
Oleg Emanouilov (Colorado State University)
"Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data."
In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.
Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data
$$
{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\tilde Gamma}¥vert
- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}
$$
where $¥tilde ¥Gamma$ is an arbitrary fixed open set of
$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.
2012/02/21
16:30 - 18:00Room #056 (Mathematics building)
Masato Mimura (The University of Tokyo)
"Property (TT)/T and homomorphism superrigidity into mapping class groups"
Mapping class groups (MCG's), of compact oriented surfaces (possibly
with punctures), have many mysterious features: they behave not only
like higher rank lattices (namely, irreducible lattices in higher rank
algebraic groups); but also like rank one lattices. The following
theorem, the Farb--Kaimanovich--Masur superrigidity, states a rank one
phenomenon for MCG's: "every group homomorphism from higher rank
lattices (such as SL(3,Z) and cocompact lattices in SL(3,R)) into
MCG's has finite image."
In this talk, we show a generalization of the superrigidity above, to
the case where higher rank lattices are replaced with some
(non-arithmetic) matrix groups over general rings. Our main example of
such groups is called the "universal lattice", that is, the special
linear group over commutative finitely generated polynomial rings over
integers, (such as SL(3,Z[x])). To prove this, we introduce the notion
of "property (TT)/T" for groups, which is a strengthening of Kazhdan's
property (T).
We will explain these properties and relations to ordinary and bounded
cohomology of groups (with twisted unitary coefficients); and outline
the proof of our result.
2012/02/20
16:30 - 17:30Room #128 (Mathematics building)
Jan Philip SOLOVEJ (University of Copenhagen)
"Microscopic derivation of the Ginzburg-Landau model "
I will discuss how the \emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.
2012/02/14
16:30 - 18:00Room #128 (Mathematics building)
Michael Loss (Georgia Institute of Technology)
"Symmetry results for Caffarelli-Kohn-Nirenberg inequalities"
2012/02/07
14:00 - 15:00Room #370 (Mathematics building)
Piermarco Cannarsa (Mat. Univ. Roma "Tor Vergata")
"Controllability results for degenerate parabolic operators"
UnlikeCuniformly parabolic equations, parabolic operators that degenerate on subsets of the space domain exhibit very different behaviors from the point of view of controllability. For instance, null controllability in arbitrary time may be true or false according to the degree of degeneracy, and there are also examples where a finite time is needed to ensure such a property. This talk will survey most of the theory that has been established so far for operators with boundary degeneracy, and discuss recent results for operators of Grushin type which degenerate in the interior.
2012/02/03
09:45 - 11:00Room #118 (Mathematics building)
Atsushi ITO (Graduate School of Mathematical Sciences University of Tokyo)
"How to estimate Seshadri constants(セシャドリ定数を評価する方法)
"
11:00 - 12:15Room #118 (Mathematics building)
Keijyu SONO (Graduate School of Mathematical Sciences University of Tokyo)
"Spherical functions associated to the principal series representations of SL(3,R) and higher rank Epstein zeta functions(SL(3,R)の主系列表現に付随する球関数,及び高階Epsteinゼータ関数について)
"
13:00 - 14:15Room #118 (Mathematics building)
Tetsuya ITO (Graduate School of Mathematical Sciences University of Tokyo)
"Construction of invariant group orderings from topological point of view(位相幾何の視点からの群の不変順序の構成)
"
14:15 - 15:30Room #118 (Mathematics building)
TIAN Ran (Graduate School of Mathematical Sciences University of Tokyo)
"The explicit calculation of Čech cohomology and an extension of Davenport’s inequality(Čechコホモロジーの明示的計算とDavenport不等式の拡張)
"
09:45 - 11:00Room #128 (Mathematics building)
Issei OIKAWA (Graduate School of Mathematical Sciences University of Tokyo)
"Hybridized Discontinuous Galerkin Methods for Elliptic Problems(楕円型問題に対するハイブリッド型不連続ガレルキン法の研究)
"
11:00 - 12:15Room #128 (Mathematics building)
Satoshi YOKOYAMA (Graduate School of Mathematical Sciences University of Tokyo)
"Two-dimensional stochastic Navier-Stokes equations derived from a certain variational problem(ある変分問題から導かれる二次元確率ナビエ・ストークス方程式)
"
13:00 - 14:15Room #128 (Mathematics building)
Shinichiro ITOZAKI (Graduate School of Mathematical Sciences University of Tokyo)
"Scattering Theory on Manifolds with Asympotically Polynomially Growing Ends(多項式増大する無限遠境界を持つ多様体上の散乱理論)
"
14:15 - 15:30Room #128 (Mathematics building)
Shingo KAMIMOTO (Graduate School of Mathematical Sciences University of Tokyo)
"On the exact WKB analysis of Schrödinger equations(Schrödinger方程式の完全WKB解析に関して)
"
2012/02/02
16:30 - 18:00Room #002 (Mathematics building)
Yusuke Isono (Univ. Tokyo)
"Weak Exactness for $C^*$-algebras and Application to Condition (AO)"
11:00 - 12:15Room #118 (Mathematics building)
Shinnosuke OKAWA (Graduate School of Mathematical Sciences University of Tokyo )
"Studies on the geometry of Mori dream spaces(森夢空間の幾何学に関する研究)"
13:00 - 14:15Room #118 (Mathematics building)
Shun OKUBO (Graduate School of Mathematical Sciences University of Tokyo)
"The p-adic monodromy theorem in the imperfect residue field case(剰余体が非完全な場合のp進モノドロミー定理について)
"
14:15 - 15:30Room #118 (Mathematics building)
ZHANG Qizhi (Graduate School of Mathematical Sciences University of Tokyo)
"On The Discrete Logarithm Problem in Finite Fields(有限体上の離散対数問題について)
"
15:45 - 17:00Room #118 (Mathematics building)
Syohei MA (Graduate School of Mathematical Sciences University of Tokyo)
"Rationality of the moduli spaces of 2-elementary K3 surfaces(対合付きK3曲面のモジュライの有理性)
"
09:45 - 11:00Room #128 (Mathematics building)
Ryohei KAKIZAWA (Graduate School of Mathematical Sciences University of Tokyo)
"Determining nodes for semilinear parabolic evolution equations in Banach spaces(バナッハ空間上の半線型放物型発展方程式に対する確定節点)
"
11:00 - 12:15Room #128 (Mathematics building)
SUN JuanJuan (Graduate School of Mathematical Sciences University of Tokyo)
"Polynomial relations for q-characters via ODM/IM correspondence(ODE/IM対応を用いたq指標の多項式関係)
"
13:00 - 14:15Room #128 (Mathematics building)
Yusaku CHIBA (Graduaate School of Mathematical Sciences University of Tokyo)
"Entire curves in projective algebraic varieties(射影代数多様体内の正則曲線について)
"
2012/02/01
10:30 - 11:30Room #056 (Mathematics building)
Chun Liu (University of Tokyo / Penn State University)
"Energetic variational approach: generalized diffusion, stochastic differential equations and optimal transport"
In the talk, I will explore the general framework of energetic variational approaches, which are the direct consequences of classical isothermal thermodynamics, and their particular applications in generalized diffusion problems. In particular, we reveal the roles of different stochastic integrations (Ito's form, Stratonovich's form and other possible forms) and the Wasserstein metric and the procedure of optimal transport in the context of general framework of theories of linear responses.
2012/01/31
16:30 - 18:00Room #128 (Mathematics building)
Michel Chipot (University of Zurich)
"Obstacle problems in unbounded domains"
We will present a formulation of obstacle problems in unbounded
domains when the energy method does not work, i.e. whenthe force does not belong to H^{-1}.
2012/01/30
15:30 - 17:00Room #122 (Mathematics building)
Yoshinori Gongyo (University of Tokyo)
"On varieties of globally F-regular type"
I will talk about recent topics on varieties of globally F-regular type.
10:30 - 12:00Room #128 (Mathematics building)
Damian Brotbek (University of Tokyo)
"Differential equations as embedding obstructions and vanishing theorems"
Given a smooth projective variety $X$ it is natural to wonder what is the smallest integer $N$ such that one can embed $X$ into $\mathbb{P}^N$. In this talk I will first recall what can be said for any smooth projective variety, then I will explain how the existence of some particular differential equations on $X$ yields obstructions to the existence of some projective embeddings.
2012/01/27
16:30 - 17:30Room #123 (Mathematics building)
Taro YOSHINO (Graduate School of Mathematical Sciences, University of Tokyo)
"On Topological Blow-up"
Topological blow-up is a method to understand non-Hausdorff spaces. We define an obstruction to Hausdorffness, and call it crack. By `blowing up' the points in crack, we can obtain better space.
2012/01/26
16:30 - 18:00Room #117 (Mathematics building)
Catherine Oikonomides (Univ. Tokyo)
"The transverse fundamental class of linear foliations
on torus bundles over the circle"
2012/01/24
16:30 - 18:00Room #002 (Mathematics building)
Takeshi Takaishi (Hiroshima Kokusai Gakuin University)
"Phasefield model for crack simulation and its application"
http://www.infsup.jp/utnas/
2012/01/23
15:30 - 17:00Room #122 (Mathematics building)
Kimiko Yamada (Okayama university)
"Sigularities and Kodaira dimension of the moduli of stable sheaves on Enriques surfaces"
We shall estimate singularities of moduli of stable sheaves on Enriques/hyper-elliptic surfaces via the Kuranishi theory, consider when its singularities are canonical, and calculate its Kodaira dimension.
10:30 - 12:00Room #128 (Mathematics building)
Fuminori Nakata (Tokyo University of Science)
"Twistor correspondence for R-invariant indefinite self-dual metric on R^4"
13:30 - 15:00Room #122 (Mathematics building)
Mihai Paun (Institut Élie Cartan and KIAS)
"TBA(中止になりました)"
2012/01/20
14:45 - 16:15Room #056 (Mathematics building)
Albrecht Klemm (The University of Bonn)
"Refined holomorphic anomaly equations"
We propose a derivation of refined holomophic
anomaly equation from the word-sheet point of
view and discuss the interpretation of the
refined BPS invariants for local Calabi-Yau
spaces.
2012/01/19
16:00 - 17:30Room #128 (Mathematics building)
Philippe G. LeFloch (Univ. Paris 6 / CNRS)
"Undercompressible shocks and moving phase boundaries
"
I will present a study of traveling wave solutions to third-order, diffusive-dispersive equations, which arise in the modeling of complex fluid flows and represent regularization-sensitive wave patterns, especially undercompressive shock waves and moving phase boundaries. The qualitative properties of these (possibly oscillatory) traveling waves are well-understood in terms of the so-called kinetic relation, and this has led to a new theory of (nonclassical) solutions to nonlinear hyperbolic systems. Relevant papers are available at the link: www.philippelefloch.org.
2012/01/18
15:30 - 17:00Room #122 (Mathematics building)
Mihai Paun (Institut Élie Cartan and KIAS)
"TBA(中止になりました)"
2012/01/17
16:30 - 18:00Room #056 (Mathematics building)
Takao Satoh (Tokyo University of Science)
"On the Johnson cokernels of the mapping class group of a surface (joint work with Naoya Enomoto)"
In general, the Johnson homomorphisms of the mapping class group of a surface are used to investigate graded quotients of the Johnson filtration of the mapping class group. These graded quotients are considered as a sequence of approximations of the Torelli group. Now, there is a broad range of remarkable results for the Johnson homomorphisms.
In this talk, we concentrate our focus on the cokernels of the Johnson homomorphisms of the mapping class group. By a work of Shigeyuki Morita and Hiroaki Nakamura, it is known that an Sp-irreducible module [k] appears in the cokernel of the k-th Johnson homomorphism with multiplicity one if k=2m+1 for any positive integer m. In general, however, to determine Sp-structure of the cokernel is quite a difficult preblem.
Our goal is to show that we have detected new irreducible components in the cokernels. More precisely, we will show that there appears an Sp-irreducible module [1^k] in the cokernel of the k-th Johnson homomorphism with multiplicity one if k=4m+1 for any positive integer m.
17:00 - 18:00Room #123 (Mathematics building)
Daisuke Tagami (Kyushu University)
"Numerical computations of flow problems with the moving boundary by an area-preserving scheme"
http://www.infsup.jp/utnas/
2012/01/16
15:30 - 17:00Room #122 (Mathematics building)
Mihai Paun (Institut Élie Cartan and KIAS)
"TBA(Cancelled)"
10:30 - 12:00Room #128 (Mathematics building)
Yu Kawakami (Yamaguchi University)
"A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic 3-space"
We provide an effective ramification theorem for the ratio of canonical forms of weakly complete flat fronts in the hyperbolic 3-space. As an application, we give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic 3-space.
16:30 - 18:00Room #117 (Mathematics building)
Narutaka Ozawa (RIMS, Kyoto University)
"Is an irng singly generated as an ideal?"
15:30 - 17:00Room #122 (Mathematics building)
Mihai Paun (Institut Élie Cartan and KIAS)
"TBA(中止になりました)"
2012/01/12
18:15 - 19:15Room #056 (Mathematics building)
Toby Gee (Imperial College London)
"New perspectives on the Breuil-Mézard conjecture (joint with M. Emerton)
"
I will discuss joint work with Matthew Emerton on geometric approaches to the Breuil-Mézard conjecture, generalising a geometric approach of Breuil and Mézard. I will discuss a proof of the geometric version of the original conjecture, as well as work in progress on a geometric version of the conjecture which does not make use of a fixed residual representation.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
2012/01/06
16:30 - 18:00Room #118 (Mathematics building)
Yasuyuki Kawahigashi (Univ. Tokyo)
"Diagrammatical methods in theory of subfactors"
2012/01/05
16:30 - 18:00Room #117 (Mathematics building)
Yasuyuki Kawahigashi (Univ. Tokyo)
"Classification and amenability in theory of von Neumann algebras"
2011/12/27
14:30 - 18:00Room #117 (Mathematics building)
Makoto Yamashita (Universita di Roma "Tor Vergata") 14:30 - 16:00
"Deformation of algebras associated to group cocycles"
Yoh Tanimoto (Universitaet Goettingen) 16:30 - 18:00
"Construction of wedge-local nets through
Longo-Witten endomorphisms"
13:30 - 14:30Room #370 (Mathematics building)
Yichao Zhu (University of Oxford)
"The Modelling of Dislocations in the Early Stage of the Metal Fatigue"
Understanding fatigue of metal under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and the aeroplane engine. Experimentally it has been found that this type of
fatigue is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB) at a microscopic level. In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analysed by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analysed by using a method of multiple scales.
14:30 - 15:30Room #370 (Mathematics building)
Manabu Machida (University of Michigan)
"Wave Transport in Random Media and Inverse Problems"
Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.
2011/12/26
15:30 - 17:00Room #122 (Mathematics building)
Takuzo Okada (Kyoto University)
"Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces"
It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.
2011/12/21
16:30 - 17:30Room #056 (Mathematics building)
Kazuya Kato (University of Chicago)
"On Sharifi's conjecture"
2011/12/20
16:30 - 18:00Room #128 (Mathematics building)
Gueorgui Raykov (Catholic University of Chile)
"A trace formula for the perturbed Landau Hamiltonian"
The talk will be based on a joint work with A. Pushnitski
and C. Villegas-Blas, the preprint is available here:
http://arxiv.org/abs/1110.3098 .
16:30 - 18:00Room #056 (Mathematics building)
Yoshihiko Mitsumatsu (Chuo University)
"Leafwise symplectic structures on Lawson's Foliation on the 5-sphere"
We are going to show that Lawson's foliation on the 5-sphere
admits a smooth leafwise symplectic sturcture. Historically, Lawson's
foliation is the first one among foliations of codimension one which are
constructed on the 5-sphere. It is obtained by modifying the Milnor
fibration associated with the Fermat type cubic polynominal in three
variables.
Alberto Verjovsky proposed a question whether if the Lawson's
foliation or slighty modified ones admit a leafwise smooth symplectic
structure and/or a leafwise complex structure. As Lawson's one has a
Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not
be solved simultaneously both for the symplectic and the complex cases.
The main part of the construction is to show that the Fermat type
cubic surface admits an `end-periodic' symplectic structure, while the
natural one as an affine surface is conic at the end. Even though for
the other two families of the simple elliptic hypersurface singularities
almost the same construction works, at present, it seems very limited
where a Stein manifold admits an end-periodic symplectic structure. If
the time allows, we also discuss the existence of such structures on
globally convex symplectic manifolds.
2011/12/19
16:30 - 17:30Room #117 (Mathematics building)
Tamas Szamuely (Budapest)
"Galois Theory: Past and Present"
2011/12/17
13:30 - 16:00Room #123 (Mathematics building)
Masami Ohta (Professor Emeritus of Tokai Univeristy) 13:30 - 14:30
"On the finite order Q-rational points on J_1 (N) "
Shushi Harashita (Yokohama National University
) 15:00 - 16:00
"On the affineness of distinguished Deligne-Lusztig varieties"
2011/12/16
16:30 - 17:30Room #123 (Mathematics building)
TAKAGI, Shunsuke (Graduate School of Mathematical Sciences, University of Tokyo)
"Application of positive characteristic methods to singularity theory"
As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.
2011/12/14
17:30 - 18:30Room #056 (Mathematics building)
Lucien Szpiro (City University of New York)
"Good and bad reduction for algebraic dynamical systems"
We will report on a recent work with collaborators in New York on the
different ways to look at degenerations of a dynamical system in a one
parameter family. Resultants, conductors and isotriviality will be analyzed.
2011/12/13
16:30 - 18:00Room #128 (Mathematics building)
Wolfram Bauer (Mathematisches Institut, Georg-August-Universität)
"Trivializable subriemannian structures and spectral analysis of associated operators"
16:30 - 18:00Room #126 (Mathematics building)
Hung Yean Loke (National University of Singapore)
"Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups"
In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \times O(m,n)$ lies in the stable range, ie. $2p \leq \min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.
We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.
16:30 - 18:00Room #126 (Mathematics building)
Hung Yean Loke (National University of Singapore)
"Local Theta lifts of unitary lowest weight modules to the indefinite orthogonal groups"
In this talk, I will discuss the local theta lifts of unitary lowest weight modules of $Sp(2p,R)$ to the indefinite orthogonal group $O(n,m)$. In a previous paper, Nishiyama and Zhu computed the associated cycles when the dual pair $Sp(2p,R) \times O(m,n)$ lies in the stable range, ie. $2p \leq \min(m,n)$. In this talk, I will report on a joint work with Jiajun Ma and U-Liang Tang at NUS where we extend the computation beyond the stable range. Our approach is to analyze the coherent sheaves generated by the graded modules.
We will also need the Kobayashi's projection formula for discretely decomposable restrictions. Our study produces some interesting formulas on the $K$-types of the representations. In particular for some of these representations, the $K$-types formulas agree those in a conjecture of Vogan on the unipotent representations.
16:30 - 18:00Room #056 (Mathematics building)
Mircea Voineagu (IPMU, The University of Tokyo)
"Remarks on filtrations of the singular homology of real varieties."
We discuss various conjectures about filtrations on the singular homology of real and complex varieties. We prove that a conjecture relating niveau filtration on Borel-Moore homology of real varieties and the image of generalized cycle maps from reduced Lawson homology is false. In the end, we discuss a certain decomposition of Borel-Haeflinger cycle map. This is a joint work with J.Heller.
2011/12/12
10:30 - 12:00Room #128 (Mathematics building)
Shinichiroh MATSUO (Kyoto University)
"Brody curves and mean dimension"
We study the mean dimensions of the spaces of Brody curves. In particular we give the formula of the mean dimension of the space of Brody curves in the Riemann sphere.
15:30 - 17:00Room #122 (Mathematics building)
Robert Laterveer (CNRS, IRMA, Université de Strasbourg)
"A version of Barth's theorem for singular varieties (cancelled)"
2011/12/09
10:40 - 11:30Room #122 (Mathematics building)
Erwin Bolthausen (University of Zurich)
"An iterative construction of solutions of the TAP equation"
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.
10:40 - 11:30Room #122 (Mathematics building)
Erwin Bolthausen (University of Zurich)
"An iterative construction of solutions of the TAP equation"
The TAP equation (Thouless-Anderson-Palmer) describes the so-called pure states in the Sherrington-Kirkpatrick model. A mathematical rigorous derivation of the equation exists only in the high temperature regime. We propose an interative construction of solutions of the equations which is shown to converge up to the de Almayda-Thouless line. The iteration makes sense also beyond this line, but it fails to converge. However, some properties of the iteration can also been proved beyond the AT-line.
11:40 - 12:30Room #122 (Mathematics building)
Wolfgang Koenig (Weierstrass Institute Berlin)
"Eigenvalue order statistics and mass concentration in the parabolic Anderson model"
We consider the random Schr\"odinger operator on the lattice with i.i.d. potential, which is double-exponentially distributed. In a large box, we look at the lowest eigenvalues, together with the location of the centering of the corresponding eigenfunction, and derive a Poisson process limit law, after suitable rescaling and shifting, towards an explicit Poisson point process. This is a strong form of Anderson localization at the bottom of the spectrum. Since the potential is unbounded, also the eigenvalues are, and it turns out that the gaps between them are much larger than of inverse volume order. We explain an application to concentration properties of the corresponding Cauchy problem, the parabolic Anderson model. In fact, it will turn out that the total mass of the solution comes from just one island, asymptotically for large times. This is joint work in progress with Marek Biskup (Los Angeles and Budweis).
14:00 - 14:50Room #122 (Mathematics building)
Roman Kotecky (Charles University Prague/University of Warwick)
"Gradient Gibbs models with non-convex potentials"
A motivation for gradient Gibbs measures in the study of macroscopic elasticity and in proving the Cauchy-Born rule will be explained. Results concerning strict convexity of the free energy will be formulated and discussed. Based on joint works with S. Adams and S. Mueller and with S. Luckhaus.
15:00 - 15:50Room #122 (Mathematics building)
Stefano Olla (University Paris - Dauphine)
"Einstein relation and linear response for random walks in random environment"
2011/12/08
18:30 - 19:30Room #056 (Mathematics building)
Gerd Faltings (Max Planck Institute for Mathematics, Bonn)
"Nonabelian p-adic Hodge theory and Frobenius"
Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
2011/12/07
16:00 - 18:00Room #122 (Mathematics building)
Michel Cristofol (マルセイユ大学) 16:00 - 17:00
""Inverse problems associated with linear and non-linear parabolic systems ""
In this talk, I present several inverse reconstruction results for linear and non linear parabolic systems with different coupling terms : for linear systems with reaction-convection terms and for cooperative systems like Lotka Volterra systems with strong coupling terms. I will show different approaches to prove uniqueness of the coefficients via Carleman inequalities or via regularities properties of the solutions.
Guillaume Olive (マルセイユ大学) 17:00 - 18:00
""Hautus test for the approximate controllability of linear systems""
We will introduce some generalization of the Hautus test to linear parabolic systems and give some applications to the distributed and boundary approximate controllability of such systems.
2011/12/06
16:30 - 18:00Room #002 (Mathematics building)
Kanako Yasue (JAXA)
"Development of high order CFD solver for aerospace applications"
http://www.infsup.jp/saito/
2011/12/05
15:30 - 17:00Room #122 (Mathematics building)
Hirokazu Nasu (Tokai University)
"Obstructions to deforming curves on a uniruled 3-fold"
In this talk, I review some results from a joint work with Mukai:
1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and
2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.
As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.
2011/12/01
16:30 - 18:00Room #117 (Mathematics building)
Spyridon Michalakis (Caltech)
"Stability of topological phases of matter "
16:30 - 18:00Room #002 (Mathematics building)
Dmitry Kaledin (Steklov Mathematics Institute/ KIAS)
"Cyclic K-theory"
Cyclic K-theory is a variant of algebraic K-theory introduced by Goodwillie 25 years ago and more-or-less forgotten by now. I will try to convince the audience that cyclic K-theory is actually quite useful -- in particular, it can be effectively computed for varieties over a finite field.
2011/11/30
15:00 - 16:10Room #002 (Mathematics building)
HIROSE, Yuichi (Victoria University of Wellington)
"Information criteria for parametric and semi-parametric models"
Since Akaike proposed an Information Criteria, this approach to
model selection has been important part of Statistical data analysis.
Since then many Information Criteria have been proposed and it is still
an active field of research. Despite there are many contributors in this
topic, we have not have proper Information Criteria for semiparametric
models. In this talk, we give ideas to develop an Information Criteria
for semiparametric models.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/05.html
2011/11/29
16:30 - 18:00Room #126 (Mathematics building)
Spyridon Michalakis (Caltech)
"Stability of topological phases of matter"
17:00 - 18:00Room #056 (Mathematics building)
Athanase Papadopoulos (IRMA, Univ. de Strasbourg)
"Mapping class group actions"
I will describe and present some rigidity results on mapping
class group actions on spaces of foliations on surfaces, equipped with various topologies.
16:30 - 18:00Room #002 (Mathematics building)
Daniel Sternheimer (Rikkyo Univertiry and Université de Bourgogne)
"Symmetries, (their) deformations, and physics: some perspectives and open problems from half a century of personal experience"
This is a flexible general framework, based on quite a number of papers, some of which are reviewed in:
MR2285047 (2008c:53079) Sternheimer, Daniel. The geometry of space-time and its deformations from a physical perspective. From geometry to quantum mechanics, 287–301, Progr. Math., 252, Birkhäuser Boston, Boston, MA, 2007
http://monge.u-bourgogne.fr/d.sternh/papers/PiMOmori-DS.pdf
2011/11/28
15:30 - 17:00Room #122 (Mathematics building)
Kotaro Kawatani (Kyoto University)
"Comparison with Gieseker stability and slope stability via Bridgeland's stability"
In this talk we compare two classical notions of stability (Gieseker stability and slope stability) for sheaves on K3 surfaces by using stability conditions which was introduced by Bridgeland. As a consequence of this work, we give a classification of 2 dimensional moduli spaces of sheaves on K3 surface depending on the rank of the sheaves.
10:30 - 12:00Room #128 (Mathematics building)
Shin-ichi Matsumura (University of Tokyo)
"An ampleness criterion with the extendability of singular positive metrics"
Coman, Guedj and Zeriahi proved that, for an ample line bundle $L$ on a projective manifold $X$, any singular positive metric on the line bundle $L|_{V}$ along a subvariety $V \subset X$ can be extended to a global singular positive metric of $L$. In this talk, we prove that the extendability of singular positive metrics on a line bundle along a subvariety implies the ampleness of the line bundle.
2011/11/25
16:30 - 17:30Room #002 (Mathematics building)
SHIMOMURA Akihiro (Graduate School of mathematical Sciences, University of Tokyo)
"Nonlinear dispersive evolution equations"
I will talk about the time evolution of solutions to nonlinear dispersive equations.
2011/11/24
16:30 - 18:00Room #117 (Mathematics building)
Spyridon Michalakis (Caltech)
"Stability of topological phases of matter"
2011/11/22
16:30 - 18:00Room #126 (Mathematics building)
Spyridon Michalakis ( Institute for Quantum Information and Matter (Caltech))
"Stability of topological phases of matter"
The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.
16:30 - 18:00Room #056 (Mathematics building)
Toshitake Kohno (The University of Tokyo)
"Quantum and homological representations of braid groups"
Homological representations of braid groups are defined as
the action of homeomorphisms of a punctured disk on
the homology of an abelian covering of its configuration space.
These representations were extensively studied by Lawrence,
Krammer and Bigelow. In this talk we show that specializations
of the homological representations of braid groups
are equivalent to the monodromy of the KZ equation with
values in the space of null vectors in the tensor product
of Verma modules when the parameters are generic.
To prove this we use representations of the solutions of the
KZ equation by hypergeometric integrals due to Schechtman,
Varchenko and others.
In the case of special parameters these representations
are extended to quantum representations of mapping
class groups. We describe the images of such representations
and show that the images of any Johnson subgroups
contain non-abelian free groups if the genus and the
level are sufficiently large. The last part is a joint
work with Louis Funar.
16:30 - 18:00Room #002 (Mathematics building)
Takayuki Okuda (東京大学大学院 数理科学研究科)
"Smallest complex nilpotent orbit with real points"
Let $\mathfrak{g}$ be a non-compact simple Lie algebra with no complex
structures.
In this talk, we show that there exists a complex nilpotent orbit
$\mathcal{O}^{G_\mathbb{C}}_{\text{min},\mathfrak{g}}$ in
$\mathfrak{g}_\mathbb{C}$ ($:=\mathfrak{g} \otimes \mathbb{C}$)
containing all of real nilpotent orbits in $\mathfrak{g}$ of minimal
positive dimension.
For many $\mathfrak{g}$, the orbit
$\mathcal{O}^{G_\mathbb{C}}_{\text{min},\mathfrak{g}}$ is just the
complex minimal nilpotent orbit in $\mathfrak{g}_\mathbb{C}$.
However, for the cases where $\mathfrak{g}$ is isomorphic to
$\mathfrak{su}^*(2k)$, $\mathfrak{so}(n-1,1)$, $\mathfrak{sp}(p,q)$,
$\mathfrak{e}_{6(-26)}$ or $\mathfrak{f}_{4(-20)}$,
the orbit $\mathcal{O}^{G_\mathbb{C}}_{\text{min},\mathfrak{g}}$ is not
the complex minimal nilpotent orbit in $\mathfrak{g}_\mathbb{C}$.
We also determine $\mathcal{O}^{G_\mathbb{C}}_{\text{min},\mathfrak{g}}$
by describing the weighted Dynkin diagrams of these for such cases.
2011/11/21
10:30 - 12:00Room #128 (Mathematics building)
Hisashi Kasuya (University of Tokyo)
"Techniques of computations of Dolbeault cohomology of solvmanifolds"
13:30 - 14:30Room #056 (Mathematics building)
Ernie Esser (University of California, Irvine)
"A convex model for non-negative matrix factorization and dimensionality reduction on physical space"
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We focus on applications of the proposed framework to hyperspectral endmember and abundances identification and also show an application to blind source separation of NMR data.
This talk is based on joint work with Michael Moeller, Stanley Osher, Guillermo Sapiro and Jack Xin.
16:30 - 18:00Room #002 (Mathematics building)
Siu-Cheong Lau (IPMU)
"Enuemerative meaning of mirror maps for toric Calabi-Yau manifolds"
For a mirror pair of smooth manifolds X and Y, mirror symmetry associates a complex structure on Y to each Kaehler structure on X, and this association is called the mirror map. Traditionally mirror maps are defined by solving Picard-Fuchs equations and its geometric meaning was unclear. In this talk I explain a recent joint work with K.W. Chan, N.C. Leung and H.H. Tseng which proves that mirror maps can be obtained by taking torus duality (the SYZ approach) and disk-counting for a class of toric Calabi-Yau manifolds in any dimensions. As a consequence we can compute disk-counting invariants by solving Picard-Fuchs equations.
2011/11/19
10:15 - 12:30Room #117 (Mathematics building)
Jiro Sekiguchi (Tokyo Univ. of Agriculture) 10:15 - 11:15
"Hyperelliptic integrals related with dihedral groups"
Yoshihiro Ohnishi (Yamanashi University) 11:30 - 12:30
"Survey on the generalized Bernoulli-Hurwitz numbers for a higher genus algebraic function, and some problems"
2011/11/18
15:00 - 16:00Room #052 (Mathematics building)
Hiroshi Isozaki (University of Tsukuba)
"Inverse problems for heat equations with discontinuous conductivities
"
In a bounded domain $\Omega \subset {\bf R}^n$, consider the heat
equation $\partial_tu = \nabla(\gamma(t,x)\nabla u)$. The heat
conductivity is assumed to be piecewise constant : $\gamma = k^2$ on
$\Omaga_1(t) \subset\subset \Omega$, $\gamma(t,x) = 1$ on
$\Omega\setminus\Omega_1(t)$. In this talk, we present recent results
for the inverse problems of reconstructing $\gamma(t,x)$ from the
Dirichlet-to-Neumann map :
$u(t)|_{\partial\Omega} \to $\partial_{\nu}u|_{\partial\Omega}$ for a time
interval $(0,T)$. These are the joint works with P.Gaitan, O.Poisson,
S.Siltanen, J.Tamminen.
2011/11/17
17:00 - 18:00Room #370 (Mathematics building)
Oleg Emanouilov (Colorado State University)
"Recovery of weakly coupled system from partial Cauchy data"
We consider the inverse problem for recovery of coefficients of weakly coupled system of elliptic equations in a bounded 2D domain.
16:30 - 18:00Room #117 (Mathematics building)
Takehiko Yamanouchi (Tokyo Gakugei University)
"Hecke pairs in ergodic measured equivalence relations"
2011/11/16
16:30 - 18:00Room #128 (Mathematics building)
Franc Forstneric (University of Ljubljana)
"Disc functionals and Siciak-Zaharyuta extremal functions on singular varieties"
A disc functional on a complex space, X, is a function P that assign a real number P(f) (possibly minus infinity) to every analytic disc f in X. An examples is the Poisson functional P_u of an upper semicontinuous function u on X: in that case P_u(f) is the average of u over the boundary curve of the disc f. Other natural examples include the Lelong and the Riesz functionals. The envelope of a disc functional P is a function on X associating to every point x of X the infimum of the values P(f) over all analytic discs f in X satisfying f(0)=x. The main point of interest is that the envelopes of many natural disc functionals are plurisubharmonic functions solving certain extremal problems. In the classical case when X=C^n this was first discovered by E. Poletsky in the early 1990's. In this talk I will discuss recent results on plurisubharmonicity of envelopes of all the classical disc functional mentioned above on locally irreducible complex spaces. In the second part of the talk I will give formulas expressing the classical Siciak-Zaharyuta maximal function of an open set in an affine algebraic variety as the envelope of certain disc functionals.
We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the Siciak-Zaharyuta extremal function of an open set in a locally irreducible affine algebraic variety as the envelope of certain disc functionals, similarly to what has been done for open sets in $\C^n$ by Lempert and by L\'arusson and Sigurdsson.
10:00 - 11:00Room #270 (Mathematics building)
Alfred Ramani (Ecole Polytechnique)
"All you never really wanted to know about QRT, but were foolhardy enough to ask"
We discuss various extensions of the famous QRT second order, first degree, integrable mapping. We show how these extensions can be combined. A discussion of integrable correspondences related to these extended QRT mappings is also presented.
2011/11/15
16:30 - 18:00Room #056 (Mathematics building)
Francois Laudenbach (Univ. de Nantes)
"Singular codimension-one foliations
and twisted open books in dimension 3.
(joint work with G. Meigniez)
"
The allowed singularities are those of functions.
According to A. Haefliger (1958),
such structures on manifolds, called $\Gamma_1$-structures,
are objects of a cohomological
theory with a classifying space $B\Gamma_1$.
The problem of cancelling the singularities
(or regularization problem)
arise naturally.
For a closed manifold, it was solved by W.Thurston in a famous paper
(1976), with a proof relying on Mather's isomorphism (1971):
Diff$^\infty(\mathbb R)$ as a discrete group has the same homology
as the based loop space
$\Omega B\Gamma_1^+$.
For further extension to contact geometry, it is necessary
to solve the regularization problem
without using Mather's isomorphism.
That is what we have done in dimension 3. Our result is the following.
{\it Every $\Gamma_1$-structure $\xi$ on a 3-manifold $M$ whose
normal bundle
embeds into the tangent bundle to $M$ is $\Gamma_1$-homotopic
to a regular foliation
carried by a (possibily twisted) open book.}
The proof is elementary and relies on the dynamics of a (twisted)
pseudo-gradient of $\xi$.
All the objects will be defined in the talk, in particular the notion
of twisted open book which is a central object in the reported paper.
16:30 - 18:00Room #126 (Mathematics building)
Laurant Demonet (Nagoya University)
"Categorification of cluster algebras arising from unipotent subgroups of non-simply laced Lie groups"
We introduce an abstract framework to categorify some antisymetrizable cluster algebras by using actions of finite groups on stably 2-Calabi-Yau exact categories. We introduce the notion of the equivariant category and, with similar technics as in [K], [CK], [GLS1], [GLS2], [DK], [FK], [P], we construct some examples of such categorifications. For example, if we let Z/2Z act on the category of representations of the preprojective algebra of type A2n-1 via the only non trivial action on the diagram, we obtain the cluster structure on the coordinate ring of the maximal unipotent subgroup of the semi-simple Lie group of type Bn [D]. Hence, we can get relations between the cluster algebras categorified by some exact subcategories of these two categories. We also prove by the same methods as in [FK] a conjecture of Fomin and Zelevinsky stating that the cluster monomials are linearly independent.
References
[CK] P. Caldero, B. Keller, From triangulated categories to cluster algebras, Invent. Math. 172 (2008), no. 1, 169--211.
[DK] R. Dehy, B. Keller, On the combinatorics of rigid objects in 2-Calabi-Yau categories, arXiv: 0709.0882.
[D] L. Demonet, Cluster algebras and preprojective algebras: the non simply-laced case, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 379--384.
[FK] C. Fu, B. Keller, On cluster algebras with coefficients and 2-Calabi-Yau categories, arXiv: 0710.3152.
[GLS1] C. Geiss, B. Leclerc, J. Schröer, Rigid modules over preprojective algebras, Invent. Math. 165 (2006), no. 3, 589--632.
[GLS2] C. Geiss, B. Leclerc, J. Schröer, Cluster algebra structures and semicanoncial bases for unipotent groups, arXiv: math/0703039.
[K] B. Keller, Categorification of acyclic cluster algebras: an introduction, arXiv: 0801.3103.
[P] Y. Palu, Cluster characters for triangulated 2-Calabi--Yau categories, arXiv: math/0703540.
2011/11/14
17:00 - 18:00Room #470 (Mathematics building)
Oleg Emanouilov (Colorado State University)
"Recovery of weakly coupled system from partial Cauchy data"
We consider the inverse problem for recovery of coefficients of weakly coupled system of elliptic equations in a bounded 2D domain.
15:30 - 17:00Room #122 (Mathematics building)
Kiwamu Watanabe (University of Tokyo)
"On projective manifolds swept out by cubic varieties"
The structures of embedded complex projective manifolds swept out by varieties with preassigned properties have been studied by several authors. In this talk, we study structures of embedded projective manifolds swept out by cubic varieties.
2011/11/10
17:00 - 18:00Room #370 (Mathematics building)
Oleg Emanouilov (Colorado State University)
"Inverse boundary value problem for Schroedinger equation in two dimensions"
We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).
15:00 - 16:00Room #128 (Mathematics building)
Yoichiro Mori (University of Minnesota )
"Mathematical Modeling of Cellular Electrodiffusion and Osmosis "
16:30 - 17:30Room #128 (Mathematics building)
Bernold Fiedler (Free University of Berlin)
"Schoenflies spheres in Sturm attractors "
In gradient systems on compact manifolds the boundary of the unstable manifold of an equilibrium need not be homeomorphic to a sphere, or to any compact manifold.
For scalar parabolic equations in one space dimension, however, we can exlude complications like Reidemeister torsion and the Alexander horned sphere. Instead the boundary is a Schoenflies embedded sphere. This is due to Sturm nodal properties related to the Matano lap number.
2011/11/09
18:00 - 19:00Room #056 (Mathematics building)
Atsushi Shiho (University of Tokyo)
"On extension and restriction of overconvergent isocrystals "
First we explain two theorems concerning (log) extension of overconvergent isocrystals. One is a p-adic analogue of the theorem of logarithmic extension of regular integrable connections, and the other is a p-adic analogue of Zariski-Nagata purity. Next we explain a theorem which says that we can check certain property of overconvergent isocrystals by restricting them to curves.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
2011/11/08
16:30 - 18:00Room #056 (Mathematics building)
Shoji Yokura (Kagoshima University )
"Fiberwise bordism groups and related topics"
We have recently introduced the notion of fiberwise bordism. In this talk, after a quick review of some of the classical (co)bordism theories, we will explain motivations of considering fiberwise bordism and some results and connections with other known works, such as M. Kreck's bordism groups of orientation preserving diffeomorphisms and Emerson-Meyer's bivariant K-theory etc. An essential motivation is our recent work towards constructing a bivariant-theoretic analogue (in the sense of Fulton-MacPherson) of Levine-Morel's or Levine-Pandharipande's algebraic cobordism.
16:30 - 18:00Room #128 (Mathematics building)
Yutaka Terasawa (Graduate School of Mathematical Sciences,
The University of Tokyo (JSPS Research Fellow))
"Stochastic Power-Law Fluid equations: Existence and Uniqueness of weak solutions (joint work with Nobuo Yoshida)"
16:30 - 17:30Room #052 (Mathematics building)
Ralph Bruckschen (ベルリン工科大学、MATHEON)
"Interactive Data Visualization challenges, approaches and examples"
Data visualization is probably the most important method to analyze scientific datasets. In the time of petaflop supercomputers and high resolution sensors, the visualization of such datasets became a challenge because of the sheer magnitude. Using the latest technology I will describe some of the challenges and approaches to visualize large and massive datasets. The main bottle necks will be explained, as some algorithms and data structures to widen them. Finally I will show some examples of data visualization using a CAVE environment and virtual prototyping from the 3D Labor at the Technical University of Berlin.
2011/11/07
17:00 - 18:00Room #470 (Mathematics building)
Oleg Emanouilov (Colorado State University)
"Inverse boundary value problem for Schroedinger equation in two dimensions"
We relax the regularity condition on potentials of Schroedinger equations in uniqueness results on the inverse boundary value problem recently proved in A.Bukhgeim (2008) and O. Imanuvilov, G.Uhlmann and M. Yamamoto (2010).
15:30 - 17:00Room #122 (Mathematics building)
Atsushi Ito (University of Tokyo)
"Okounkov bodies and Seshadri constants"
Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.
10:30 - 12:00Room #128 (Mathematics building)
Junjiro Nocuchi (University of Tokyo)
"Oka's extra-zero problem and related topics"
The main part of this talk is a joint work with my colleagues, M. Abe and S. Hamano. After the solution of Cousin II problem by K. Oka III in 1939, he thought an extra-zero problem in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. Some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was obtained. We will give a complete solution of this problem with examples and to discuss some new questions. An example on a toric variety of which idea is based on K. Stein's paper in 1941 has some special interest and will be discussed. I would like also to discuss some analytic intersections form the viewpoint of Nevanlinna theory.
2011/11/04
16:30 - 17:30Room #123 (Mathematics building)
KANAI Masahiko (Graduate School of Mathematical Sciences, University of Tokyo)
" Cross ratio, and all that
"
Although the origin of cross ratio goes back to ancient Greek mathematics, new discoveries about it has been made even in the past few decades. It seems that our understanding as to cross ratio is still limited. I am going to show you the present status and my own concerns, as well.
2011/11/02
16:30 - 17:30Room #056 (Mathematics building)
Kensaku Kinjo (University of Tokyo)
"Hypergeometric series and arithmetic-geometric mean over 2-adic fields"
Dwork proved that the Gaussian hypergeometric function on p-adic numbers
can be extended to a function which takes values of the unit roots of
ordinary elliptic curves over a finite field of characteristic p>2.
We present an analogous theory in the case p=2.
As an application, we give a relation between the canonical lift
and the unit root of an elliptic curve over a finite field of
characteristic 2
by using the 2-adic arithmetic-geometric mean.
2011/11/01
16:30 - 18:00Room #056 (Mathematics building)
Kiyoshi Takeuchi (University of Tsukuba)
"Motivic Milnor fibers and Jordan normal forms of monodromies "
We introduce a method to calculate the equivariant
Hodge-Deligne numbers of toric hypersurfaces.
Then we apply it to motivic Milnor
fibers introduced by Denef-Loeser and study the Jordan
normal forms of the local and global monodromies
of polynomials maps in various situations.
Especially we focus our attention on monodromies
at infinity studied by many people. The results will be
explicitly described by the ``convexity" of
the Newton polyhedra of polynomials. This is a joint work
with Y. Matsui and A. Esterov.
2011/10/31
15:30 - 17:00Room #122 (Mathematics building)
Osamu Fujino (Kyoto University)
"Minimal model theory for log surfaces"
We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.
13:30 - 14:30Room #056 (Mathematics building)
Horst Heck
(Technische Universität Darmstadt)
"Stationary Weak Solutions of the Navier-Stokes Equations Past an Obstacle"
Consider the stationary Navier-Stokes equations in an exterior smooth domain $\Omega$. If the flow condition $u_\infty$ for $u$ at infinity is non-zero and the external force $f\in \dot H^{-1}_2(\Omega)$ is given Leray constructed a weak solution $u\in \dot H^1_2(\Omega)$, the homogeneous Sobolev space, with $u-u_\infty\in L^6(\Omega)$.
We show that if in addition $f\in \dot H^{-1}_q(\Omega)$ for some $q\in (4/3,4)$ then the weak solution has the property $u-u_\infty\in L^{4q/(4-q)}(\Omega)$.
This additional integrability implies that $u$ satisfies the energy identity. Further consequences are uniqueness results for small $u_\infty$ and $f$ and continuous dependence of the solution with respect to $u_\infty$.
The presented results are joint work with Hyunseok Kim and Hideo Kozono.
10:30 - 12:00Room #128 (Mathematics building)
Nobuhiro Honda (Tohoku Univeristy)
"Classification of Moishezon twistor spaces on 4CP^2"
2011/10/29
11:00 - 14:30Room #117 (Mathematics building)
Alexander Orlov (Nonlinear Wave Processes Laboratory, Oceanology Institute (Moscow)) 11:00 - 12:00
"CKP Hierarchy, Bosonic Tau Function, Bosonization Formulae and Orthogonal Polynomials both in Odd and Even Variables
(based on a joint work with Johan van de Leur and Takahiro Shiota)"
We develop the theory of CKP hierarchy introduced in the papers of Kyoto school where the CKP tau function is written as a vacuum expectation value in terms of free bosons. We show that a sort of odd currents naturaly appear. We consider bosonization formulae which relate bosonic Fock vectors to polynomials in even and odd Grassmannian variables, where both sets play a role of higher times.
Yasuho Masuda (Kobe Univ. ) 13:30 - 14:30
"Kernel function identities associated with van Diejen's $q$-difference operators
and transformation formulas for multiple $q$-hypergeometric series"
2011/10/26
15:00 - 16:10Room #000 (Mathematics building)
SEI, Tomonari (Department of Mathematics, Keio University)
"Statistical models constructed by optimal stationary coupling"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/04.html
2011/10/25
16:30 - 18:00Room #056 (Mathematics building)
Andrei Pajitnov (Univ. de Nantes, Univ. of Tokyo)
"Circle-valued Morse theory for complex hyperplane arrangements"
Let A be a complex hyperplane arrangement
in an n-dimensional complex vector space V.
Denote by H the union of the hyperplanes
and by M the complement to H in V.
We develop the real-valued and circle-valued Morse
theory on M. We prove that if A is essential then
M has the homotopy type of a space
obtained from a finite n-dimensional
CW complex fibered over a circle,
by attaching several cells of dimension n.
We compute the Novikov homology of M and show
that its structure is similar to the
homology with generic local coefficients:
it vanishes for all dimensions except n.
This is a joint work with Toshitake Kohno.
16:30 - 18:00Room #126 (Mathematics building)
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
"Localization of Cohomological Induction"
Cohomological induction is defined for (g,K)-modules in an algebraic way and construct important representations such as (Harish-Chandra modules of) discrete series representations,
principal series representations and Zuckerman's modules of
semisimple Lie groups.
Hecht, Milicic, Schmid, and Wolf proved that modules induced from
one-dimensional representations of Borel subalgebra can be realized as D-modules on the flag variety.
In this talk, we show a similar result for modules induced from
more general representations.
2011/10/22
13:30 - 16:00Room #117 (Mathematics building)
Leonid Rybnikov (IITP, and State University Higher School of Economics,
Department of Mathematics) 13:30 - 14:30
"Quantization of Quasimaps' Spaces (joint work with M. Finkelberg)"
Quasimaps' space Z_d (also known as Drinfeld's Zastava space) is a
remarkable compactification of the space of based degree d maps from
the projective line to the flag variety of type A. The space Z_d has a
natural Poisson structure,
which goes back to Atiyah and Hitchin. We describe
the Quasimaps' space as some quiver variety, and define the
Atiyah-Hitchin Poisson structure in quiver terms.
This gives a natural way to quantize this Poisson structure.
The quantization of the coordinate ring of the Quasimaps' space turns
to be some natural subquotient of the Yangian of type A.
I will also discuss some generalization of this result to the BCD types.
Anton Zabrodin (
Instituteof Biochemical Physics) 15:00 - 16:00
"Quantum integrable models with elliptic R-matrices
and elliptic hypergeometric series"
Intertwining operators for infinite-dimensional representations of the
Sklyanin algebra with spins l and -l-1 are constructed using the technique of
intertwining vectors for elliptic L-operator. They are expressed in
terms of
elliptic hypergeometric series with operator argument. The intertwining
operators obtained (W-operators) serve as building blocks for the
elliptic R-matrix
which intertwines tensor product of two L-operators taken in
infinite-dimensional
representations of the Sklyanin algebra with arbitrary spin. The
Yang-Baxter equation
for this R-matrix follows from simpler equations of the star-triangle
type for the
W-operators. A natural graphic representation of the objects and
equations involved
in the construction is used.
2011/10/20
16:30 - 18:00Room #270 (Mathematics building)
O. Emanouilov (Colorado State University)
"On reconstruction of Lame coefficients from partial Cauchy data"
For the isotropic Lame system, we prove that if the Lame coefficient ¥mu is a positive constant, then both Lame coefficients can be recovered from the partial Cauchy data.
2011/10/19
17:30 - 18:30Room #056 (Mathematics building)
Andrei Suslin (Northwestern University)
"K_2 of the biquaternion algebra"
http://www.ihes.fr/~abbes/SGA/suslin.pdf
2011/10/17
10:30 - 12:00Room #128 (Mathematics building)
Yoshinobu Kamishima (Tokyo Metropolitan University)
"Compact locally homogeneous Kaehler manifolds $\Gamma\backslash G/K$"
2011/10/12
15:00 - 16:10Room #000 (Mathematics building)
SUZUKI, Taiji (University of Tokyo)
"On Convergence Rate of Multiple Kernel Learning with Various Regularization Types"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html
2011/10/11
17:00 - 18:00Room #056 (Mathematics building)
Gael Meigniez (Univ. de Bretagne-Sud, Chuo Univ.)
"Making foliations of codimension one,
thirty years after Thurston's works
"
In 1976 Thurston proved that every closed manifold M whose
Euler characteristic is null carries a smooth foliation F of codimension
one. He actually established a h-principle allowing the regularization of
Haefliger structures through homotopy. I shall give some accounts of a new,
simpler proof of Thurston's result, not using Mather's homology equivalence; and also show that this proof allows to make F have dense leaves if dim M is at least 4. The emphasis will be put on the high dimensions.
16:30 - 18:00Room #128 (Mathematics building)
Hidemitsu Wadade (Waseda University (JSPS-PD))
"On the best constant of the weighted Trudinger-Moser
type inequality"
2011/10/07
16:30 - 18:00Room #122 (Mathematics building)
Takeshi Katsura (Keio University)
"Towards the classification of non-simple $C^*$-algebras of real rank zero"
2011/10/05
10:00 - 11:00Room #056 (Mathematics building)
Chun Liu (University of Tokyo / Pennsylvania State University)
"Energetic Variational Approaches for Ionic Fluids"
In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.
2011/10/04
16:30 - 18:00Room #056 (Mathematics building)
Yoshifumi Matsuda (The University of Tokyo)
"Relatively quasiconvex subgroups of relatively hyperbolic groups"
Relative hyperbolicity of groups was introduced by Gromov as a
generalization of word hyperbolicity. Motivating examples of relatively
hyperbolic groups are fundamental groups of noncompact complete
hyperbolic manifolds of finite volume. The class of relatively
quasiconvex subgroups of a realtively hyperbolic group is defined as a
genaralization of that of quasicovex subgroups of a word hyperbolic
group. The notion of hyperbolically embedded subgroups of a relatively
hyperbolic group was introduced by Osin and such groups are
characterized as relatively quasiconvex subgroups with additional
algebraic properties. In this talk I will present an introduction to
relatively quasiconvex subgroups and discuss recent joint work with Shin
-ichi Oguni and Saeko Yamagata on hyperbolically embedded subgroups.
2011/09/20
16:30 - 18:00Room #056 (Mathematics building)
Clara Loeh (Univ. Regensburg)
"Functorial semi-norms on singular homology"
Functorial semi-norms on singular homology add metric information to
homology classes that is compatible with continuous maps. In particular,
functorial semi-norms give rise to degree theorems for certain classes
of manifolds; an invariant fitting into this context is Gromov's
simplicial volume. On the other hand, knowledge about mapping degrees
allows to construct functorial semi-norms with interesting properties;
for example, so-called inflexible simply connected manifolds give rise
to functorial semi-norms that are non-trivial on certain simply connected
spaces.
2011/08/12
16:00 - 17:00Room #370 (Mathematics building)
Benny Hon (Department of Mathematics City University of Hong Kong)
"Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations"
In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.
2011/08/03
10:00 - 11:15Room #123 (Mathematics building)
Yoshinori GONGYO (Graduate School of Mathematical Sciences the University of Tokyo)
"Abundance conjecture and canonical bundle formula"
2011/07/29
16:30 - 17:30Room #123 (Mathematics building)
Shihoko Ishii (Graduate School of Mathematical Sciences, University of Tokyo)
"Arc spaces and algebraic geometry"
2011/07/27
16:00 - 18:15Room #123 (Mathematics building)
Takeshi Saito (University of Tokyo) 16:00 - 17:00
"Discriminants and determinant of a hypersurface of even dimension"
The determinant of the cohomology of a smooth hypersurface
of even dimension as a quadratic character of the absolute
Galois group is computed by the discriminant of the de Rham
cohomology. They are also computed by the discriminant of a
defining polynomial. We determine the sign involved by testing
the formula for the Fermat hypersurfaces.
This is a joint work with J-P. Serre.
Dennis Eriksson (University of Gothenburg) 17:15 - 18:15
"Multiplicities of discriminants"
The discriminant of a homogenous polynomial is another homogenous
polynomial in the coefficients of the polynomial, which is zero
if and only if the corresponding hypersurface is singular. In
case the coefficients are in a discrete valuation ring, the
order of the discriminant (if non-zero) measures the bad
reduction. We give some new results on this order, and in
particular tie it to Bloch's conjecture/the Kato-T.Saito formula
on equality of localized Chern classes and Artin conductors. We
can precisely compute all the numbers in the case of ternary
forms, giving a partial generalization of Ogg's formula for
elliptic curves.
2011/07/21
16:30 - 18:00Room #122 (Mathematics building)
Jean Roydor (Univ. Tokyo)
"Almost completely isometric maps and applications"
2011/07/14
16:30 - 18:00Room #122 (Mathematics building)
Raphael Ponge (IPMU)
"New perspectives for the local index formula in noncommutative geometry"
2011/07/13
15:00 - 16:10Room #002 (Mathematics building)
YATA, Kazuyoshi (Institute of Mathematics, University of Tsukuba)
"Statistical Inference for High-Dimension, Low-Sample-Size Data"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/02.html
2011/07/12
16:30 - 18:00Room #128 (Mathematics building)
Masaharau Kobayashi (Tokyo University of Science)
"The inclusion relation between Sobolev and modulation spaces"
In this talk, we consider the inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces. As an application, we give mapping properties of unimodular Fourier multiplier $e^{i|D|^\alpha}$ between $L^p$-Sobolev spaces and modulation spaces.
Joint work with Mitsuru Sugimoto (Nagoya University).
16:30 - 18:00Room #056 (Mathematics building)
Keiko Kawamuro (University of Iowa)
"The self linking number and planar open book decomposition"
I will show a self linking number formula, in language of
braids, for transverse knots in contact manifolds that admit planar
open book decompositions. Our formula extends the Bennequin's for
the standar contact 3-sphere.
2011/07/11
10:30 - 12:00Room #128 (Mathematics building)
Yusaku Chiba (University of Tokyo)
"Kobayashi hyperbolic imbeddings into toric varieties"
2011/07/08
14:30 - 16:00Room #128 (Mathematics building)
T. Suzuki (Osaka Prefecture University)
"$q$-Drinfeld-Sokolov hierarchy, $q$-Painlev¥'e equations, and $q$-hypergeometric functions"
2011/07/06
10:00 - 11:00Room #056 (Mathematics building)
Hitoshi Tanaka (University of Tokyo)
"Trace inequality and Morrey spaces"
2011/07/05
16:30 - 18:00Room #002 (Mathematics building)
Takuya Ooura (RIMS, Kyoto University)
"High-accuracy computation of Goursat-Hardy's integral--- Computation example of unbounded infinite integral---
"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Catherine Oikonomides (The University of Tokyo, JSPS)
"The C*-algebra of codimension one foliations which
are almost without holonomy"
Foliation C*-algebras have been defined abstractly by Alain Connes,
in the 1980s, as part of the theory of Noncommutative Geometry.
However, very few concrete examples of foliation C*-algebras
have been studied until now.
In this talk, we want to explain how to compute
the K-theory of the C*-algebra of codimension
one foliations which are "almost without holonomy",
meaning that the holonomy of all the noncompact leaves
of the foliation is trivial. Such foliations have a fairly
simple geometrical structure, which is well known thanks
to theorems by Imanishi, Hector and others. We will give some
concrete examples on 3-manifolds, in particular the 3-sphere
with the Reeb foliation, and also some slighty more
complicated examples.
2011/07/04
16:30 - 18:00Room #126 (Mathematics building)
Yasunari Nagai (Waseda University)
"Birational Geometry of O'Grady's six dimensional example over the Donaldson-Uhlenbeck compactification"
O'Grady constructed two sporadic examples of compact irreducible symplectic Kaehler manifold, by resolving singular moduli spaces of sheaves on a K3 surface or an abelian surface. We will give a full description of the birational geometry of O'Grady's six dimensional example over the corresponding Donaldson-Uhlenbeck compactification, using an explicit calculation of certain kind of GIT quotients.
If time permits, we will also discuss an involution of the example induced by a Fourier-Mukai transformation.
10:30 - 12:00Room #128 (Mathematics building)
Raphael Ponge (University of Tokyo)
"Toward a Hirzebruch-Riemann-Roch formula in CR geometry"
2011/06/30
16:00 - 17:30Room #128 (Mathematics building)
Yohei Kashima (Graduate School of Mathematical Sciences, The University of Tokyo)
"On the macroscopic models for type-II superconductivity in 3D"
2011/06/29
10:30 - 11:30Room #056 (Mathematics building)
Yoshitaka Masutani (University of Tokyo)
"Computational understanding of diverse structures in human anatomy by landmark detection in medical images"
Robust recognition of anatomical structures in medical images is indispensable for clinical support of diagnosis and therapy. In this lecture, the diverse system of human anatomy is shortly introduced first. Then, the overview of detection techniques for such structures in medical images is shown. Finally, our approach of anatomical structure recognition is presented and is discussed, which is realized by a unified framework of landmark detection based on appearance model matching and MAP estimation on inter-landmark distance probabilities.
http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html
15:00 - 16:10Room #002 (Mathematics building)
OKADA, Yukinori (Laboratory for Statistical Analysis, Center for Genomic Medicine, RIKEN)
"Statistics in genetic association studies"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/01.html
2011/06/28
16:30 - 18:00Room #056 (Mathematics building)
Masahiro Futaki (The University of Tokyo)
"On a Sebastiani-Thom theorem for directed Fukaya categories "
The directed Fukaya category defined by Seidel is a "
categorification" of the Milnor lattice of hypersurface singularities.
Sebastiani-Thom showed that the Milnor lattice and its monodromy behave
as tensor product for the sum of singularities. A directed Fukaya
category version of this theorem was conjectured by Auroux-Katzarkov-
Orlov (and checked for the Landau-Ginzburg mirror of P^1 \times P^1). In
this talk I introduce the directed Fukaya category and show that a
Sebastiani-Thom type splitting holds in the case that one of the
potential is of complex dimension 1.
2011/06/27
10:30 - 12:00Room #128 (Mathematics building)
Kyoji Saito (IPMU, University of Tokyo)
"Vanishing cycles for the entire functions of type $A_{\frac{1}{2}\infty$ and $D_{\frac{1}{2}\infty$"
We introduce two elementary transcendental functions $f_{A_{\frac{1}{2}\infty}$ and $f_{D_{\frac{1}{2}\infty}$ of two variables. They have countably infinitely many critical points. Then, the vanishing cycles associated with the critical points form Dynkin diagrams of type $A_{\frac{1}{2}\infty$ and $D_{\frac{1}{2}\infty$. We calculate the spectral decomposition of the monodromy transformation by embedding the lattice of vanishing cycles into a Hilbert space.
All these stories are connected with a new understanding of KP and KdV integral hierarchy. But the relationship is not yet clear.
16:30 - 18:00Room #126 (Mathematics building)
Vladimir Lazić (Imperial College London)
"MMP revisited, II"
I will talk about how finite generation of certain adjoint rings implies everything we currently know about the MMP. This is joint work with A. Corti.
2011/06/24
13:15 - 14:30Room #123 (Mathematics building)
Yoshihiro OTA (Graduate School of Mathematical Sciences University of Tokyo)
"Spatial-temporal Modeling and Simulation of Transcription"
15:00 - 16:30Room #128 (Mathematics building)
J. Sekiguchi (Tokyo University of Agriculture and Technology)
"A Schwarz map of Appell's $F_2$ whose monodromy group is
related to the reflection group of type $D_4$"
The system of differential equations for Appell's hypergeometric function $F_2(a,b,b',c,c';x,y)$ has four fundamental solutions.
Let $u_1,u_2,u_3,u_4$ be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map $U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y))$
is a hypersurface $S$ of the 3-dimensional projective space ${\bf P}^3$. Then $S$ is defined by $P(u_1,u_2,u_3,u_4)=0$ for a polynomial $P(t_1,t_2,t_3,t_4)$.
It is M. Kato (Univ. Ryukyus) who determined the parameter
$a,b,b',c,c'$ such that the monodromy group of the system for $F_2(a,b,b',c,c';x,y)$ is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group $G$ of rank four by an abelian group.
In this talk, we treat the system for $F_2(a,b,b',c,c';x,y)$ with
$(a,b,b',c,c')=(1/2,1/6,-1/6,1/3,2/3$. In this case, the monodromy group is the semidirect group of $G$ by $Z/3Z$, where $G$ is the reflection group of type $D_4$. The polynomial $P(t_1,t_2,t_3,t_4)$ in this case is of degree four. There are 16 ordinary singular points in the hypersurface $S$.
In the rest of my talk, I explain the background of the study.
16:30 - 17:30Room #123 (Mathematics building)
Jun SHIHO (Graduate School of Mathematical Sciences, University of Tokyo)
"On logarithmic extension of p-adic differential equations"
2011/06/22
15:00 - 16:10Room #002 (Mathematics building)
KOBAYASHI, Kei (The Institute of Statistical Mathematics)
"計算機代数を用いた統計的漸近論"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/00.html
2011/06/21
16:30 - 18:00Room #002 (Mathematics building)
Keiichi Kitamura (Japan Aerospace Exploration Agency (JAXA))
"Research on CFD (Computational Fluid Dynamics) and Its Application to Development of Spacecraft and Rockets
"
http://www.infsup.jp/utnas/
2011/06/20
10:30 - 12:00Room #128 (Mathematics building)
Makoto Abe (Hiroshima University)
"Domains which satisfy the Oka-Grauert principle in a Stein space"
2011/06/16
16:30 - 18:00Room #122 (Mathematics building)
Yusuke Isono (Univ. Tokyo)
"Introduction to rigidity theory of von Neumann algebras"
2011/06/15
17:30 - 18:30Room #056 (Mathematics building)
Tomoyuki Abe (IPMU)
"Product formula for $p$-adic epsilon factors "
I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.
2011/06/14
17:00 - 18:00Room #056 (Mathematics building)
Toshiki Mabuchi (Osaka University)
"Donaldson-Tian-Yau's Conjecture"
For polarized algebraic manifolds, the concept of K-stability
introduced by Tian and Donaldson is conjecturally strongly correlated
to the existence of constant scalar curvature metrics (or more
generally extremal K\"ahler metrics) in the polarization class. This is
known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable
progress has been made by many authors toward its solution. In this
talk, I'll discuss the topic mainly with emphasis on the existence
part of the conjecture.
2011/06/13
10:30 - 12:00Room #128 (Mathematics building)
Takeo Ohsawa (Nagoya Univeristy)
"On the complement of effective divisors with semipositive normal bundle"
16:00 - 17:30Room #128 (Mathematics building)
CHEN Hua (Wuhan University)
"Regularity of Solutions for a Class of Degenerate Equations"
In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including
(1) generalized Kolmogorov equations,
(2) Fokker-Planck equations,
(3) Landau equations and
(4) sub-elliptic Monge-Ampere equations.
2011/06/09
16:30 - 18:00Room #122 (Mathematics building)
Hiroaki Yoshida (Ochanomizu Univ.)
"On the free Fisher information distance and the free logarithmic Sobolev inequality"
16:30 - 18:00Room #128 (Mathematics building)
Kiyoshi Mochizuki (Tokyo Metropolitan University, Emeritus Professor)
"Spectral representations and scattering for Schr\"odinger operators on star graphs"
We consider Schr\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.
2011/06/08
16:30 - 17:30Room #056 (Mathematics building)
Yuichi Hirano (University of Tokyo)
"Congruences of modular forms and the Iwasawa λ-invariants"
2011/06/07
16:30 - 18:00Room #126 (Mathematics building)
Chenyang Xu (MIT)
"Log canonical closure"
(joint with Christopher Hacon) In this talk, we will address the problem on given a log canonical variety, how we compactify it. Our approach is via MMP. The result has a few applications. Especially I will explain the one on the moduli of stable schemes.
If time permits, I will also talk about how a similar approach can be applied to give a proof of the existence of log canonical flips and a conjecture due to Kollár on the geometry of log centers.
16:30 - 18:00Room #002 (Mathematics building)
Takashi Nakazawa (Okayama University)
"Linear stability analyses of flow fields driven by propellers on
the water surface for water quality improvement
"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Masahiko Kanai (the University of Tokyo)
"Rigidity of group actions via invariant geometric structures
"
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
16:30 - 18:00Room #056 (Mathematics building)
Masahiko Kanai (The University of Tokyo)
"Rigidity of group actions via invariant geometric structures"
It is a homomorphism into a FINITE dimensional Lie group that is concerned with in the classical RIGIDITY theorems such as those of Mostow and Margulis. In the meantime, differentiable GROUP ACTIONS for which we ask rigidity problems is a homomorphism into a diffeomorphism group, which is a typical example of INFINITE dimensional Lie groups. The purpose of the present talk is exhibiting several rigidity theorems for group actions in which I have been involved for years. Although quite a few fields of mathematics, such as ergodic theory, the theory of smooth dynamical systems, representation theory and so on, have made remarkable contributions to rigidity problems, I would rather emphasis geometric aspects: I would focus on those rigidity phenomenon for group actions that are observed by showing that the actions have INVARIANT GEOMETRIC STRUCTURES.
2011/06/06
10:30 - 12:00Room #128 (Mathematics building)
Tomoko Shinohara (Tokyo Metropolitan College of Industrial Technology)
"An invariant surface of a fixed indeterminate point for rational mappings"
16:30 - 18:00Room #126 (Mathematics building)
Shihoko Ishii (University of Tokyo)
"Multiplier ideals via Mather discrepancies"
For an arbitrary variety we define a multiplier ideal by using Mather discrepancy.
This ideal coincides with the usual multiplier ideal if the variety is normal and complete intersection.
In the talk I will show a local vanishing theorem for this ideal and as corollaries we obtain restriction theorem, subadditivity theorem, Skoda type theorem, and Briancon-Skoda type theorem.
2011/06/02
16:30 - 17:30Room #056 (Mathematics building)
Yoshihisa Saito (Graduate School of Mathematical Sciences, Univ. of Tokyo)
"On the module category of $¥overline{U}_q(¥mathfrak{sl}_2)$"
In the representation theory of quantum groups at roots of unity, it is
often assumed that the parameter $q$ is a primitive $n$-th root of unity
where $n$ is a odd prime number. However, there has recently been
increasing interest in the the cases where $n$ is an even integer ---
for example, in the study of logarithmic conformal field theories, or in
knot invariants. In this talk,
we work out a fairly detailed study on the category of finite
dimensional
modules of the restricted quantum $¥overline{U}_q(¥mathfrak{sl}_2)$
where
$q$ is a $2p$-th root of unity, $p¥ge2$.
2011/05/31
17:00 - 18:00Room #056 (Mathematics building)
Takehiko Morita (Osaka University)
"Measures with maximum total exponent and generic properties of $C^
{1}$ expanding maps"
This is a joint work with Yusuke Tokunaga. Let $M$ be an $N$
dimensional compact connected smooth Riemannian manifold without
boundary and let $\mathcal{E}^{r}(M,M)$ be the space of $C^{r}$
expandig maps endowed with $C^{r}$ topology. We show that
each of the following properties for element $T$ in $\mathcal{E}
^{1}(M,M)$ is generic.
\begin{itemize}
\item[(1)] $T$ has a unique measure with maximum total exponent.
\item[(2)] Any measure with maximum total exponent for $T$ has
zero entropy.
\item[(3)] Any measure with maximum total exponent for $T$ is
fully supported.
\end{itemize}
On the contrary, we show that for $r\ge 2$, a generic element
in $\mathcal{E}^{r}(M,M)$ has no fully supported measures with
maximum total exponent.
16:30 - 17:30Room #126 (Mathematics building)
Hirotake Kurihara (Tohoku University)
"On character tables of association schemes based on attenuated
spaces"
An association scheme is a pair of a finite set $X$
and a set of relations $\{R_i\}_{0\le i\le d}$
on $X$ which satisfies several axioms of regularity.
The notion of association schemes is viewed as some axiomatized
properties of transitive permutation groups in terms of combinatorics, and also the notion of association schemes is regarded as a generalization of the subring of the group ring spanned by the conjugacy classes of finite groups.
Thus, the theory of association schemes had been developed in the
study of finite permutation groups and representation theory.
To determine the character tables of association schemes is an
important first step to a systematic study of association schemes, and is helpful toward the classification of those schemes.
In this talk, we determine the character tables of association schemes based on attenuated spaces.
These association schemes are obtained from subspaces of a given
dimension in attenuated spaces.
2011/05/30
16:30 - 18:00Room #126 (Mathematics building)
Jungkai Alfred Chen (National Taiwan University and RIMS)
"Kodaira Dimension of Irregular Varieties"
$f:X\to Y$ be an algebraic fiber space with generic geometric fiber $F$, $\dim X=n$ and $\dim Y=m$. Then Iitaka's $C_{n,m}$ conjecture states $$\kappa (X)\geq \kappa (Y)+\kappa (F).$$ In particular, if $X$ is a variety with $\kappa(X)=0$ and $f: X \to Y$ is the Albanese map, then Ueno conjecture that $\kappa(F)=0$. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
10:30 - 12:00Room #128 (Mathematics building)
Atusi Yamamori (Meiji University)
"On the Forelli-Rudin construction and explicit formulas of the Bergman kernels"
2011/05/26
16:00 - 17:30Room #128 (Mathematics building)
Takeshi Fukao (Kyoto University of Education)
"Obstacle problem of Navier-Stokes equations in thermohydraulics"
In this talk, we consider the well-posedness of a variational inequality for the Navier-Stokes equations in 2 or 3 space dimension with time dependent constraints. This problem is motivated by an initial-boundary value problem for a thermohydraulics model. The velocity field is constrained by a prescribed function,
depending on the space and time variables, so this is called the obstacle problem. The abstract theory of nonlinear evolution equations governed by subdifferentials of time dependent convex functionals is quite useful for showing their well-posedness. In their mathematical treatment one of the key is to specify the class of time-dependence of convex functionals. We shall discuss the existence and uniqueness questions for Navier-Stokes variational inequalities, in which a bounded constraint is imposed on the velocity field, in higher space dimensions. Especially, the uniqueness of a solution is due to the advantage of the prescribed constraint to the velocity fields.
2011/05/25
17:00 - 18:00Room #056 (Mathematics building)
Yuya Matsumoto (University of Tokyo)
"On good reduction of some K3 surfaces"
2011/05/24
16:30 - 18:00Room #002 (Mathematics building)
Daisuke Murai (Nagoya University)
"Error analysis of a solution to topology optimization problem of density type
"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Masahiko Yoshinaga (Kyoto University)
"Minimal Stratifications for Line Arrangements"
The homotopy type of complements of complex
hyperplane arrangements have a special property,
so called minimality (Dimca-Papadima and Randell,
around 2000). Since then several approaches based
on (continuous, discrete) Morse theory have appeared.
In this talk, we introduce the "dual" object, which we
call minimal stratification for real two dimensional cases.
A merit is that the minimal stratification can be explicitly
described in terms of semi-algebraic sets.
We also see associated presentation of the fundamental group.
16:30 - 18:00Room #126 (Mathematics building)
Jun-ichi Mukuno (Nagoya University)
"Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds"
If a homogeneous space $G/H$ is acted properly discontinuously
upon by a subgroup $\Gamma$ of $G$ via the left action, the quotient space $\Gamma \backslash G/H$ is called a
Clifford--Klein form. In 1962, E. Calabi and L. Markus proved that there is no infinite subgroup of the Lorentz group $O(n+1, 1)$ whose left action on the de Sitter space $O(n+1, 1)/O(n, 1)$ is properly discontinuous.
It follows that a compact Clifford--Klein form of the de Sitter space never exists.
In this talk, we present a new extension of the theorem of E. Calabi and L. Markus to a certain class of Lorentzian manifolds that are not necessarily homogeneous.
13:15 - 14:30Room #128 (Mathematics building)
Koichiro TAKAOKA (Graduate School of Mathematical Sciences University of Tokyo)
"Martingale theory"
2011/05/23
17:00 - 18:30Room #126 (Mathematics building)
Yuji Sano (Kumamoto University)
"Alpha invariant and K-stability of Fano varieties"
From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).
2011/05/19
16:00 - 17:30Room #128 (Mathematics building)
Shingo Ito (Tokyo University of Science)
"Wave front set defined by wave packet transform and its application"
2011/05/18
10:30 - 11:30Room #056 (Mathematics building)
Yohei Kashima (University of Tokyo)
"On the perturbation theory for many-electron systems at positive temperature"
http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html
16:30 - 17:30Room #056 (Mathematics building)
Masaki Nishimoto (University of Tokyo)
"On the linear independence of values of some Dirichlet series"
2011/05/17
16:30 - 18:00Room #056 (Mathematics building)
Atsushi Ishii (University of Tsukuba)
"Quandle colorings with non-commutative flows"
This is a joint work with Masahide Iwakiri, Yeonhee Jang and Kanako Oshiro.
We introduce quandle coloring invariants and quandle cocycle invariants
with non-commutative flows for knots, spatial graphs, handlebody-knots,
where a handlebody-knot is a handlebody embedded in the $3$-sphere.
Two handlebody-knots are equivalent if one can be transformed into the
other by an isotopy of $S^3$.
The quandle coloring (resp. cocycle) invariant is a ``twisted'' quandle
coloring (resp. cocycle) invariant.
2011/05/16
10:30 - 12:00Room #128 (Mathematics building)
Chifune Kai (Kanazawa Univeristy)
"Linearity of order isomorphisms of regular convex cones"
17:00 - 18:30Room #126 (Mathematics building)
Shinnosuke Okawa (University of Tokyo)
"On images of Mori dream spaces"
Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties whose geometry can be controlled via the VGIT of the Cox ring. It is a generalization of both toric varieties and log Fano varieties.
The purpose of this talk is to study the image of a morphism from a MDS.
Firstly I prove that such an image again is a MDS.
Secondly I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source.
This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of the GIT equivalence. In toric case, this fan coincides with the so called GKZ decomposition.
The point is that these results can be clearly explained via the VGIT description for MDS.
If I have time, I touch on generalizations and an application to the Shokurov polytopes.
2011/05/11
17:30 - 18:30Room #056 (Mathematics building)
Michel Raynaud (Universite Paris-Sud)
"Permanence following Temkin"
When one proceeds to a specialization, the good properties of algebraic equations may be destroyed. Starting with a bad specialization, one can try to improve it by performing modifications under control. If, at the end of the process, the initial good properties are preserved, one speaks of permanence. I shall give old and new examples of permanence. The new one concerns the relative semi-stable reduction of curves recently proved by Temkin.
2011/05/10
16:30 - 18:00Room #002 (Mathematics building)
Yukitaka Minesaki (Tokushima Bunri University)
"Conservative finite difference method for the three body problem"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Tetsuya Ito (The University of Tokyo)
"Isotated points in the space of group left orderings"
The set of all left orderings of a group G admits a natural
topology. In general the space of left orderings is homeomorphic to the
union of Cantor set and finitely many isolated points. In this talk I
will give a new method to construct left orderings corresponding to
isolated points, and will explain how such isolated orderings reflect
the structures of groups.
2011/05/09
16:30 - 18:00Room #126 (Mathematics building)
Hokuto Uehara (Tokyo Metropolitan University)
"Fourier--Mukai partners of elliptic ruled surfaces"
Atiyah classifies vector bundles on elliptic curves E over an algebraically closed field of any characteristic. On the other hand, a rank 2 vector bundle on E defines a surface S with P^1-bundle structure on E.
We study when S has an elliptic fibration according to the Atiyah's classification. As its application, we determines the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field.
10:30 - 12:00Room #128 (Mathematics building)
Junjiro Noguchi (University of Tokyo)
"Order of meromorphic maps and rationality of the image space"
2011/05/02
16:30 - 18:00Room #126 (Mathematics building)
Katsuhisa Furukawa (Waseda University)
"Projective varieties admitting an embedding with Gauss map of rank zero"
I will talk about the study of Gauss map in positivity characteristic which is a joint work with S. Fukasawa and H. Kaji. I will also talk about my resent research of this topic.
We call that a projective variety $X$ satisfies (GMRZ) if there exists an embedding $¥iota: X ¥hookrightarrow ¥mathbb{P}^M$ whose Gauss map $X ¥dashrightarrow G(¥dim(X), ¥mathbb{P}^M)$ is of rank zero at a general point.
We study the case where $X$ has a rational curve $C$. Then, as a fundamental theorem, it follows that the property (GMRZ) makes the splitting type of the normal bundle $N_{C/X}$ very special. We also have a characterization of the Fermat cubic hypersurface in characteristic two in terms of (GMRZ). In this talk, I will also explain the relation of blow-ups and the property (GMRZ).
2011/04/27
16:30 - 17:30Room #056 (Mathematics building)
Yuuki Takai (University of Tokyo)
"An analogue of Sturm's theorem for Hilbert modular forms"
2011/04/26
16:30 - 18:00Room #002 (Mathematics building)
Fumio Kikuchi (Hitotsubashi University)
"Remarks on the discontinuous Galerkin finite element method"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Taro YOSHINO (the University of Tokyo)
"Topological Blow-up"
Suppose that a Lie group $G$ acts on a manifold
$M$. The quotient space $X:=G\backslash M$ is locally compact,
but not Hausdorff in general. Our aim is to understand
such a non-Hausdorff space $X$.
The space $X$ has the crack $S$. Rougly speaking, $S$ is
the causal subset of non-Hausdorffness of $X$, and especially
$X\setminus S$ is Hausdorff.
We introduce the concept of `topological blow-up' as a `repair'
of the crack. The `repaired' space $\tilde{X}$ is
locally compact and Hausdorff space containing $X\setminus S$
as its open subset. Moreover, the original space $X$ can be
recovered from the pair of $(\tilde{X}, S)$.
16:30 - 18:00Room #056 (Mathematics building)
Taro Yoshino (The University of Tokyo)
"Topological Blow-up"
Suppose that a Lie group $G$ acts on a manifold
$M$. The quotient space $X:=G\backslash M$ is locally compact,
but not Hausdorff in general. Our aim is to understand
such a non-Hausdorff space $X$.
The space $X$ has the crack $S$. Roughly speaking, $S$ is
the causal subset of non-Hausdorffness of $X$, and especially
$X\setminus S$ is Hausdorff.
We introduce the concept of `topological blow-up' as a `repair'
of the crack. The `repaired' space $\tilde{X}$ is
locally compact and Hausdorff space containing $X\setminus S$
as its open subset. Moreover, the original space $X$ can be
recovered from the pair of $(\tilde{X}, S)$.
16:30 - 18:00Room #128 (Mathematics building)
Kiyoomi KATAOKA (Graduate School of Mathematical Sciences, the University of Tokyo)
"On the system of fifth-order differential equations which describes surfaces containing six continuous families of circles"
2011/04/25
16:30 - 18:00Room #126 (Mathematics building)
Hiromichi Takagi (University of Tokyo)
"Mirror symmetry and projective geometry of Reye congruences"
This is a joint work with Shinobu Hosono.
It is well-known that the projective dual of the second Veronese variety v_2(P^n) is the symmetric determinantal hypersurface H. However, in the context of homological projective duality after Kuznetsov, it is natural to consider that the Chow^2 P^n and H are dual (note that Chow^2 P^n is the secant variety of v_2(P^n)).
Though we did not yet formulate what this duality exactly means in full generality, we show some results in this context for the values n¥leq 4.
For example, let n=4. We consider Chow^2 P^4 in P(S^2 V) and H in P(S^2 V^*), where V is the vector space such that P^4 =P(V). Take a general 4-plane P in
P(S^2 V^*) and let P' be the orthogonal space to P in P(S^2 V). Then X:=Chow^2 P^4 ¥cap P' is a smooth Calabi-Yau 3-fold, and there exists a natural double cover Y -> H¥cap P with a smooth Calabi-Yau 3-fold Y. It is easy to check
that X and Y are not birational each other.
Our main result asserts the derived equivalence of X and Y. This derived equivalence is given by the Fourier Mukai functor D(X)-> D(Y) whose kernel is the ideal sheaf in X×Y of a flat family of curves on Y parameterized by X.
Curves on Y in this family have degree 5 and arithmetic genus 3, and these have a nice interpretation by a BPS number of Y. The proof of the derived equivalence is slightly involved so I explain a similar result in the case where n=3. In this case, we obtain a fully faithful functor from D(X)-> D(Y), where X is a so called the Reye congruence Enriques surface and Y is the 'big resolution' of the Artin-Mumford quartic double solid.
10:30 - 12:00Room #128 (Mathematics building)
Atsushi Hayashimoto (Nagano National College of Technology)
"On the classification of CR mappings between generalized pseudoellipsoids"
2011/04/20
10:30 - 11:30Room #056 (Mathematics building)
Yoshida, Nobuo (Department of Mathematics, Kyoto University)
"Stochastic power law fluids"
This talk is based in part on a joint work with Yutaka Terasawa.
We consider a SPDE (stochastic partial differential equation) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force.
Here, the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force.
We first investigate the existence and the uniqueness of weak solutions to this SPDE.
We next turn to the special case: $p \in [1 + {d \over 2},{2d\overd-2})$,
where $d$ is the dimension of the space. We prove there that the Galerkin scheme approximates the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.
http://www.math.kyoto-u.ac.jp/~nobuo/
2011/04/18
16:30 - 18:00Room #126 (Mathematics building)
Masayuki Kawakita (Research Institute for Mathematical Sciences, Kyoto University)
"Ideal-adic semi-continuity problem for minimal log discrepancies"
De Fernex, Ein and Mustaţă, after Kollár, proved the ideal-adic semi-continuity of log canonicity to obtain Shokurov's ACC conjecture for log canonical thresholds on l.c.i. varieties. I discuss its generalisation to minimal log discrepancies, proposed by Mustaţă.
10:30 - 12:00Room #128 (Mathematics building)
Shinichi Matsumura (University of Tokyo)
"Asymptotic cohomology vanishing and a converse of the Andreotti-Grauert theorem on surface"
2011/04/14
16:30 - 18:00Room #122 (Mathematics building)
Masayoshi Matsumura (Univ. Tokyo)
"Amenable actions and crossed products of $C^*$-algebras"
16:00 - 17:30Room #128 (Mathematics building)
Marek FILA (Comenius University (Slovakia))
"Homoclinic and heteroclinic orbits for a semilinear parabolic equation"
We study the existence of connecting orbits for the Fujita equation
u_t=\Delta u+u^p
with a critical or supercritical exponent $p$. For certain ranges of the exponent we prove the existence of heteroclinic connections from positive steady states to zero and the existence of a homoclinic orbit with respect to zero. This is a joint work with Eiji Yanagida.
2011/04/13
15:00 - 17:00Room #128 (Mathematics building)
Alexander Pushnitski (King's College, London)
"Spectral theory for functions of self-adjoint operators"
Let A, B be self-adjoint operators such that the standard assumptions of smooth scattering theory for the pair A, B are satisfied. The spectral theory of the operators of the type f(A)-f(B) will be discussed, with a particular attention to the case of discontinuous functions f. It turns out that the spectrum of f(A)-f(B) can often be explicitly described in terms of the spectrum of the scattering matrix for the pair A,B. This is joint work with D.Yafaev.
2011/04/12
16:30 - 18:00Room #056 (Mathematics building)
Susumu Hirose (Tokyo University of Science)
"On diffeomorphisms over non-orientable surfaces embedded in the 4-sphere"
For a closed orientable surface standardly embedded in the 4-sphere,
it was known that a diffeomorphism over this surface is extendable to
the 4-sphere if and only if this diffeomorphism preserves
the Rokhlin quadratic form of this surafce.
In this talk, we will explain an approach to the same kind of problem for
closed non-orientable surfaces.
2011/04/11
10:30 - 12:00Room #128 (Mathematics building)
Shinichi Tajima (University of Tsukuba)
"Algebraic analysis of resolvents and an exact algorithm for computing Spectral decomposition matrices"
2011/03/31
13:00 - 14:00Room #118 (Mathematics building)
Alain Joye (Univ. Grenoble)
"Dynamical localization for unitary Anderson models"
14:30 - 15:30Room #118 (Mathematics building)
Gerard Ben Arous (Courant Institute, New York Univ.)
"Stable limits for biased random walks on random trees"
It is well know that transport in random media can be hampered by dead-end regions and that the velocity can even vanish for strong drifts. We study this phenomenon in great detail for random trees. That is, we study the behavior of biased random walks on supercritical random trees with leaves, in the sub-ballistic regime. When the drift is strong enough it is well known that trapping in the dead-ends of the tree, causes the velocity to vanish. We study the behavior of the walk in this regime, and in particular find the exponents for the mean displacement and the time to reach a given large distance. We also establish a scaling limit result in the case where the drift are random and a non-lattice condition is satisfied. (Joint work with Alexander Fribergh, Alan Hammond, Nina Gantert)
2011/03/22
14:00 - 15:00Room #128 (Mathematics building)
Amir Dembo (Stanford Univ.)
"Potts models and Bethe states on sparse random graphs"
Theoretical models of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying mathematical structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph. Focusing on ferromagnetic Potts measures on random finite graphs that converge locally to trees we validate the `cavity' prediction for the limiting free energy per spin and show that local marginals are approximated well by the belief propagation algorithm. This is a concrete example of the more general approximation by Bethe measures, namely, the local convergence of the Boltzmann distribution on the original graph to the Boltzmann distribution on an appropriate infinite random tree (this talk is based on a joint work with Andrea Montanari and Nike Sun).
2011/03/08
15:00 - 16:30Room #128 (Mathematics building)
Dimitri Yafaev (Univ. Rennes 1)
"Diagonal singularities of the scattering matrix and the inverse problem at a fixed energy"
2011/03/04
17:00 - 18:00Room #370 (Mathematics building)
Oleg Emanouilov (Colorado State University)
"Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets"
We discuss the inverse boundary value problem of determining the conductivity in two dimensions from the pair of all input Dirichlet data supported on an open subset S1 and all the corresponding Neumann data measured on an open subset S2.
We prove the global uniqueness under some additional geometric condition, in the case where the intersection of S_1 and S_2 has no interior points, and we prove also the uniqueness for a similar inverse problem for the stationary Schr"odinger equation.
The key of the proof isthe construction of appropriate complex geometrical optics solutions using Carleman estimates with a singular weight.
2011/03/03
13:30 - 14:30Room #270 (Mathematics building)
Stefano Olla (Univ. Paris Dauphine)
"Energy Diffusion: hydrodynamic, weak coupling, kinetic limits"
I will review recent results about weak coupling and kinetic limits for the energy diffusive evolution in hamiltonian systems perturbed by energy-conservating noise. Two universality classes of diffusion are obtained: Ginzburg-Landau dynamics that arise from weak coupling limit of anharmonic oscillators, and exclusion type processes that arise from kinetic limit (rarefied collisions) of interacting billiards. Works in collaboration with Carlangelo Liverani (weak coupling) and Francois Huveneers (kinetic limits).
14:45 - 15:45Room #270 (Mathematics building)
Hirofumi Osada (Kyushu Univ.)
"Singularity and absolute continuity of Palm measures of Ginibre random fields
"
The Ginibre random point field is a probability measure on the configuration space over the complex plane $\mathbb{C}$, which is translation and rotation invariant. Intuitively, the interaction potential of this random point field is the two dimensional Coulomb potential with $\beta = 2 $. This fact is justified by the integration by parts formula.
Since the two dimensional Coulomb potential is quite strong at infinity, the property of the Ginibre random point field is different from that of Gibbs measure with Ruelle class potentials. As an instance, we prove that the Palm measure of the Ginibre random point field is singular to the original Ginibre random point field. Moreover, all Palm measures conditioned at $x \in \mathbb{C}$ are mutually absolutely continuous.
16:00 - 16:30Room #270 (Mathematics building)
Yuu Hariya (Tohoku Univ.)
"A proof of the Brascamp-Lieb inequality based on Skorokhod embedding"
In this talk, we provide a probabilistic approach to the Brascamp-Lieb inequality based on Skorokhod embedding. An extension of the inequality to non-convex potentials will also be discussed.
2011/02/28
17:00 - 18:00Room #470 (Mathematics building)
Ying Tan (The University of Melbourne)
"Extremum Seeking Control: history and recent developments"
A control system which is to determine and maintain the extremum value of a function is called extremum seeking control. The first extremum seeking control application appeared in 1922, in which the extremum seeking control was applied to electric railways. The first rigorous local stability analysis for an ESC scheme was recently proved in 2000 and later extended to semi-global stability analysis 2006.. This has spurred a renewed interest in this research area, leading to numerous practical implementations of the scheme. This talk will first revisit the history of extremum seeking control. It is followed by an explanation how the extremum seeking works. Finally, it will focus on the latest unifying framework that combines arbitrary continuous optimization algorithms with an estimator for derivatives of the unknown reference-to-output steady state map that contains an extremum.
2011/02/24
16:00 - 18:10Room #002 (Mathematics building)
Arnaud Ducrot (University of Bordeaux 2) 16:00 - 17:00
"Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections"
This work is devoted to the study of travelling wave solutions for some size structured model in population dynamics. The population under consideration is also spatially structured and has a nonlocal spatial reproduction. This phenomenon may model the invasion of plants within some empty landscape. Since the corresponding unspatially structured size structured models may induce oscillating dynamics due to Hopf bifurcations, the aim of this work is to prove the existence of point to sustained oscillating solution travelling waves for the spatially structured problem. From a biological viewpoint, such solutions represent the spatial invasion of some species with spatio-temporal patterns at the place where the population is established.
Enrique Zuazua (Basque Center for Applied Mathematics) 17:10 - 18:10
"Some open problems in PDE control"
The field of PDE control has experienced a great progress in the last decades, developing new theories and tools that have also influenced other disciplines as Inverse Problem and Optimal Design Theories and Numerical Analysis. PDE control arises in most applications ranging from classical problems in fluid mechanics or structural engineering to modern molecular design experiments.
From a mathematical viewpoint the problems arising in this field are extremely challenging since the existing theory of existence and uniqueness of solutions and the corresponding numerical schemes is insufficient when addressing realistic control problems. Indeed, an efficient controller requires of an in depth understanding of how solutions depend on the various parameters of the problem (shape of the domain, time of control, coefficients of the equation, location
of the controller, nonlinearity in the equation,...)
In this lecture we shall briefly discuss some important advances and some challenging open problems. All of them shear some features. In particular they are simple to state and very likely hard to solve. We shall discuss in particular:
1.- Semilinear wave equations and their control properties.
2.- Microlocal optimal design of wave processes
3.- Sharp observability estimates for heat processes.
4.- Robustness on the control of finite-dimensional systems.
5.- Unique continuation for discrete elliptic models
6.- Control of Kolmogorov equations and other hypoelliptic models.
2011/02/23
14:00 - 18:00Room #118 (Mathematics building)
Dimitri Yafaev (Univ. Rennes 1) 14:00 - 14:45
"The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited"
David Damanik (Rice University) 15:00 - 15:45
"Uniform localization"
Erik Skibsted (Aarhus University) 16:15 - 17:00
"Global solutions to the eikonal equation"
Christian Gerard (Univ. Paris Sud 11) 17:15 - 18:00
"Applications of microlocal analysis to quantum field theory on curved space-times"
2011/02/18
10:30 - 12:00Room #122 (Mathematics building)
Pedram Hekmati (Univ. Adelaide)
"Dirac families and 1-cocycles"
Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.
11:00 - 15:45Room #126 (Mathematics building)
T. Morita (Osaka University) 11:00 - 12:00
"Connection problem on the Hahn-Exton $q$-Bessel functions"
M. Yamaguchi (University of Tokyo) 13:30 - 14:30
"Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)
"
L. Di Vizio (Universite Paris 7) 14:45 - 15:45
"Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)
"
10:15 - 10:45Room #126 (Mathematics building)
Y. Ohyama (Osaka University)
"Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations"
2011/02/17
16:00 - 17:30Room #002 (Mathematics building)
Thomas Giletti (University of Paul Cezanne (Marseilles))
"Study of propagation phenomena in some reaction-diffusion systems"
This talk deals with the existence and qualitative properties of traveling wave solutions of a nonlinear reaction-diffusion system with losses inside the domain, which has numerous applications in various fields ranging from chemical and biological contexts to combusion. Under some KPP type hypotheses, the existence of a continuum of admissible speeds for traveling waves can be shown, thus generalizing the single equation case. Lastly, by considering losses concentrated near the edge of the domain, those results can be compared with those of the boundary losses case.
11:00 - 17:00Room #126 (Mathematics building)
L. Di Vizio (Universite Paris 7) 11:00 - 12:00
"Overview of local theory of $q$-difference equations and summation, 1
"
Y. Katsushima (University of Tokyo) 13:30 - 14:30
"Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order)"
K. Matsuya (University of Tokyo) 14:45 - 15:45
"Blow-up of solutions for a nonlinear difference equation"
L. Di Vizio (Universite Paris 7) 16:00 - 17:00
"Overview of local theory of $q$-difference equations and summation, 2"
2011/02/16
13:30 - 17:00Room #126 (Mathematics building)
H. Sakai (University of Tokyo) 13:30 - 14:30
"Isomonodromic deformation and 4-dimensional Painlev\'e type equations"
H. Kawakami (University of Tokyo) 14:45 - 15:45
"Degeneration scheme of 4-dimensional Painlev¥'e type equations
(Joint work with H. Sakai and A. Nakamura)
"
S. Nishioka (University of Tokyo) 16:00 - 17:00
"Solvability of difference Riccati equations"
2011/02/14
13:00 - 14:00Room #270 (Mathematics building)
Jin Cheng (Fudan University)
"Unique continuation on the analytic curve and its application to inverse problems."
The unique continuation is one of the important properties for the partial differential equations, which is applied to the study of inverse problems for PDE. In this talk, we will show the unique continuation on the analytic curve for the elliptic equations with analytic coefficients. Some applications to inverse problems are mentioned.
2011/02/10
16:30 - 18:00Room #122 (Mathematics building)
Alan Weinstein (UC Berkeley)
"Symplectic and quantum categories"
15:30 - 16:30Room #002 (Mathematics building)
Jean-Michel Coron (University of Paris 6)
"Control and nonlinearity"
We present methods to study the controllability and the stabilizability of nonlinear control systems. The emphasis is put on specific phenomena due to the nonlinearities. In particular we study cases where the nonlinearities are essential for the controllability or the stabilizability.
We illustrate these methods on control systems modeled by ordinary differential equations or partial differential equations (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg de Vries equations).
11:00 - 12:00Room #056 (Mathematics building)
Joseph Ayoub (University of Zurich)
"The motivic Galois group and periods of algebraic varieties"
We give a construction of the motivic Galois group of $\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.
2011/02/04
09:45 - 11:00Room #118 (Mathematics building)
Takashi HARA (Graduate School of Mathematical Sciences University of Tokyo)
" Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p(総実代数体の羃指数p型非可換p拡大に対するp-進ゼータ関数の帰納的構成)"
11:00 - 12:15Room #118 (Mathematics building)
Akiyoshi SANNAI (Graduate School of Mathematical Sciences University of Tokyo)
"Galois extensions,pls closure,and maps on local cohomology(ガロア拡大、プラス閉包、及び局所コホモロジー間の射について)"
13:00 - 14:15Room #118 (Mathematics building)
Shin HARASE (Graduate School of Mathematical Sciences University of Tokyo)
"Fast lattice reduction algorithms for optimizing F2-linear pseudorandom number generators(F2-線形擬似乱数発生法の最適化のための高速格子簡約アルゴリズム)"
11:00 - 12:15Room #122 (Mathematics building)
Takahiro KITAYAMA (Graduate School of Mathematical Sciences University of Tokyo)
"Non-commutative Reidemeister torsion, Morse-Novikov theory and homology cylinders of higher-order(非可換ライデマイスタートーション,モース‐ノビコフ理論及び高次のホモロジーシリンダー)"
14:15 - 15:30Room #122 (Mathematics building)
Kenji NAKAHARA (Graduate School of Mathematical Sciences University of Tokyo)
"Uniform Estimates for Distributions of Sums of i.i.d Random Variables with Fat Tail(分布がファットテールをもつ場合の独立同分布の和の分布の一様評価について)"
09:45 - 11:00Room #128 (Mathematics building)
Zhang Guanghui (Graduate School of Mathematical Sciences University of Tokyo)
"Regularity of two dimensional steady capillary gravity water waves(二次元定常表面張力重力波の正則性)"
11:00 - 12:15Room #128 (Mathematics building)
Liu Qing (Graduate School of Mathematical Sciences University of Tokyo)
"Singular Problems Related to Curvature Flow and Hamilton-Jacobi Equations(曲率流とハミルトン・ヤコビ方程式における特異問題)"
13:00 - 14:15Room #128 (Mathematics building)
Makiko SASADA (Graduate School of Mathematical Sciences University of Tokyo)
"Hydrodynamic limit and equilibrium fluctuation for nongradient systems(非勾配型の系に対する流体力学極限と平衡揺動)"
14:15 - 15:30Room #128 (Mathematics building)
Masaaki UESAKA (Graduate School of Mathematical Sciences University of Tokyo)
"Coefficient inverse problems for partial differential equations in the viscoelasticity, the material science and population studies by Carleman estimates(カーレマン評価を用いた、粘弾性論・材料科学・人口学における偏微分方程式系の係数決定問題について)"
2011/02/03
09:45 - 11:00Room #118 (Mathematics building)
Shuhei YOSHITOMI (Graduate School of Mathematical Sciences the University of Tokyo)
"Generators of modules in tropical geometry(トロピカル幾何における加群の生成元)"
11:00 - 12:15Room #118 (Mathematics building)
Kenji HASHIMOTO (Graduate School of Mathematical Sciences University of Tokyo)
"Finite Symplectic Actions on the K3 Lattice(K3格子への有限シンプレクティック作用)"
13:00 - 14:15Room #118 (Mathematics building)
Katsuyuki NAOI (Graduate School of Mathematical Sciences University of Tokyo)
"Weyl modules, Demazure modules and finite crystals for non-simply laced type(Bn, Cn, F4, G2型のワイル加群、デマズール加群および有限クリスタルについて)"
14:15 - 15:30Room #118 (Mathematics building)
Ryosuke KODERA (Graduate School of Mathematical Sciences University of Tokyo )
"Extensions between finite-dimensional simple modules over a generalized current Lie algebra(一般化されたカレントリー代数上の有限次元単純加群の間の拡大)"
09:45 - 11:00Room #122 (Mathematics building)
Masato MIMURA (Graduate School of Mathematical Sciences University of Tokyo)
"Rigidity theorems for universal and symplectic universal lattices(普遍格子と斜交普遍格子の剛性定理)"
11:00 - 12:15Room #122 (Mathematics building)
Makoto YAMASHITA (Graduate School of Mathematical Sciences University of Tokyo)
"Deformation of torus equivariant spectral triples(トーラス同変なスペクトラル三つ組の変形) "
14:15 - 15:30Room #122 (Mathematics building)
Zhang Qin (Graduate School of Mathematical Sciences University of Tokyo)
"Noncommutative Maximal Ergodic Inequality For Non-tracial L1-spaces(非トレース的L1空間に対する非可換極大エルゴード不等式)"
14:15 - 15:30Room #128 (Mathematics building)
Haruya MIZUTANI (Graduate School of Mathematical Sciences University of Tokyo)
"Dispersive and Strichartz estimates for Schrödinger equations(シュレディンガー方程式に対する分散型及びストリッカーツ評価)"
15:45 - 17:00Room #128 (Mathematics building)
Atsushi KAWAMOTO (Graduate School of Mathematical Sciences University of Tokyo)
"Conditional stability by Carleman estimates for inverse problems : coefficient inverse problems for the Dirac equation, the determination of subboundary by the heat equation and the continuation of solution of the Euler equation(逆問題に対するカーレマン評価による条件付き安定性: ディラック方程式に対する係数逆問題,熱方程式による部分境界の決定とオイラー方程式に対する解の接続性)"
2011/02/02
16:30 - 17:30Room #002 (Mathematics building)
Yong Jung Kim (Korea Advanced Institute of Science and Technology (KAIST))
"Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities"
The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.
15:15 - 16:15Room #002 (Mathematics building)
Guanghui ZHANG (Graduate School of Mathematical Sciences, the University of Tokyo)
"Regularity of two dimensional capillary gravity water waves"
We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.
15:00 - 16:10Room #006 (Mathematics building)
MIURA, Ryozo (Hitotsubashi University)
"An Attempt to formalize Statistical Inferences for Weakly Dependent Time-Series Data and Some Trials for Statistical Analysis of Financial Data"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/08.html
2011/01/31
16:40 - 18:10Room #126 (Mathematics building)
Sukmoon Huh (KIAS)
"Restriction maps to the Coble quartic"
The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.
16:30 - 18:00Room #002 (Mathematics building)
Kwok-Wai Chan (IPMU, the University of Tokyo)
"Mirror symmetry for toric Calabi-Yau manifolds from the SYZ viewpoint"
In this talk, I will discuss mirror symmetry for toric
Calabi-Yau (CY) manifolds from the viewpoint of the SYZ program. I will
start with a special Lagrangian torus fibration on a toric CY manifold,
and then construct its instanton-corrected mirror by a T-duality modified
by quantum corrections. A remarkable feature of this construction is that
the mirror family is inherently written in canonical flat coordinates. As
a consequence, we get a conjectural enumerative meaning for the inverse
mirror maps. If time permits, I will explain the verification of this
conjecture in several examples via a formula which computes open
Gromov-Witten invariants for toric manifolds.
10:30 - 12:00Room #128 (Mathematics building)
Damian Brotbek (Rennes Univ.)
"Varieties with ample cotangent bundle and hyperbolicity"
Varieties with ample cotangent bundle satisfy many interesting properties and are supposed to be abundant, however relatively few concrete examples are known. In this talk we will construct such examples as complete intersection surfaces in projective space, and explain how this problem is related to the study of hyperbolicity properties for hypersurfaces.
2011/01/28
16:30 - 17:30Room #117 (Mathematics building)
Shirai Tomoyuki (Kyushu University)
"Conformal invariance in probability theory"
14:45 - 16:15Room #122 (Mathematics building)
Takeshi Katsura (Keio University)
"Semiprojectivity of graph algebras"
2011/01/27
16:30 - 18:00Room #122 (Mathematics building)
Hiroshi Takai (Tokyo Metropolitan University)
"Entire Cyclic Cohomology of Noncommutative Riemann Surfaces"
16:00 - 17:30Room #002 (Mathematics building)
Nitsan Ben-Gal (The Weizmann Institute of Science)
"Attraction at infinity: Constructing non-compact global attractors in the slowly non-dissipative realm"
One of the primary tools for understanding the much-studied realm of reaction-diffusion equations is the global attractor, which provides us with a qualitative understanding of the governing behaviors of solutions to the equation in question. Nevertheless, the classic global attractor for such systems is defined to be compact, and thus attractor theory has previously excluded such analysis from being applied to non-dissipative reaction-diffusion equations.
In this talk I will present recent results in which I developed a non-compact analogue to the classical global attractor, and will discuss the methods derived in order to obtain a full decomposition of the non-compact global attractor for a slowly non-dissipative reaction-diffusion equation. In particular, attention will be paid to the nodal property techniques and reduction methods which form a critical underpinning of asymptotics research in both dissipative and non-dissipative evolutionary equations. I will discuss the concepts of the ‘completed inertial manifold’ and ‘non-compact global attractor’, and show how these in particular allow us to produce equivalent results for a class of slowly non-dissipative equations as have been achieved for dissipative equations. Additionally, I will address the behavior of solutions to slowly non-dissipative equations approaching and at infinity, the realm which presents both the challenges and rewards of removing the necessity of dissipativity.
2011/01/26
16:30 - 17:30Room #056 (Mathematics building)
Shinichi Kobayashi (Tohoku University)
"The p-adic Gross-Zagier formula for elliptic curves at supersingular primes "
The p-adic Gross-Zagier formula is a formula relating the derivative of the p-adic L-function of elliptic curves to the p-adic height of Heegner points. For a good ordinary prime p, the formula is proved by B. Perrin-Riou more than 20 years ago. Recently, the speaker proved it for a supersingular prime p. In this talk, he explains the proof.
10:30 - 11:30Room #056 (Mathematics building)
Jong-Shenq Guo (Department of Mathematics, Tamkang University
)
"Quenching Problem Arising in Micro-electro Mechanical Systems
"
In this talk, we shall present some recent results on quenching problems which arise in Micro-electro Mechanical Systems.
We shall also give some open problems in this research area.
15:00 - 16:10Room #002 (Mathematics building)
HIROSE, Yuichi (Victoria University of Wellington)
"Semi-parametric profile likelihood estimation and implicitly defined functions"
The object of talk is the differentiability of implicitly defined functions which we
encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild
(1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly
defined functions by reparametrizing parameters in the profile likelihood and using an approximate least
favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach
developed in Hirose (2010) which uses the differentiability of implicitly defined functions.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/07.html
2011/01/25
16:30 - 17:30Room #056 (Mathematics building)
Chikara Haruta (Graduate School of Mathematical Sciences, the University of Tokyo )
"On unknotting of surface-knots with small sheet numbers
"
A connected surface smoothly embedded in ${\mathbb R}^4$ is called a surface-knot. In particular, if a surface-knot $F$ is homeomorphic to the $2$-sphere or the torus, then it is called an $S^2$-knot or a $T^2$-knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a $1$-knot. M. Saito and S. Satoh proved some results concerning the sheet number of an $S^2$-knot. In particular, it is known that an $S^2$-knot is trivial if and only if its sheet number is $1$, and there is no $S^2$-knot whose sheet number is $2$. In this talk, we show that there is no $S^2$-knot whose sheet number is $3$, and a $T^2$-knot is trivial if and only if its sheet number is $1$.
2011/01/24
10:30 - 12:00Room #128 (Mathematics building)
Masahide Kato (Sophia Univ.)
"Toward a complex analytic 3-dimensional Kleinian group theory"
2011/01/20
16:30 - 18:00Room #122 (Mathematics building)
Masato Mimura (Univ. Tokyo)
"Property (TT)/T and homomorphism rigidity into Out$(F_n)$"
2011/01/19
10:30 - 11:30Room #056 (Mathematics building)
Yoshihito Ogasawara (Waseda University Faculty of Science and Engineering)
"Exploration of essence of Mullins equation"
15:00 - 16:10Room #000 (Mathematics building)
SHIMIZU, Yasutaka (Osaka University)
"Notes on estimating the probability of ruin and some generalization"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/06.html
2011/01/18
16:30 - 18:00Room #118 (Mathematics building)
Claude-Alain Pillet (Univ. de Toulon et du Var)
"Scattering induced current in a tight binding band"
17:00 - 18:00Room #126 (Mathematics building)
Pierre Clare (Universite Orleans and the University of Tokyo)
"Connections between Noncommutative Geometry and Lie groups
representations"
One of the principles of Noncommutative Geometry is to study singular spaces that the tools of classical analysis like algebras of continuous functions fail to describe, replacing them by more general C*-algebras. After recalling fundamental facts about C*-algebras, Hilbert modules and group C*-algebras, we will present constructions and results aiming to understand principal series representations and Knapp-Stein theory in the noncommutative geometrical framework. Eventually we will explain the relationship between the analysis of reduced group C*-algebras and the computation of the Connes-Kasparov isomorphisms.
2011/01/17
16:40 - 18:10Room #126 (Mathematics building)
Dano Kim (KIAS)
"L^2 methods and Skoda division theorems"
Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.
10:30 - 12:00Room #128 (Mathematics building)
Toshihiro Nose (Kyushu Univ.)
"Asymptotics of the Bergman function for semipositive holomorphic line bundles"
In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.
2011/01/13
16:30 - 18:00Room #122 (Mathematics building)
Robert Coquereaux (CNRS/CPT)
"Global dimensions for fusion categories of type $(G,k)$"
2011/01/12
16:30 - 18:45Room #056 (Mathematics building)
Zhonghua Li (University of Tokyo) 16:30 - 17:30
"On regularized double shuffle relation for multiple zeta values"
Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.
Dan Yasaki (North Carolina University) 17:45 - 18:45
"Spines with View Toward Modular Forms"
The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of
its action on the upper half plane. In this talk, we will examine spines, which are the ``smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.
2011/01/11
16:30 - 18:00Room #056 (Mathematics building)
Nariya Kawazumi (The University of Tokyo)
"The Chas-Sullivan conjecture for a surface of infinite genus"
Let \Sigma_{\infty,1} be the inductive limit of compact
oriented surfaces with one boundary component. We prove the
center of the Goldman Lie algebra of the surface \Sigma_{\infty,1}
is spanned by the constant loop.
A similar statement for a closed oriented surface was conjectured
by Chas and Sullivan, and proved by Etingof. Our result is deduced
from a computation of the center of the Lie algebra of oriented chord
diagrams.
If time permits, the Lie bracket on the space of linear chord diagrams
will be discussed. This talk is based on a joint work with Yusuke Kuno
(Hiroshima U./JSPS).
16:30 - 18:00Room #122 (Mathematics building)
Raphael Ponge (Univ. Tokyo)
"Noncommutative geometry and diffeomorphism-invariant geometries"
16:30 - 18:00Room #002 (Mathematics building)
Takehiko Kinoshita (RIMS)
"Norm estimates of inverse linear ordinary differential operator and its applications"
http://www.infsup.jp/utnas/
2010/12/22
11:00 - 12:00Room #570 (Mathematics building)
Mourad Bellassoued (Faculté des Sciences de Bizerte)
"Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map"
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).
16:30 - 17:30Room #056 (Mathematics building)
Takashi Hara (University of Tokyo)
"Inductive construction of the p-adic zeta functions for non-commutative
p-extensions of totally real fields with exponent p"
We will discuss how to construct p-adic zeta functions and verify
the main conjecture in special cases in non-commutative Iwasawa theory
for totally real number fields.
The non-commutative Iwasawa main conjecture for totally real number
fields has been verified in special cases by Kazuya Kato,
Mahesh Kakde and the speaker by `patching method of p-adic zeta functions'
introduced by David Burns and Kazuya Kato (Jurgen Ritter and Alfred Weiss
have also constructed the successful example of the main conjecture
under somewhat different formulations).
In this talk we will explain that we can prove the main conjecture
for cases where the Galois group is isomorphic
to the direct product of the ring of p-adic integer and a finite p-group
of exponent p by utilizing Burns-Kato's method and inductive arguments.
Finally we remark that in 2010 Ritter-Weiss and Kakde independently
justified the non-commutative main conjecture
for totally real number fields under general settings.
2010/12/21
16:30 - 18:00Room #126 (Mathematics building)
Katsuyuki NAOI (Graduate School of Mathematical Sciences, the University of Tokyo)
"Some relation between the Weyl module and the crystal basis of the tensor product of fudamental representations"
2010/12/20
10:30 - 12:00Room #128 (Mathematics building)
Hiroshi Yamaguchi (Shiga Univ*)
"Pseudoconvex domains in Hopf surfaces"
16:40 - 18:10Room #126 (Mathematics building)
Yoshinori Gongyo (Univ. of Tokyo)
"On the minimal model theory from a viewpoint of numerical invariants"
I will introduce the numerical Kodaira dimension for pseudo-effective divisors after N. Nakayama and explain the minimal model theory of numerical Kodaira dimension zero. I also will talk about the applications. ( partially joint work with B. Lehmann.)
2010/12/16
16:30 - 18:00Room #122 (Mathematics building)
Marco Merkli (Memorial Univ. Newfoundland)
"Evolution of Quantum Dynamical Systems"
15:15 - 16:15Room #122 (Mathematics building)
Nicolas Monod (EPFL)
"Fixed point theorems and derivations"
13:00 - 14:30Room #123 (Mathematics building)
Sebastien Hitier (BNP Paribas, Head of Quantitative Research, Credit Asia)
"Credit Derivatives Modelling and the concept of Background Intensity I"
Session 1: Introducing background intensity models
- Motivation for the concept of background intensity
- The default realisation marker
- Definition of background filtration and background intensity
- Reformulating the H hypothesis, and Kusuoka’s “remark”
- Generalised HJM formula and Credit Risk neutral dynamics
Session 2: Five useful properties of background intensity models
- Generalised HJM formula for credit
- Definition of conditionally independent defaults
- Diversification effects: results on forward loss distribution
- Stronger conditional independence effect for spot loss
- Existence of a canonical copula
- Properties of the portfolio loss copula
14:40 - 16:10Room #123 (Mathematics building)
Sebastien Hitier (BNP Paribas, Head of Quantitative Research, Credit Asia)
"Credit Derivatives Modelling and the concept of Background Intensity II"
Session 1: Introducing background intensity models
- Motivation for the concept of background intensity
- The default realisation marker
- Definition of background filtration and background intensity
- Reformulating the H hypothesis, and Kusuoka’s “remark”
- Generalised HJM formula and Credit Risk neutral dynamics
Session 2: Five useful properties of background intensity models
- Generalised HJM formula for credit
- Definition of conditionally independent defaults
- Diversification effects: results on forward loss distribution
- Stronger conditional independence effect for spot loss
- Existence of a canonical copula
- Properties of the portfolio loss copula
2010/12/14
16:30 - 18:00Room #056 (Mathematics building)
Kenneth Schackleton (IPMU)
"On the coarse geometry of Teichmueller space"
We discuss the synthetic geometry of the pants graph in
comparison with the Weil-Petersson metric, whose geometry the
pants graph coarsely models following work of Brock’s. We also
restrict our attention to the 5-holed sphere, studying the Gromov
bordification of the pants graph and the dynamics of pseudo-Anosov
mapping classes.
2010/12/13
10:30 - 12:00Room #128 (Mathematics building)
Katsutoshi Yamanoi (Tokyo Institute of Technology)
"An equality estimate for the second main theorem"
16:40 - 18:10Room #126 (Mathematics building)
Sergey Fomin (University of Michigan)
"Enumeration of plane curves and labeled floor diagrams"
Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and G. Mikhalkin. Tropical geometry arguments yield combinatorial descriptions of (ordinary and relative) Gromov-Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In the case of the projective plane, these descriptions can be used to obtain new formulas for the corresponding enumerative invariants. In particular, we give a proof of Goettsche's polynomiality conjecture for plane curves, and enumerate plane rational curves of given degree passing through given points and having maximal tangency to a given line. On the combinatorial side, we show that labeled floor diagrams of genus 0 are equinumerous to labeled trees, and therefore counted by the celebrated Cayley's formula. The corresponding bijections lead to interpretations of the Kontsevich numbers (the genus-0 Gromov-Witten invariants of the projective plane) in terms of certain statistics on trees.
This is joint work with Grisha Mikhalkin.
2010/12/10
16:30 - 17:30Room #117 (Mathematics building)
Yoshikazu Giga (The University of Tokyo, Graduate School of Mathematical Sciences)
"Hamilton-Jacobi equations and crystal growth"
2010/12/09
16:30 - 18:00Room #122 (Mathematics building)
Ryszard Nest (Univ. Copenhagen)
"Spectral flow associated to KMS states with periodic KMS group action"
2010/12/07
16:30 - 18:00Room #056 (Mathematics building)
Raphael Ponge (The University of Tokyo)
"Diffeomorphism-invariant geometries and noncommutative geometry"
In many geometric situations we may encounter the action of
a group $G$ on a manifold $M$, e.g., in the context of foliations. If
the action is free and proper, then the quotient $M/G$ is a smooth
manifold. However, in general the quotient $M/G$ need not even be
Hausdorff. Furthermore, it is well-known that a manifold has structure
invariant under the full group of diffeomorphisms except the
differentiable structure itself. Under these conditions how can one do
diffeomorphism-invariant geometry?
Noncommutative geometry provides us with the solution of trading the
ill-behaved space $M/G$ for a non-commutative algebra which
essentially plays the role of the algebra of smooth functions on that
space. The local index formula of Atiyah-Singer ultimately holds in
the setting of noncommutative geometry. Using this framework Connes
and Moscovici then obtained in the 90s a striking reformulation of the
local index formula in diffeomorphism-invariant geometry.
An important part the talk will be devoted to reviewing noncommutative
geometry and Connes-Moscovici's index formula. We will then hint to on-
going projects about reformulating the local index formula in two new
geometric settings: biholomorphism-invariant geometry of strictly
pseudo-convex domains and contactomorphism-invariant geometry.
16:30 - 18:00Room #002 (Mathematics building)
Akitoshi Takayasu (Waseda University)
"Numerical verification of existence for solutions to Dirichlet
boundary value problems of semilinear elliptic equations
"
http://www.infsup.jp/utnas/
2010/12/06
10:30 - 12:00Room #128 (Mathematics building)
Hajime Ono (Tokyo Univ of Science)
"Chow semistability of polarized toric manifolds"
2010/12/04
09:30 - 10:30Room #056 (Mathematics building)
Toshihiko Matsuki (Kyoto University)
"Orbit decomposition of multiple flag varieties and representations of of quiver"
10:40 - 11:40Room #056 (Mathematics building)
Kouichi Takemura (Chuo University)
"Integral transformations on the Heun equation and its applications "
13:00 - 14:00Room #056 (Mathematics building)
Kazuki Hiroe (University of Tokyo)
"Weyl group symmetries of double confluent Heun equations"
14:10 - 15:10Room #056 (Mathematics building)
Takao Suzuki (Kobe University)
"Affine root systems, monodromy preserving deformation, and hypergeometric functions"
15:30 - 16:30Room #056 (Mathematics building)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
"On the uniformization equations which have singularities along discriminant of complex reflection groups of rank three "
2010/12/03
11:00 - 12:00Room #270 (Mathematics building)
Jarmo Hietarinta (University of Turku)
"Discrete Integrability and Consistency-Around-the-Cube (CAC)"
For integrable lattice equations we can still apply many integrability criteria that are regularly used for continuous systems, but there are also some that are specific for discrete systems. One particularly successful discrete integrability criterion is the multidimensional consistency, or CAC. We review the classic results of Nijhoff and of Adler-Bobenko-Suris and then present some extensions.
13:30 - 14:30Room #370 (Mathematics building)
Nalini Joshi (University of Sydney)
"Geometric asymptotics of the first Painleve equation"
I will report on my recent collaboration with Hans Duistermaat on the geometry of the space of initial values of the first Painleve equation, which was first constructed by Okamoto. We show that highly accurate information about solutions can be found by utilizing the regularized and compactified space of initial values in Boutroux's coordinates. I will also describe numerical explorations based on this work obtained in collaboration with Holger Dullin.
16:30 - 18:00Room #056 (Mathematics building)
Daisuke Yamakawa (Kobe University)
"The third Painlev¥'e equation and quiver varieties"
2010/12/01
16:30 - 18:45Room #056 (Mathematics building)
Yuichiro Hoshi (RIMS, Kyoto University) 16:30 - 17:30
"On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves"
In this talk, we will discuss the following problem posed by Makoto Matsumoto and Akio Tamagawa concerning monodromic fullness of hyperbolic curves.
For a hyperbolic curve X over a number field, are the following three conditions equivalent?
(A) For any prime number l, X is quasi-l-monodromically full.
(B) There exists a prime number l such that X is l-monodromically full.
(C) X is l-monodromically full for all but finitely many prime numbers l.
The property of being (quasi-)monodromically full may be regarded as an analogue for hyperbolic curves of the property of not admitting complex multiplication for elliptic curves, and the above equivalence may be regarded as an analogue for hyperbolic curves of the following result concerning the Galois representation on the Tate module of an elliptic curve over a number field proven by Jean-Pierre Serre.
For an elliptic curve E over a number field, the following four conditions are equivalent:
(0) E does not admit complex multiplication.
(1) For any prime number l, the image of the l-adic Galois representation associated to E is open.
(2) There exists a prime number l such that the l-adic Galois representation associated to E is surjective.
(3) The l-adic Galois representation associated to E is surjective for all but finitely many prime numbers l.
In this talk, I will present some results concerning the above problem in the case where the given hyperbolic curve is of genus zero. In particular, I will give an example of a hyperbolic curve of type (0,4) over a number field which satisfies condition (C) but does not satisfy condition (A).
Marco Garuti (University of Padova) 17:45 - 18:45
"Galois theory for schemes"
We discuss some aspects of finite group scheme actions: the Galois correspondence and the notion of Galois closure.
2010/11/30
16:30 - 18:00Room #002 (Mathematics building)
Yasunori Aoki (University of Waterloo/NII)
"Finite volume element method for singular solutions of elliptic PDEs
"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Nobuhiro Nakamura (The University of Tokyo)
"Pin^-(2)-monopole equations and intersection forms with local coefficients of 4-manifolds"
We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and explain its applications to intersection forms with local coefficients of 4-manifolds.
The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients.
The second one is a local coefficient version of Furuta's 10/8-inequality.
As a corollary, we construct nonsmoothable spin 4-manifolds satisfying Rohlin's theorem and the 10/8-inequality.
16:30 - 18:00Room #122 (Mathematics building)
Yi-Jun Yao (Fudan Univ.)
"Noncommutative geometry and Rankin-Cohen brackets"
2010/11/29
16:30 - 18:00Room #002 (Mathematics building)
Scott Carnahan (IPMU)
"Borcherds products in monstrous moonshine."
During the 1980s, Koike, Norton, and Zagier independently found an
infinite product expansion for the difference of two modular j-functions
on a product of half planes. Borcherds showed that this product identity
is the Weyl denominator formula for an infinite dimensional Lie algebra
that has an action of the monster simple group by automorphisms, and used
this action to prove the monstrous moonshine conjectures.
I will describe a more general construction that yields an infinite
product identity and an infinite dimensional Lie algebra for each element
of the monster group. The above objects then arise as the special cases
assigned to the identity element. Time permitting, I will attempt to
describe a connection to conformal field theory.
16:40 - 18:10Room #126 (Mathematics building)
Hisanori Ohashi (Nagoya Univ. )
"K3 surfaces and log del Pezzo surfaces of index three"
Alexeev and Nikulin have classified log del Pezzo surfaces of index 1 and 2 by using the classification of non-symplectic involutions on K3 surfaces. We want to discuss the generalization of this result to the index 3 cases. In this case we are also able to construct log del Pezzos $Z$ from K3 surfaces $X$, but the converse is not necessarily true. The condition on $Z$ is exactly the "multiple smooth divisor property", which we will define. Our theorem is the classification of log del Pezzo surfaces of index 3 with this property.
The idea of the proof is similar to that of Alexeev and Nikulin, but the methods are different because of the existence of singularities: although the singularity is mild, the description of nef cone by reflection groups cannot be used. Instead
we construct and analyze good elliptic fibrations on K3 surfaces $X$ and use it to obtain the classification. It includes a partial but geometric generalization of the classification of non-symplectic automorphisms of order three, recently done by Artebani, Sarti and Taki.
2010/11/26
14:40 - 16:10Room #002 (Mathematics building)
Tomoo Matsumura (Cornell University)
"Hamiltonian torus actions on orbifolds and orbifold-GKM theorem (joint
work with T. Holm)"
When a symplectic manifold M carries a Hamiltonian torus R action, the
injectivity theorem states that the R-equivariant cohomology of M is a
subring of the one of the fixed points and the GKM theorem allows us
to compute this subring by only using the data of 1-dimensional
orbits. The results in the first part of this talk are a
generalization of this technique to Hamiltonian R actions on orbifolds
and an application to the computation of the equivariant cohomology of
toric orbifolds. In the second part, we will introduce the equivariant
Chen-Ruan cohomology ring which is a symplectic invariant of the
action on the orbifold and explain the injectivity/GKM theorem for this ring.
2010/11/25
16:30 - 18:00Room #122 (Mathematics building)
Reiji Tomatsu (Tokyo Univ. Science)
"Classification of actions of Kac algebras"
2010/11/18
16:30 - 18:00Room #122 (Mathematics building)
Jean Roydor (Univ. Tokyo)
"Perturbation of dual operator algebras and similarity"
2010/11/17
16:30 - 17:30Room #056 (Mathematics building)
Shin Harase (University of Tokyo)
"Fast lattice reduction for F_2-linear pseudorandom number generators"
2010/11/16
16:30 - 18:00Room #002 (Mathematics building)
Xuefeng Liu (Waseda University/CREST, JST)
"On verified evaluation of eigenvalues for elliptic operator over arbitrary polygonal domain"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #056 (Mathematics building)
Noboru Ito (Waseda University)
"On a colored Khovanov bicomplex"
We discuss the existence of a bicomplex which is a Khovanov-type
complex associated with categorification of a colored Jones polynomial.
This is an answer to the question proposed by A. Beliakova and S. Wehrli.
Then the second term of the spectral sequence of the bicomplex corresponds
to the Khovanov-type homology group. In this talk, we explain how to define
the bicomplex. If time permits, we also define a colored Rasmussen invariant
by using another spectral sequence of the colored Jones polynomial.
16:30 - 18:00Room #122 (Mathematics building)
Viacheslav Nikulin (Univ Liverpool and Steklov Moscow)
"Self-corresponences of K3 surfaces via moduli of sheaves"
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.
16:30 - 18:00Room #122 (Mathematics building)
Viacheslav Nikulin (Univ Liverpool and Steklov Moscow)
"Self-corresponences of K3 surfaces via moduli of sheaves"
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.
16:00 - 18:30Room #123 (Mathematics building)
Keisuke Uchikoshi (National Defense Academy of Japan) 16:00 - 16:45
"Hyperfunctions and vortex sheets"
L. Boutet de Monvel (University of Paris 6) 17:00 - 18:30
"Residual trace and equivariant asymptotic trace of Toeplitz operators"
2010/11/15
10:30 - 12:00Room #128 (Mathematics building)
Tatsuo Suwa (Hokkaido Univ*)
"Excess intersections and residues in improper dimension"
This talk concerns localization of characteristic classes and associated residues, in the context of intersection theory and residue theory of singular holomorphic foliations. The localization comes from the vanishing of certain characteristic forms, usually caused by the existence of some geometric object, away from the "singular set" of the object. This gives rise to residues in the homology of the singular set and residue theorems relating local and global invariants. In the generic situation, i.e., if the dimension of the singular set is "proper", we have a reasonable understanding of the residues. We indicate how to cope with the problem when the dimension is "excessive" (partly a joint work with F. Bracci).
16:40 - 18:10Room #126 (Mathematics building)
Shuhei Yoshitomi (Univ. of Tokyo)
"Generators of tropical modules"
2010/11/09
17:00 - 18:00Room #056 (Mathematics building)
Ken'ichi Ohshika (Osaka University)
"Characterising bumping points on deformation spaces of Kleinian groups"
It is known that components of the interior of a deformation space of a Kleinian group can bump, and a component of the interior can bump itself, on the boundary of the deformation space.
Anderson-Canary-McCullogh gave a necessary and sufficient condition for two components to bump.
In this talk, I shall give a criterion for points on the boundary to be bumping points.
2010/11/08
10:30 - 12:00Room #128 (Mathematics building)
Hajime Tsuji (Sophia Univ)
"Variation of canonical measures under Kaehler deformations"
16:30 - 18:00Room #128 (Mathematics building)
Michael Eastwood (Australian National University)
"Invariant differential operators on the sphere"
The circle is acted upon by the rotation group SO(2) and there are plenty of differential operators invariant under this action. But the circle is also acted upon by SL(2,R) and this larger symmetry group cuts down the list of invariant differential operators to something smaller but more interesting! I shall explain what happens and how this phenomenon generalises to spheres. These constructions are part of a general theory but have numerous unexpected applications, for example in suggesting a new stable finite-element scheme in linearised elasticity (due to Arnold, Falk, and Winther).
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood
2010/11/05
16:30 - 18:00Room #123 (Mathematics building)
Michael Eastwood (Australian National University)
"How to recognise the geodesics of a metric connection"
The geodesics on a Riemannian manifold form a distinguished family of curves, one in every direction through every point. Sometimes two metrics can provide the same family of curves: the Euclidean metric and the round metric on the hemisphere have this property. It is also possible that a family of curves does not arise from a metric at all. Following a classical procedure due to Roger Liouville, I shall explain how to tell these cases apart on a surface. This is joint work with Robert Bryant and Maciej Dunajski.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood
2010/11/04
16:30 - 18:00Room #122 (Mathematics building)
Yoshiko Ogata (Univ.Tokyo)
"Nonequilibrium Statistical Mechanics"
10:40 - 12:10Room #123 (Mathematics building)
Jean Meyer, Yasuko HISAMATSU (Risk Capital Market Tokyo, BNP Paribas)
"Market, Liquidity and Counterparty Risk"
1. Introduction to the market risk
- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks
2. Market & Liquidity Risks –Basics
-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)
3. Risk measure
- Stress test
- Value at risk
- Risks measure for counterparty risk
2010/11/02
13:00 - 16:10Room #122 (Mathematics building)
Vladimir Bogachev (Moscow)
"The Malliavin calculus on configuration spaces and applications"
It is planned to discuss first a general scheme of the Malliavin
calculus on an abstract measurable
manifold with minimal assumptions about the manifold.
Then a practical realization of this scheme will be discussed in
several concrete examples with emphasis
on configuration spaces, i.e., spaces of locally finite configurations
in a given manifold (for example, just
a finite-dimensional Euclidean space), which can be alternatively
described as the spaces of integer-valued
discrete measures equipped with suitable differential structures.
No acquaintance with the Malliavin calculus and differential geometry
is assumed.
16:30 - 18:00Room #056 (Mathematics building)
Daniel Ruberman (Brandeis University)
"Periodic-end manifolds and SW theory"
We study an extension of Seiberg-Witten invariants to
4-manifolds with the homology of S^1 \times S^3. This extension has
many potential applications in low-dimensional topology, including the
study of the homology cobordism group. Because b_2^+ =0, the usual
strategy for defining invariants does not work--one cannot disregard
reducible solutions. In fact, the count of solutions can jump in a
family of metrics or perturbations. To remedy this, we define an
index-theoretic counter-term that jumps by the same amount. The
counterterm is the index of the Dirac operator on a manifold with a
periodic end modeled at infinity by the infinite cyclic cover of the
manifold. This is joint work with Tomasz Mrowka and Nikolai Saveliev.
16:30 - 18:00Room #126 (Mathematics building)
Michael Eastwood (University of Adelaide)
"Twistor theory and the harmonic hull"
Harmonic functions are real-analytic and so automatically extend from being functions of real variables to being functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated geometry. I shall base the constructions on a formula of Bateman from 1904. This is joint work with Feng Xu.
2010/11/01
16:40 - 18:10Room #126 (Mathematics building)
Atsushi Ito (Univ. of Tokyo)
"How to estimate Seshadri constants"
Seshadri constant is an invariant which measures the positivities of ample line bundles. This relates with adjoint bundles, Nagata conjecture, slope stabilities, Gromov width (an invariant of symplectic manifolds) and so on. But it is very diffiult to compute or estimate Seshadri constants in general, especially in higher dimension.
In this talk, we first study Seshadri constants of toric varieties, and next consider about non-toric cases using toric degenerations. For example, good estimations are obtained for complete intersections in projective spaces.
16:00 - 18:15Room #270 (Mathematics building)
Michel Cristofol (マルセイユ大学) 16:00 - 17:00
"Inverse problems in non linear parabolic equations : Two differents approaches"
http://www.ms.u-tokyo.ac.jp/~kengok/abstractTokyo.pdf
Patricia Gaitan (マルセイユ大学) 17:15 - 18:15
"Inverse Problems for parabolic System
"
I will present a review of stability and controllability results for linear parabolic coupled systems with coupling of first and zeroth-order terms by data of reduced number of components. The key ingredients are global Carleman estimates.
2010/10/29
16:30 - 17:30Room #002 (Mathematics building)
Robin Graham (University of Washington)
"Ambient metrics and exceptional holonomy"
The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$. The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.
2010/10/28
16:30 - 18:00Room #122 (Mathematics building)
Makoto Yamashita (Univ. Tokyo)
"Type III representations of the infinite symmetric group"
Based on earlier results about the structure of the II$_1$ representations of the infinite symmetric group, we investigate its type III representations and the related inclusion of von Neumann algebras of type III.
10:40 - 12:10Room #123 (Mathematics building)
Jean Meyer, Yasuko HISAMATSU (Risk Capital Market Tokyo, BNP Paribas)
"Market, Liquidity and Counterparty Risk"
1. Introduction to the market risk
- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks
2. Market & Liquidity Risks –Basics
-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)
3. Risk measure
- Stress test
- Value at risk
- Risks measure for counterparty risk
2010/10/26
13:00 - 14:30Room #123 (Mathematics building)
Dan Popovici (Toulouse)
"Limits of Moishezon Manifolds under Holomorphic Deformations"
We prove that if all the fibres, except one, of a holomorphic family of compact complex manifolds are supposed to be Moishezon (i.e. bimeromorphic to projective manifolds), then the remaining (limit) fibre is again Moishezon. The two ingredients of the proof are the relative Barlet space of divisors contained in the fibres for which we show properness over the base of the family and the "strongly Gauduchon" (sG) metrics that we have introduced for the purpose of controlling volumes of cycles. These new metrics enjoy stability properties under both deformations and modifications and play a crucial role in obtaining a uniform control on volumes of relative divisors that prove the above-mentioned properness.
17:00 - 18:00Room #056 (Mathematics building)
Kazuo Habiro (RIMS, Kyoto University)
"Quantum fundamental groups and quantum representation varieties for 3-manifolds"
We define a refinement of the fundamental groups of 3-manifolds and
a generalization of representation variety of the fundamental group
of 3-manifolds. We consider the category $H$ whose morphisms are
nonnegative integers, where $n$ corresponds to a genus $n$ handlebody
equipped with an embedding of a disc into the boundary, and whose
morphisms are the isotopy classes of embeddings of handlebodies
compatible with the embeddings of the disc into the boundaries. For
each 3-manifold $M$ with an embedding of a disc into the boundary, we
can construct a contravariant functor from $H$ to the category of
sets, where the object $n$ of $H$ is mapped to the set of isotopy
classes of embedding of the genus $n$ handlebody into $M$, compatible
with the embeddings of the disc into the boundaries. This functor can
be regarded as a refinement of the fundamental group of $M$, and we
call it the quantum fundamental group of $M$. Using this invariant, we
can construct for each co-ribbon Hopf algebra $A$ an invariant of
3-manifolds which may be regarded as (the space of regular functions
on) the representation variety of $M$ with respect to $A$.
16:30 - 18:00Room #128 (Mathematics building)
Tomoaki Okayama (Hitotsubashi University)
"Theoretical analysis of Sinc schemes for integral equations of the second kind"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #126 (Mathematics building)
Daniel Sternheimer (Keio University and Institut de Mathematiques de Bourgogne)
"Some instances of the reasonable effectiveness (and limitations) of symmetries and deformations in fundamental physics"
In this talk we survey some applications of group theory and deformation theory (including quantization) in mathematical physics. We start with sketching applications of rotation and discrete groups representations in molecular physics (``dynamical" symmetry breaking in crystals, Racah-Flato-Kibler; chains of groups and symmetry breaking). These methods led to the use of ``classification Lie groups" (``internal symmetries") in particle physics. Their relation with space-time symmetries will be discussed. Symmetries are naturally deformed, which eventually brought to Flato's deformation philosophy and the realization that quantization can be viewed as a deformation, including the many avatars of deformation quantization (such as quantum groups and quantized spaces). Nonlinear representations of Lie groups can be viewed as deformations (of their linear part), with applications to covariant nonlinear evolution equations. Combining all these suggests an Ansatz based on Anti de Sitter space-time and group, a deformation of the Poincare group of Minkowski space-time, which could eventually be quantized, with possible implications in particle physics and cosmology. Prospects for future developments between mathematics and physics will be indicated.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html
2010/10/21
16:30 - 18:00Room #122 (Mathematics building)
Benoit Collins (Univ. Ottawa)
"Free probability and entropy additivity problems for Quantum information theory"
2010/10/20
10:30 - 11:30Room #056 (Mathematics building)
Naohisa Ogawa (Hokkaido Institute of Technology)
"Curvature Dependent Diffusion Flow on Surface with Thickness"
Particle diffusion in a two dimensional curved surface with thickness
embedded in $R_3$ is considered.
In addition to the usual diffusion flow, we find a new flow with an explicit
curvature dependence in $\epsilon$ (thickness of surface) expansion.
As an example, the surface of elliptic cylinder is considered, and curvature
dependent diffusion coefficient is calculated. In addition, we consider the
1 dimensional object in $R_3$ (Tube),
and check the physical meaning of curvature effect.
2010/10/19
16:30 - 18:00Room #002 (Mathematics building)
Jinseok Cho (Waseda University)
"Optimistic limits of colored Jones invariants"
Yokota made a wonderful theory on the optimistic limit of Kashaev
invariant of a hyperbolic knot
that the limit determines the hyperbolic volume and the Chern-Simons
invariant of the knot.
Especially, his theory enables us to calculate the volume of a knot
combinatorially from its diagram for many cases.
We will briefly discuss Yokota theory, and then move to the optimistic
limit of colored Jones invariant.
We will explain a parallel version of Yokota theory based on the
optimistic limit of colored Jones invariant.
Especially, we will show the optimistic limit of colored Jones
invariant coincides with that of Kashaev invariant modulo 2\pi^2.
This implies the optimistic limit of colored Jones invariant also
determines the volume and Chern-Simons invariant of the knot, and
probably more information.
This is a joint-work with Jun Murakami of Waseda University.
2010/10/18
10:30 - 11:30Room #128 (Mathematics building)
Sergey Ivashkovitch (Univ. de Lille)
"Limiting behavior of minimal trajectories of parabolic vector fields on the complex projective plane."
The classical Poincare-Bendixson theory describes the way a trajectory of a vector field on the real plane behaves when accumulating to the singular locus of the vector field. We shall describe, in the first approximation, the way a minimal trajectory of a parabolic complex polynomial vector field (or, a holomorphic foliation) on the complex projective plane approaches the singular locus. In particular we shall prove that if a holomorphic foliation has an exceptional minimal set then its nef model is necessarily hyperbolic.
13:00 - 14:00Room #128 (Mathematics building)
Philippe Eyssidieux (Institut Fourier, Grenoble)
"Degenerate complex Monge-Ampere equations"
16:30 - 18:00Room #002 (Mathematics building)
Todor Milanov (IPMU)
"Quasi-modular forms and Gromov--Witten theory of elliptic orbifold $\mathbb{P}^1$"
This talk is based on my current work with Y. Ruan. Our project is part of the so called Landau--Ginzburg/Calabi-Yau correspondence. The latter is a conjecture, due to Ruan, that describes the relation between the $W$-spin invariants of a Landau-Ginzburg potential $W$ and the Gromov--Witten invariants of a certain Calabi--Yau orbifold. I am planning first to explain the higher-genus reconstruction formalism of Givental. This formalism together with the work of M. Krawitz and Y. Shen allows us to express the Gromov--Witten invariants of the orbifold $\mathbb{P}^1$'s with weights $(3,3,3)$, $(2,4,4)$, and $(2,3,6)$ in terms of Saito's Frobenius structure associated with the simple elliptic singularities $P_8$, $X_9$, and $J_{10}$ respectively. After explaining Givental's formalism, my goal would be to discuss the Saito's flat structure, and to explain how its modular behavior fits in the Givental's formalism. This allows us to prove that the Gromov--Witten invariants are quasi-modular forms on an appropriate modular group.
16:40 - 18:10Room #126 (Mathematics building)
Akiyoshi Sannai (Univ. of Tokyo)
"Galois extensions and maps on local cohomology "
2010/10/14
16:30 - 18:00Room #122 (Mathematics building)
Yasuyuki Kawahigashi (Univ. Tokyo)
"Nonstandard analysis for operator algebraists"
2010/10/12
16:30 - 18:00Room #056 (Mathematics building)
Andrei Pajitnov (Univ. de Nantes, The University of Tokyo)
"Asymptotics of Morse numbers of finite coverings of manifolds"
Let X be a closed manifold;
denote by m(X) the Morse number of X
(that is, the minimal number of critical
points of a Morse function on X).
Let Y be a finite covering of X of degree d.
In this survey talk we will address the following question
posed by M. Gromov: What are the asymptotic properties
of m(N) as d goes to infinity?
It turns out that for high-dimensional manifolds with
free abelian fundamental group the asymptotics of
the number m(N)/d is directly related to the Novikov homology
of N. We prove this theorem and discuss related results.
2010/10/08
16:30 - 17:30Room #123 (Mathematics building)
Ryu Sasaki (Yukawa Institute for Theoretical Physics, Kyoto University)
"Exceptional Jacobi polynomials as solutions of a Schroedinger
(Sturm-Liouville) equation with $3 +¥ell$ ($¥ell=1,2,¥ldots) regular
singularities"
Global solutions of Fuchsian differential equations with more than 3 (hypergeometric) or four (Heun) regular singularities had been virtually unkown. Here I present a complete set of eigenfunctions of a Schroedinger (Sturm-Liouville) equation with $3 + ¥ell$ ($¥ell=1,2,¥ldots$) regular singularities. They are deformations of the Darboux-P¥" oschl-Teller potential with the Hamiltonian (Schroedinger operator) ¥[ ¥mathcal{H}=-¥frac{d^2}{dx^2}+¥frac{g(g-1)}{¥sin^2x}+¥frac{h(h-1)} {¥cos^2x}¥] The eigenfunctions consist of the {¥em exceptional Jacobi polynomials} $¥{P_{¥ell,n}(¥eta)¥}$, $n=0,1,2,¥ldots$, with deg($P_{¥ell,n}$)$=n+¥ell$. Thus the restriction due to Bochner's theorem does not apply. The confluent limit produces two sets of the exceptional Laguerre polynomials for $¥ell=1,2,¥ldots$. Similar deformation method provides the exceptional Wilson and Askey-Wilson polynomials for $¥ell=1,2,¥ldots$.
2010/10/06
14:45 - 18:00Room #056 (Mathematics building)
Kei Irie (Kyoto Univ.) 14:45 - 16:15
"Handle attaching in wrapped Floer homology and brake orbits in classical Hamiltonian systems"
In this talk, the term "classical Hamiltonian systems" means special types of Hamiltonian systems, which describe solutions of classical equations of motion. The study of periodic solutions of Hamiltonian systems is an interesting problem, and for classical Hamiltonian systems, the following result is known : for any compact and regular energy surface $S$, there exists a brake orbit (a particular type of periodic solutions) on $S$. This result is first proved by S.V.Bolotin in 1978, and it is a special case of the Arnold chord conjecture. In this talk, I will explain that calculations of wrapped Floer homology (which is a variant of Lagrangian Floer homology) give a new proof of the above result.
Atsushi Takahashi (Osaka Univ.) 16:30 - 18:00
"Mirror Symmetry for Weighted Homogeneous Polynomials"
First we give an overview of the algebraic and the geometric aspects of the mirror symmetry conjecture for weighted homogeneous polynomials. Then we concentrate on polynomials in three variables, and show the existence of full (strongly) exceptional collection of categories of maximally graded matrix factorizations for invertible weighted homogeneous polynomials. We will also explain how the mirror symmetry naturally explains and generalizes the Arnold's strange duality between the 14 exceptional unimodal singularities.
16:30 - 17:30Room #117 (Mathematics building)
Hélène Esnault (Universität Duisburg-Essen)
"Finite group actions on the affine space"
If $G$ is a finite $\ell$-group acting on an affine space $\A^n$ over a
finite field $K$ of cardinality prime to $\ell$, Serre shows that there
exists a rational fixed point. We generalize this to the case where $K$ is a
henselian discretely valued field of characteristic zero with algebraically
closed residue field and with residue characteristic different from $\ell$.
We also treat the case where the residue field is finite of cardinality $q$
such that $\ell$ divides $q-1$. To this aim, we study group actions on weak
N\'eron models.
(Joint work with Johannes Nicaise)
15:00 - 16:10Room #000 (Mathematics building)
SUZUKI, Taiji (University of Tokyo)
"On multiple kernel learning with elasticnet type regularization"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/05.html
2010/10/04
10:30 - 12:00Room #128 (Mathematics building)
Hideyuki ISHI (Nagoya Univ)
"The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain"
For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.
Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.
2010/09/28
16:30 - 18:00Room #128 (Mathematics building)
Pavel Exner (Czech Academy of Sciences)
"Some spectral and resonance properties of quantum graphs"
In this talk I will discuss three new results about Schr¨odinger operators
on metric graphs obtained in collaboration with Jiri Lipovskyand Brian Davies.
The first one is related to invalidity of the uniform continuation principle for such
operators. One manifestation of this fact are embedded eigenvalues due to
rational relations of graph edge lengths. This effect is non-generic and we show
how geometric perturbations turn these embedded eigenvalues into resonances.
Then second problem is related to high-energy behavior of resonances: we extend
a recent result of Davies and Pushnitski to graphs with general vertex couplings
and find conditions under which the asymptotics does not have Weyl character.
Finally, the last question addressed here concerns the absolutely continuous spectrum
of radial-tree graphs. In a similar vein, we generalize a recent result by Breuer and
Frank that in case of the free (or Kirhhoff) coupling the ac spectrum is absent
provided the edge length are increasing without a bound along the tree.
We show that the result remains valid for a large class of vertex couplings,
but on the other hand, there are nontrivial couplings leading to an ac spectrum.
2010/09/14
10:30 - 14:00Room #117 (Mathematics building)
Shintarou Yanagida (Kobe Univ.) 10:30 - 11:30
"AGT conjectures and recursion formulas"
Yuji Yamada (Rikkyo Univ.) 13:00 - 14:00
"classification of solutions to the reflection equation associated to
trigonometrical $R$-matrix of Belavin"
2010/09/13
10:30 - 15:30Room #117 (Mathematics building)
Masahiro Kasatani (Tokyo Univ.) 10:30 - 11:30
"Polynomial representations of DAHA of type $C^¥vee C$ and boundary qKZ equations"
First I will review basic facts about
the double affine Hecke algebra of type $C^¥vee C$
and its polynomial representation.
Next I will intrduce a boundary qKZ equation
and construct its solution in terms of the polynomial representation.
Yasuhiko Yamada (Kobe Univ.) 13:00 - 14:00
"CFT, Isomonodromy deformations and Nekrasov functions"
This talk is an introduction to the relation between conformal filed
theories
and super symmetric gauge theories (Alday-Gaiotto-Tachikawa conjecture)
from the point of view of differential equations (in particular
isomonodromy
deformations).
Katsuhisa Mimachi (Tokyo Institute of Technology) 14:30 - 15:30
"Twisted de Rham theory---resonances and the non-resonance"
2010/09/12
10:30 - 17:00Room #117 (Mathematics building)
Hideaki Morita (Muroran Institute of Technology) 10:30 - 11:30
"A factorization formula for Macdonald polynomials at roots of unity"
We consider a combinatorial property of Macdonald polynomials at roots
of unity.
If we made some plethystic substitution to the variables,
Macdonald polynomials are subjected to a certain decomposition rule
when a parameter is specialized at roots of unity.
We review the result and give an outline of the proof.
This talk is based on a joint work with F. Descouens.
Junichi Shiraishi (Tokyo Univ.) 13:00 - 14:00
"W algebras and symmetric polynomials"
It is well known that we have the factorization property of the Macdonald polynomials under the principal specialization $x=(1,t,t^2,t^3,¥cdots)$. We try to better understand this situation in terms of the Ding-Iohara algebra or the deformend $W$-algebra. Some conjectures are presented in the case of $N$-fold tensor representation of the Fock modules.
Koji Hasegawa (Tohoku Univ.) 14:30 - 15:30
"Quantizing the difference Painlev¥'e VI equation"
I will review two constructions for quantum (=non-commutative) version of
q-difference Painleve VI equation.
Yasuhide Numata (Graduate School of Information Science and Technology, Tokyo Univ.) 16:00 - 17:00
"On a bijective proof of a factorization formula for Macdonald
polynomials at roots of unity"
The subject of this talk is a factorization formula for the special
values of modied Macdonald polynomials at roots of unity.
We give a combinatorial proof of the formula, via a result by
Haglund--Haiman--Leohr, for some special classes of partitions,
including two column partitions.
(This talk is based on a joint work with F. Descouens and H. Morita.)
2010/09/11
13:00 - 17:00Room #117 (Mathematics building)
Masahiko Ito (School of Science and Technology for Future Life, Tokyo Denki University) 13:00 - 14:00
"Three-term recurrence relations for a $BC_n$-type basic hypergeometric function and their application"
$BC_n$-type basic hypergeometric series are a certain $q$-analogue
of an integral representation for the Gauss hypergeometric function.
They are defined as multiple $q$-series satisfying Weyl group symmetry of type $C_n$,
and they are a multi-sum generalization of the basic hypergeometric series
in a class of what is called (very-)well-poised. In my talk I will explain
an explicit expression for the $q$-difference system of rank $n+1$
satisfied by a $BC_n$-type basic hypergeometric series with 6+1 parameters
as first order simultaneous $q$-difference equations with a concrete basis.
For this purpose I introduce two types of symmetric Laurent polynomials
which I call the $BC$-type interpolation polynomials. The polynomials satisfy
three-term relations like a contiguous relation for the Gauss hypergeometric
function. As an application, I will show another proof for the product formula
of the $q$-integral introduced by Gustafson.
Masatoshi Noumi (Kobe Univ.) 14:30 - 15:30
"TBA"
Masato Taki (YITP Kyoto Univ.) 16:00 - 17:00
"AGT conjecture and geometric engineering"
2010/09/09
16:30 - 18:00Room #126 (Mathematics building)
Bernhard Mühlherr (Justus-Liebig-Universität Gießen)
"Mini-course on Buildings (3/3)"
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
The third lecture will be then devoted to classification results,
mainly the classification of spherical buildings. However, I will try to say some words on the classification of affine buildings and twin buildings as well.
This is Part 3 of a 3-part lecture.
2010/09/06
16:40 - 18:10Room #126 (Mathematics building)
Prof. Remke Kloosterman (Humboldt University, Berlin)
"Non-reduced components of the Noether-Lefschetz locus"
Let $M_d$ be the moduli space of complex smooth degree $d$ surfaces in $\mathbb{P}3$. Let $NL_d \subset M_d$ be the subset corresponding to surfaces with Picard number at least 2. It is known that $NL_r$ is Zariski-constructable, and each irreducible component of $NL_r$ has a natural scheme structure. In this talk we describe the largest non-reduced components of $NL_r$. This extends work of Maclean and Otwinowska.
This is joint work with my PhD student Ananyo Dan.
2010/09/04
09:30 - 11:00Room #126 (Mathematics building)
Bernhard Mühlherr (Justus-Liebig-Universität Gießen)
"Mini-course on Buildings (1/3)"
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my first lecture I will begin by introducing generalized polygons, namely rank two spherical buildings, and discussing several aspects of them which will be generalized later, and then move on to defining Coxeter complexes and giving the classical definition of buildings as simplicial complexes. I will try to include as many examples as possible.
This is Part 1 of a 3-part lecture. The second lecture will follow after a ten-minute break.
11:10 - 12:40Room #126 (Mathematics building)
Bernhard Mühlherr (Justus-Liebig-Universität Gießen)
"Mini-course on Buildings (2/3)"
The goal of this course is to provide an overview on the theory of buildings which was developed by Jacques Tits.
In my second lecture I will start with chamber systems and coset
geometries, introducing some special properties of chamber systems in order to give another definition of a building. This definition is less standard but it will give some results on presentations of groups acting on buildings for free. In particular it will enable me to present a sketch of a proof of the Curtis-Tits theorem for Chevalley groups and to formulate Tits' extension theorem.
This is Part 2 of a 3-part lecture. Part 1 takes place ealier on the same day. Part 3 will take place on Thursday, September 9.
2010/09/03
14:30 - 15:30Room #370 (Mathematics building)
Luc Robbiano (University of Versailles)
"Carleman estimates and boundary problems."
In this presentation, based on joint works with Jerome LeRousseau and Matthieu Leautaud, we consider boundary problems for elliptic/parabolic operators. We prove Carleman estimates in such cases. One of the interest for such an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition separating high and low tangential frequencies.
If time permits, we will present how such an approach can be used to prove Carleman estimates in the case of non smooth coefficients at an interface, possibly with an additional diffusion process along the interface.
2010/09/01
16:30 - 18:00Room #002 (Mathematics building)
Bernhard M\"uhlherr (Justus-Liebig-Universit\"at Giessen)
"Groups of Kac-Moody type"
Groups of Kac-Moody type are natural generalizations of Kac-Moody groups over fields in the sense that they have an RGD-system. This is a system of subgroups indexed by the roots of a root system and satisfying certain commutation relations.
Roughly speaking, there is a one-to-one correspondence between groups of Kac-Moody type and Moufang twin buildings. This correspondence was used in the last decade to prove several group theoretic results on RGD-systems and in particular on Kac-
Moody groups over fields.
In my talk I will explain RGD-systems and how they provide twin
buildings in a natural way. I will then present some of the group theoretic applications mentioned above and describe how twin buildings are used as a main tool in their proof.
16:30 - 17:45Room #123 (Mathematics building)
Naoki IMAI (Graduate School of Mathematical Sciences the University of Tokyo )
"On the moduli spaces of finite flat models of Galois representations"
2010/08/06
15:30 - 17:45Room #370 (Mathematics building)
Leevan Ling (Hong Kong Baptist University) 15:30 - 16:30
"A Spectral Method for Space--
Time Fractional Diffusion Equation"
Mourad Choulli (University of Metz) 16:45 - 17:45
"A multidimensional Borg-Levinson theorem"
15:00 - 16:30Room #122 (Mathematics building)
Matthieu Alfaro (University Montpellier 2)
"Motion by mean curvature and Allen-Cahn equations"
After introducing the classical and the generalized motion by mean curvature, we give some connections with the singular limit of Allen-Cahn equations in both framework. New results and estimates shall be provided.
2010/08/05
16:30 - 17:30Room #370 (Mathematics building)
Yongzhi Steve Xu (University of Louisville, USA)
"Radiation Conditions for Wave in Stratified Medium and Related Inverse
Problems"
16:30 - 17:30Room #370 (Mathematics building)
Yongzhi Steve Xu (University of Louisville, USA)
"Radiation Conditions for Wave in Stratified Medium and Related Inverse Problems "
2010/07/30
16:30 - 17:30Room #370 (Mathematics building)
Oleg Emanouilov (Colorado State University)
"Global uniqueness in determining a coefficient by boundary data on small subboundaries"
We consider the Dirichlet problem for the stationary two-dimensional Schroedinger equation. We discuss an inverse boundary value problem of determining the potential from a pair of all Dirichlet data supported in a subboundary S+ and all the corresponding Neumann data taken only on a subboundary S-. In the case where S+ = S- are the whole boundary, the data are the classical Dirichlet to Neumann map and there are many uniqueness results, while in the case where S+=S- is an arbitrary subboundary, Imanuvilov-Uhlmann-Yamamoto (2010) proves the uniqueness. In this talk, for the case where S+ and S- are not same, we prove the global uniqueness for this inverse problem under a condition only on the locations of S+, S-. We note that within the condition, S+ and S- can be arbitrarily small. The key of the proof is the construction of suitable complex geometrical optics solutions by a Carleman estimate with singular weight function.
2010/07/29
14:30 - 16:00Room #126 (Mathematics building)
Masahiro Futaki (The University of Tokyo)
"Homological Mirror Symmetry for 2-dimensional toric Fano stacks"
Homological Mirror Symmetry (HMS for short) is a conjectural
duality between complex and symplectic geometry, originally proposed
for mirror pairs of Calabi-Yau manifolds and later extended to
Fano/Landau-Ginzburg mirrors (both due to Kontsevich, 1994 and 1998).
We explain how HMS is established in the case of 2-dimensional smooth
toric Fano stack X as an equivalence between the derived category of X
and the derived directed Fukaya category of its mirror Lefschetz
fibration W. This is related to Kontsevich-Soibelman's construction of
3d CY category from the quiver with potential.
We also obtain a local mirror extension following Seidel's suspension
theorem, that is, the local HMS for the canonical bundle K_X and the
double suspension W+uv. This talk is joint with Kazushi Ueda (Osaka
U.).
2010/07/28
16:30 - 18:00Room #002 (Mathematics building)
及川 一誠 (東京大学大学院数理科学研究科)
"定常移流拡散方程式に対するハイブリッド型不連続Galerkin法"
本講演では,ハイブリッド型不連続Galerkin(HDG)法による,定常移流拡散方程式の新しい数値計算スキームを紹介し,定式化や誤差評価,安定性等について述べる.新スキームの有効性を確認するために,数値計算例もいくつか示す.なお,講演前半は準備として,Poisson方程式に対するHDG法について解説する.
http://www.infsup.jp/utnas/
16:30 - 18:00Room #002 (Mathematics building)
Issei Oikawa (University of Tokyo)
"Hybridized discontinuous Galerkin method for a convection-diffusion equation"
http://www.infsup.jp/utnas/
2010/07/27
16:30 - 18:00Room #056 (Mathematics building)
Ayumu Inoue (Tokyo Institute of Technology)
"Quandle homology and complex volume
(Joint work with Yuichi Kabaya)"
For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.
In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.
He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.
To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.
On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.
It means that we can compute the complex volume combinatorially from a link diagram.
16:00 - 17:15Room #123 (Mathematics building)
Ryoko TOMIYASU (graduate school of Mathematical Sciences)
"On some algebraic properties of CM-types of CM-fields and their reflexes"
2010/07/22
16:30 - 18:00Room #128 (Mathematics building)
Owen Sizemore (UCLA)
"$W^*$ Rigidity for actions of wreath product groups"
The past 8 years have seen much progress in the classification of
actions of groups on measure spaces. Much of this is due to new powerful
techniques in operator algebras. We will survey some of these results
as well as the new operator algebra techniques. We will then give new
results concerning the classification of actions of wreath product groups.
2010/07/20
17:00 - 18:00Room #056 (Mathematics building)
Keiko Kawamuro (University of Iowa)
"A polynomial invariant of pseudo-Anosov maps"
Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)
2010/07/15
14:30 - 16:00Room #122 (Mathematics building)
Soo Teck Lee (Singapore National University)
"Pieri rule and Pieri algebras for the orthogonal groups"
16:30 - 18:00Room #128 (Mathematics building)
Narutaka Ozawa (Univ. Tokyo)
"Type II$_1$ von Neumann representations for Hecke operators on Maass forms (after F. Radulescu)"
15:00 - 16:10Room #000 (Mathematics building)
MASUDA, Hiroki (Graduate School of Mathematics, Kyushu University)
"Mighty convergence in LAD type estimation"
We propose a LAD (least absolute deviation) type contrast function for estimating Levy driven Ornstein-Uhlenbeck processes sampled at high frequency. The asymptotic behavior and polynomial-type large deviation inequality concerning the statistical random fields in question are derived, entailing an asymptotic normality and convergence of moments of the LAD estimator. Also, we will mention some numerical experiments done by the R software and some possible extensions of the framework.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/04.html
2010/07/13
16:30 - 18:00Room #056 (Mathematics building)
Marion Moore (University of California, Davis)
"High Distance Knots in closed 3-manifolds"
Let M be a closed 3-manifold with a given Heegaard splitting.
We show that after a single stabilization, some core of the
stabilized splitting has arbitrarily high distance with respect
to the splitting surface. This generalizes a result of Minsky,
Moriah, and Schleimer for knots in S^3. We also show that in the
complex of curves, handlebody sets are either coarsely distinct
or identical. We define the coarse mapping class group of a
Heeegaard splitting, and show that if (S,V,W) is a Heegaard
splitting of genus greater than or equal to 2, then the coarse
mapping class group of (S,V,W) is isomorphic to the mapping class
group of (S, V, W). This is joint work with Matt Rathbun.
17:00 - 18:00Room #128 (Mathematics building)
Carlos Villegas Blas (Universidad Nacional Autonoma de Mexico)
"On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom"
Let H be the hydrogen atom Hamiltonian. We will show that
the operator H+P can have well defined clusters of eigenvalues
for a suitable perturbation P=f(h)Q where Q is a pseudo-differential
operator of order zero and f(h) is a small quantity depending of
the Planck's parameter h. We will show that the distribution of
eigenvalues in those clusters has a semi-classical limit involving
the averages of the principal symbol of Q along the classical orbits
of the Kepler problem.
2010/07/12
10:30 - 12:00Room #128 (Mathematics building)
Yu KAWAKAMI (Kyushu Univ.)
"The value distribution of the Gauss map of wave fronts and its applications"
16:40 - 18:10Room #126 (Mathematics building)
Ryo Ohkawa (Tokyo Institute of Technology)
"Flips of moduli of stable torsion free sheaves with $c_1=1$ on
$\mathbb{P}^2$"
We study flips of moduli schemes of stable torsion free sheaves
on the projective plane via wall-crossing phenomena of Bridgeland stability.
They are described as stratified Grassmann bundles by variation of
stability of modules over certain finite dimensional algebra.
2010/07/08
16:00 - 17:30Room #002 (Mathematics building)
Anna Vainchtein (University of Pittsburgh, Department of Mathematics)
"Effect of nonlinearity on the steady motion of a twinning dislocation"
We consider the steady motion of a twinning dislocation in a Frenkel-Kontorova lattice with a double-well substrate potential that has a non-degenerate spinodal region. Semi-analytical traveling wave solutions are constructed for the piecewise quadratic potential, and their stability and further effects of nonlinearity are investigated numerically. We show that the width of the spinodal region and the nonlinearity of the potential have a significant effect on the dislocation kinetics, resulting in stable steady motion in some low-velocity intervals and lower propagation stress. We also conjecture that a stable steady propagation must correspond to an increasing portion of the kinetic relation between the applied stress and dislocation velocity.
16:30 - 18:00Room #122 (Mathematics building)
Dave Penneys (UC Berkeley)
"Killing weeds with annular multiplicities $*10$ via quadratic tangles"
In recent work with Morrison, Peters, and Snyder, we eliminate two
families of possible principal graphs with graph norms less than 5 using
techniques derived from Jones' work on quadratic tangles.
2010/07/07
10:30 - 11:30Room #056 (Mathematics building)
Masahide Sato (Information Media Center, Kanazawa University)
"Instabilities of steps on a vicinal face induced by the
asymmetry of diffusion field."
17:00 - 18:00Room #002 (Mathematics building)
天野 要 (愛媛大学大学院理工学研究科)
"代用電荷法による多重連結領域の数値等角写像"
多重連結領域の等角写像では,平行スリット領域,円弧スリット領域,放射スリット領域,円弧スリット円板領域,円弧スリット円環領域という5種の正準スリット領域が広く知られている(Nehari, 1952).遡って,Koebe(1916)はこれらを含む39種の正準スリット領域を挙げている.近年,このような多重連結領域の問題が新たに注目されている.代用電荷法を適用して,このような様々な等角写像の表現が簡潔で精度の高い近似写像関数を簡単に構成することができる.ここでは,非有界な多重連結領域から(実軸となす角を任意に指定した一般的な)直線スリット領域と,円弧放射スリット(混在)領域への場合中心に,代用電荷法による多重連結領域の数値等角写像の方法を紹介する.
http://www.infsup.jp/utnas/
17:00 - 18:00Room #002 (Mathematics building)
Kaname Amano (Ehime University)
"Numerical conformal mappings of multiply connected domains by the charge simulation method"
http://www.infsup.jp/utnas/
16:30 - 17:30Room #056 (Mathematics building)
Takahiro Tsushima (University of Tokyo)
"On the stable reduction of $X_0(p^4)$"
2010/07/06
17:00 - 18:00Room #056 (Mathematics building)
Akira Kono (Kyoto University)
"On the cohomology of free and twisted loop spaces"
A natural extension of cohomology suspension to a free loop space is
constructed from the evaluation map and is shown to have a good
properties in cohomology calculation. This map is generalized to a
twisted loop space.
As an application, the cohomology of free and twisted loop space of
classifying spaces of compact Lie groups, including certain finite
Chevalley groups is calculated.
16:30 - 18:00Room #118 (Mathematics building)
Robert Sims (Univ. Arizona)
"On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems"
2010/07/05
10:30 - 12:00Room #128 (Mathematics building)
Shin-ichi MATSUMURA (Univ. of Tokyo)
"Expression of restricted volumes with current integration"
16:40 - 18:10Room #126 (Mathematics building)
Katsuhisa Furukawa (Waseda University)
"Rational curves on hypersurfaces"
Our purpose is to study the family of smooth rational curves of degree $e$ lying on a hypersurface of degree $d$ in $\mathbb{P}^n$, and to investigate properties of this family (e.g., dimension, smoothness, connectedness).
Our starting point is the research about the family of lines (i.e., $e = 1$), which was studied by W. Barth and A. Van de Ven over $\mathbb{C}$, and by J. Koll\'{a}r over an algebraically closed field of arbitrary characteristic.
For the degree $e > 1$, the family of rational curves was studied by J. Harris, M. Roth, and J. Starr over $\mathbb{C}$ in the case of $d < (n+1)/2$.
In this talk, we study the family of rational curves in arbitrary characteristic under the assumption $e = 2,3$ and $d > 1$, or $e > 3$ and $d > 2e-4$.
2010/07/02
16:30 - 17:30Room #123 (Mathematics building)
Mitsuhiro Shishikura (Kyoto University)
"Hausdorff dimension and measure of conformal fractals "
2010/06/29
16:30 - 18:00Room #056 (Mathematics building)
Takahiro Kitayama (The University of Tokyo)
"Non-commutative Reidemeister torsion and Morse-Novikov theory"
For a circle-valued Morse function of a closed oriented manifold, we
show that Reidemeister torsion over a non-commutative formal Laurent
polynomial ring equals the product of a certain non-commutative
Lefschetz-type zeta function and the algebraic torsion of the Novikov
complex over the ring. This gives a generalization of the results of
Hutchings-Lee and Pazhitnov on abelian coefficients. As a consequence we
obtain Morse theoretical and dynamical descriptions of the higher-order
Alexander polynomials.
2010/06/28
10:30 - 12:00Room #128 (Mathematics building)
Kengo HIRACHI (Univ. of Tokyo)
"Total Q-curvature vanishes on integrable CR manifolds"
2010/06/26
13:50 - 14:50Room #056 (Mathematics building)
Feng Xu (UC Riverside)
"On a subfactor generalization of Wall's conjecture"
10:00 - 16:10Room #056 (Mathematics building)
Yoshimichi Ueda (Kyushu Univ.) 10:00 - 11:00
"On the predual of non-commutative $H^\infty$"
Hiroki Matui (Chiba Univ.) 11:20 - 12:20
"${\mathbf Z}^N$-actions on UHF algebras of infinite type"
Feng Xu (UC Riverside) 13:50 - 14:50
"On a subfactor generalization of Wall's conjecture"
Masaki Izumi (Kyoto Univ.) 15:10 - 16:10
"Group actions on Kirchberg algebras"
2010/06/25
16:30 - 18:00Room #122 (Mathematics building)
Kazuki Hiroe (University of Tokyo)
"Euler transform and Weyl groups of symmetric Kac-Moody Lie algebras"
15:00 - 17:30Room #056 (Mathematics building)
Narutaka Ozawa (Univ. Tokyo) 15:00 - 16:00
"Quasi-homomorphism rigidity with noncommutative targets"
Yoshiko Ogata (Univ. Tokyo) 16:30 - 17:30
"Ruelle-Lanford functions for quantum spin systems"
2010/06/24
16:30 - 18:00Room #128 (Mathematics building)
Thomas Sinclair (Vanderbilt Univ.)
"Strong solidity of factors from lattices in SO(n,1) and SU(n,1)"
Generalizing techniques found in Ozawa and Popa,
``On a class of II$_1$ factors with at most one Cartan subalgebra, II''
(Amer. J. Math., to appear), we show that the group factors of ICC
lattices in SO(n,1) and SU(n,1), $n\ge2$, are strongly solid. If
time permits, we will also discuss applications to $L^2$-rigidity.
16:00 - 17:30Room #002 (Mathematics building)
Hideki Murakawa (University of Toyama)
"Reaction-diffusion approximation to nonlinear diffusion problems"
16:00 - 17:30Room #002 (Mathematics building)
村川 秀樹 (富山大学大学院理工学研究部)
"非線形拡散問題の反応拡散系近似"
氷の融解・水の凝固の過程を記述するステファン問題、地下水の流れを表す多孔質媒体流方程式、2種生物種の競合問題における互いの動的な干渉作用を記述する重定-川崎-寺本交差拡散系など、様々な問題を含む非線形拡散問題を取り扱う。本講演では、非線形拡散問題の解が、拡散が線形である半線形反応拡散系の解により近似されることを示す。この結果は、非線形拡散問題の解構造が、ある種の半線形反応拡散系の中に再現されることを示唆するものである。一般に、非線形問題を扱うよりも半線形問題を取り扱う方が容易であるため、本研究は非線形問題の解析や数値解析に応用できることが期待される。
2010/06/23
16:30 - 18:00Room #002 (Mathematics building)
村川 秀樹 (富山大学大学院理工学研究部(理学))
"非線形交差拡散系の数値解法―反応拡散系近似理論の応用―"
多成分反応拡散系において、他の成分同士、拡散が相互に依存しあっているときに、拡散が交差していると言い、そのような系は交差拡散系と呼ばれる。2種生物種の競合問題におけるお互いの動的な干渉作用を記述する重定-川崎-寺本モデルは非線形交差拡散を含む問題の代表例である。非線形交差拡散系に対する効果的な数値解法は個別の問題に対して構成され、解析されるのが現状である。現象のモデリングを行う場合など、パラメータの変更のみでなく、非線形項そのものを変えて多くの数値実験を行いたい場合がある。この様な状況に対応するために、汎用的で簡便な数値解法が望まれる。講演では、非線形交差拡散系を近似するある半線形反応拡散系を媒介することにより、そのような数値解法を導出、解析し、数値計算を通してその有用性を示す。時間が許せば、半線形反応拡散系を用いた退化放物型方程式の数値解法についても触れたい。
http://www.infsup.jp/utnas/
16:30 - 18:00Room #002 (Mathematics building)
Hideki Murakawa (University of Toyama)
"Numerical methods for nonlinear cross diffusion system: application of reaction-diffusion approximation theory"
http://www.infsup.jp/utnas/
2010/06/22
16:30 - 18:00Room #128 (Mathematics building)
Ivana Alexandrova (East Carolina University)
"Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation"
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions, and we study how a trajectory
oscillating between the two fields gives rise to resonances near the real axis when
the distance between two centers of fields goes to infinity. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.
2010/06/21
16:40 - 18:10Room #126 (Mathematics building)
Toru Tsukioka (Osaka Prefecture University)
"Pseudo-index and minimal length of extremal rays for Fano manifolds"
The minimum of intersection numbers of the anticanonical
divisor with rational curves on a Fano manifold is called pseudo-index.
In view of the fact that the geometry of Fano manifolds is governed by
its extremal rays, it is important to consider the extremal rational
curves. In this talk, we show that for Fano 4-folds having birational
contractions, the minimal length of extremal rays coincides with the
pseudo-index.
10:30 - 12:00Room #128 (Mathematics building)
Sachiko HAMANO (Fukushima Univ)
"A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces"
2010/06/17
16:30 - 18:00Room #128 (Mathematics building)
Feng Xu (UC Riverside)
"On a relative version of Wall's conjecture"
16:30 - 18:00Room #128 (Mathematics building)
Feng Xu (UC Riverside)
"On a relative version of Wall's conjecture"
16:30 - 18:00Room #122 (Mathematics building)
Teruhisa Tsuda (University of Kyushu)
"On a class of the Schlesinger systems"
2010/06/16
16:30 - 17:30Room #056 (Mathematics building)
Luc Illusie (Universite de Paris-Sud)
"Vanishing theorems revisited, after K.-W. Lan and J. Suh"
Let k be an algebraically closed field of characteristic p and X,
Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar
type for certain nef and big line bundles L on Y and morphisms f : X -> Y
having semistable reduction along a divisor with simple normal crossings. It
holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2
and dimension assumptions, and generalizes vanishing theorems of Esnault-
Viehweg and of mine. I'll give an outline of the proof and sketch some
applications, due to K.-W. Lan and J. Suh, to the cohomology of certain
automorphic bundles arising from PEL type Shimura varieties.
2010/06/15
16:30 - 18:00Room #128 (Mathematics building)
Takashi Takiguchi (Department of Mathematics, National Defense Academy)
"Sato's counterexample and the structure of generalized functions"
In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.
16:30 - 18:00Room #056 (Mathematics building)
Kazuhiro Ichihara (Nihon University)
"On exceptional surgeries on Montesinos knots
(joint works with In Dae Jong and Shigeru Mizushima)"
I will report recent progresses of the study on exceptional
surgeries on Montesinos knots.
In particular, we will focus on how homological invariants (e.g.
khovanov homology,
knot Floer homology) on knots can be used in the study of Dehn surgery.
2010/06/14
16:40 - 18:10Room #126 (Mathematics building)
Yongnam Lee (Sogang University)
"Slope of smooth rational curves in an anticanonically polarized Fano manifold"
Ross and Thomas introduce the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature metric. Since K-stability implies slope stability, slope stability gives an algebraic obstruction to theexistence of constant scalar curvature. This talk presents a systematic study of slope stability of anticanonically polarized Fano manifolds with respect to smooth rational curves. Especially, we prove that an anticanonically polarized Fano maniold is slope semistable with respect to any free smooth rational curves, and that an anticanonically polarized Fano threefold X with Picard number 1 is slope stable with respect to any smooth rational curves unless X is the project space. It is a joint work with Jun-Muk Hwang and Hosung Kim.
10:30 - 12:00Room #128 (Mathematics building)
Kazuko MATSUMOTO (Osaka Prefecture University)
"Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n"
2010/06/11
17:00 - 18:00Room #123 (Mathematics building)
Masaaki Umehara (Osaka University)
"The Gauss-Bonnet Theorem and singular points on surfaces"
We generalize the classical Gauss-Bonnet formula for closed surfaces as wave fronts. Using it, we can find a new view point of inflection points and the topology of immersed surfaces in Euclidean 3-space via the singularities of their Gauss maps.
2010/06/10
16:00 - 17:30Room #002 (Mathematics building)
Christian Klingenberg (Wuerzburg 大学 )
"Hydrodynamic limit of microscopic particle systems to conservation laws to fluid models"
In this talk we discuss the hydrodynamic limit of a microscopic description of a fluid to its macroscopic PDE description.
In the first part we consider flow through porous media, i.e. the macroscopic description is a scalar conservation law. Here the new feature is that we allow sudden changes in porosity and thereby the flux may have discontinuities in space. Microscopically this is described through an interacting particle system having only one conserved quantity, namely the total mass. Macroscopically this gives rise to a scalar conservation laws with space dependent flux functions
u_t + f(u, x)_x = 0 .
We are able to derive the PDE together with an entropy condition as a hydrodynamic limit from a microscopic interacting particle system.
In the second part we consider a Hamiltonian system with boundary conditions. Microscopically this is described through a system of coupled oscillators. Macroscopically this will lead to a system of conservation laws, namely the p-system. The proof of the hydrodynamic limit is restricted to smooth solutions. The new feature is that we can derive this with boundary conditions.
16:30 - 18:00Room #128 (Mathematics building)
Mikael Pichot (IPMU)
"Random groups and nonarchimedean lattices"
2010/06/09
16:15 - 17:15Room #052 (Mathematics building)
Richard Hain (Duke University)
"Universal mixed elliptic motives"
This is joint work with Makoto Matsumoto. A mixed elliptic
motive is a mixed motive (MHS, Galois representation, etc) whose
weight graded quotients are Tate twists of symmetric powers of the the
motive of elliptic curve. A universal mixed elliptic motive is an
object that can be specialized to a mixed elliptic motive for any
elliptic curve and whose specialization to the nodal cubic is a mixed
Tate motive. Universal mixed elliptic motives form a tannakian
category. In this talk I will define universal mixed elliptic motives,
give some fundamental examples, and explain what we know about the
fundamental group of this category. The "geometric part" of this group
is an extension of SL_2 by a prounipotent group that is generated by
Eisenstein series and which has a family of relations for each cusp
form. Although these relations are not known, we have a very good idea
of what they are, thanks to work of Aaron Pollack, who determined
relations between the generators in a very large representation of
this group.
17:30 - 18:30Room #056 (Mathematics building)
Fabrice Orgogozo (CNRS, École polytechnique)
"Constructibilité uniforme des images directes supérieures en
cohomologie étale
"
Motivé par une remarque de N. Katz sur le lien entre la
torsion de la Z_ℓ-cohomologie étale et les ultraproduits de groupes de
F_ℓ-cohomologie, nous démontrons un théorème d'uniformité en ℓ pour la
constructibilité des images directes supérieures entre schémas de type fini
sur un trait excellent. (Un tel théorème avait été considéré par
O. Gabber il y a plusieurs années déjà.)
La méthode est maintenant classique : on utilise des
théorèmes de A. J. de Jong et un peu de log-géométrie.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted from IHES by the internet.)
16:30 - 18:00Room #002 (Mathematics building)
Junichi Matsumoto (National Institute of Advanced Industrial Science and Technology)
"A bubble finite-element method with orthogonal property and applications to flow problems"
http://www.infsup.jp/saito/
16:30 - 18:00Room #002 (Mathematics building)
松本 純一 (産業技術総合研究所)
"直交基底気泡関数有限要素法による流体解析と応用計算"
http://www.infsup.jp/utnas/
15:00 - 16:10Room #000 (Mathematics building)
KAMATANI, Kengo (Graduate school of Mathematical Sciences, Univ. of Tokyo)
"Weak convergence of Markov chain Monte Carlo method and its application to Yuima"
We examine some asymptotic properties of Markov chain Monte Carlo methods by the weak convergence framework of MCMC. Our purpose is to compare this framework to the Harris recurrence framework. Numerical illustrations will be given via R. The connection to the YUIMA package will also be discussed.
This talk will be held at IT Studio.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/03.html
2010/06/08
17:00 - 18:30Room #126 (Mathematics building)
Soji Kaneyuki (Sophia University)
"Automorphism groups of causal Makarevich spaces"
Let G^ be a simple Lie group of Hermitian type and U^ be a maximal parabolic subgroup of G^ with abelian nilradical. The flag manifold M^= G^/ U^ is the Shilov
boundary of an irreducible bounded symmetric domain of tube type. M^ has the G-invariant causal structure. A causal Makarevich space is, by definition, an open symmetric G-orbit M in M^, endowed with the causal structure induced from that
of the ambient space M^, G being a reductive subgroup of G^. All symmetric cones fall in the class of causal Makarevich spaces.
In this talk, we determine the causal automorphism groups of all causal Makarevich spaces.
2010/06/07
16:40 - 18:10Room #126 (Mathematics building)
Xavier Roulleau (The University of Tokyo)
"Genus 2 curve configurations on Fano surfaces"
10:30 - 12:00Room #128 (Mathematics building)
Tomoyuki HISAMOTO (Univ. of Tokyo)
"Restricted Bergman kernel asymptotics"
2010/06/03
16:30 - 18:00Room #122 (Mathematics building)
Makoto Yamashita (Univ. Tokyo)
"Fixed Points in the Stone-Cech boundary of Groups"
We discuss the class of discrete groups which admit fixed points under the adjoint action on the Stone-Cech boundary. Such groups have vanishing $L^2$-Betti numbers, and nonamenable ones fail to have property (AO).
16:30 - 18:00Room #470 (Mathematics building)
Birgit Speh (Cornel University)
"Introduction to the cohomology of locally symmetric spaces 2
"
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\Gamma =K \backslash G / \Gamma $.
If $X_\Gamma $ is cocompact this cohomology can be expressed as the $(\bg,K) $-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2010/06/02
16:30 - 17:30Room #056 (Mathematics building)
Ryoko Tomiyasu (KEK)
"On some algebraic properties of CM-types of CM-fields and their
reflex fields"
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.
For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \rtimes S_n$.
Using properties of the embedding, a set of CM-types $\Phi$ of $K$ and their
dual CM-types $(K, \Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual
CM-type.
I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.
2010/06/01
17:00 - 18:30Room #056 (Mathematics building)
Taro Asuke (The University of Tokyo)
"On Fatou-Julia decompositions"
We will explain that Fatou-Julia decompositions can be
introduced in a unified manner to several kinds of one-dimensional
complex dynamical systems, which include the action of Kleinian groups,
iteration of holomorphic mappings and complex codimension-one foliations.
In this talk we will restrict ourselves mostly to the cases where the
dynamical systems have a certain compactness, however, we will mention
how to deal with dynamical systems without compactness.
16:30 - 18:00Room #126 (Mathematics building)
Birgit Speh (Cornel University)
"Introduction to the cohomology of locally symmetric spaces
"
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\Gamma =K \backslash G / \Gamma $.
If $X_\Gamma $ is cocompact this cohomology can be expressed as the $(g,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2010/05/31
16:40 - 18:10Room #126 (Mathematics building)
Atsushi Kanazawa (The University of Tokyo)
"On Pfaffian Calabi-Yau Varieties and Mirror Symmetry"
We construct new smooth CY 3-folds with 1-dimensional Kaehler moduli and
determine their fundamental topological invariants. The existence of CY
3-folds with the computed invariants was previously conjectured. We then
report mirror symmetry for these non-complete intersection CY 3-folds.
We explicitly build their mirror partners, some of which have 2 LCSLs,
and carry out instanton computations for g=0,1.
10:30 - 12:00Room #128 (Mathematics building)
Ken-ichi YOSHIKAWA (Kyoto Univ.)
"Singularities and analytic torsion"
2010/05/28
16:30 - 18:00Room #126 (Mathematics building)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
"On solutions of uniformization equations"
2010/05/27
16:30 - 18:00Room #128 (Mathematics building)
Catherine Oikonomides (Univ. Tokyo)
"The C*-algebra of codimension one foliations which are almost without holonomy"
2010/05/26
16:20 - 17:30Room #000 (Mathematics building)
FUKASAWA, Masaaki (CSFI, Osaka Univ.)
"Financial data analysis with R-YUIMA"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html
10:30 - 11:30Room #056 (Mathematics building)
Giovanni Pisante (Department of Mathematics
Hokkaido University)
"A SELECTION CRITERION FOR SOLUTIONS OF A
SYSTEM OF EIKONAL EQUATIONS
"
We deal with the system of eikonal equations |ðu/ðx1|=1, |ðu/ðx2|=1 in a planar Lipschitz domain with zero boundary condition. Exploiting the classical pyramidal construction introduced by Cellina, it is easy to prove that there exist infinitely many Lipschitz solutions. Then, the natural problem that has arisen in this framework is to find a way to select and characterize a particular meaningful class of solutions.
We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient. More precisely we select an optimal weighted measure for the jump set of the second derivatives of a given solution v of the system and we prove the existence of minimizers of the corresponding variational problem.
16:30 - 18:00Room #002 (Mathematics building)
Keisuke Matsuya (University of Tokyo)
"Existence and non-existence of global solutions for a discrete semilinear heat equation"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #002 (Mathematics building)
松家 敬介 (東京大学大学院数理科学研究科)
"Existence and non-existence of global solutions for a discrete semilinear heat equation "
http://www.infsup.jp/utnas/
2010/05/25
17:00 - 18:00Room #126 (Mathematics building)
Kaoru Hiraga (Kyoto University)
"On endoscopy, packets, and invariants"
The theory of endoscopy came out of the Langlands functoriality and the trace formula.
In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.
I would like to talk about the connection between these topics and the endoscopy.
2010/05/24
16:40 - 18:10Room #126 (Mathematics building)
Hokuto Uehara (Tokyo Metropolitan University)
"A counterexample of the birational Torelli problem via Fourier--Mukai transforms"
We study the Fourier--Mukai numbers of rational elliptic surfaces. As
its application, we give an example of a pair of minimal 3-folds $X$
with Kodaira dimensions 1, $h^1(O_X)=h^2(O_X)=0$ such that they are
mutually derived equivalent, deformation equivalent, but not
birationally equivalent. It also supplies a counterexample of the
birational Torelli problem.
2010/05/19
10:30 - 11:30Room #056 (Mathematics building)
Hiroshi Suito (Okayama University)
"Mathematical sciences collaborating with clinical medicine"
15:00 - 16:10Room #002 (Mathematics building)
YOSHIDA, Nakahiro (University of Tokyo)
"Estimation of the variance-covariance structure for stochastic processes and applications of YUIMA"
We discuss limit theorems and asymptotic expansions in estimation of the variance-covariance structure for Ito processes. We will show some numerical examples by YUIMA, a package for statistical analysis and simulation of stochastic differential equations.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html
2010/05/18
16:30 - 18:00Room #056 (Mathematics building)
Naoyuki Monden (Osaka University)
"On roots of Dehn twists"
Let $t_{c}$ be the Dehn twist about a nonseparating simple closed curve
$c$ in a closed orientable surface. If a mapping class $f$ satisfies
$t_{c}=f^{n}$ in mapping class group, we call $f$ a root of $t_{c}$ of
degree $n$. In 2009, Margalit and Schleimer constructed roots of $t_{c}$.
In this talk, I will explain the data set which determine a root of
$t_{c}$ up to conjugacy. Moreover, I will explain the minimal and the
maximal degree.
16:30 - 18:00Room #126 (Mathematics building)
B. Speh (Cornel University)
"On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces"
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.
Let $X$ be the real hyperbolic n-space and $\Gamma \subset $ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $ X / \Gamma $ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.
This is joint work with T.N. Venkataramana
2010/05/17
16:40 - 18:10Room #126 (Mathematics building)
Yuji Odaka (Research Institute for Mathematical Sciences)
"On the GIT stability of Polarized Varieties"
Background:
Original GIT-stability notion for polarized variety is
"asymptotic stability", studied by Mumford, Gieseker etc around 1970s.
Recently a version appeared, so-called "K-stability", introduced by
Tian(1997) and reformulated by Donaldson(2002), by the way of seeking
the analogue of Kobayashi-Hitchin correspondence, which gives
"differential geometric" interpretation of "stability". These two have
subtle but interesting differences in dimension higher than 1.
Contents:
(1*) Any semistable (in any sense) polarized variety should have only
"semi-log-canonical" singularities. (Partly observed around 1970s)
(2) On the other hand, we proved some stabilities, which corresponds to
"Calabi conjecture", also with admitting mild singularities.
As applications these yield
(3*) Compact moduli spaces with GIT interpretations.
(4) Many counterexamples (as orbifolds) to folklore conjecture:
"K-stability implies asymptotic stability".
(*: Some technical points are yet to be settled.
Some parts for (1)(2) are available on arXiv:0910.1794.)
10:30 - 12:00Room #128 (Mathematics building)
Masaharu TANABE (Tokyo Inst. Tech.)
"On the norm defined on the holomorphic maps of compact Riemann surfaces"
2010/05/15
13:30 - 16:00Room #123 (Mathematics building)
NARITA, Hiroaki (Kumamoto University, Fac. of Science) 13:30 - 14:30
"Strict positivity of the central values of some Rankin-Selberg
L-functions"
We consider the Arakawa lift which is an automprphic form on an inner twist of $GSp(2)$. We construct examples the case when the central values of the $L$-functions of Rankin-Selberg type with degree 8 Euler factors take positive values. ....
YAMAUCHI, Takuya (Osaka Pref. Univ. ) 15:00 - 16:00
"Calabi-Yau manifolds associated to hypergeometric sheaves and their application
Osaka Pref. Univ. "
Let U be the P_1 munus 3 points, and form hypergeometric sheaves on U, by iterative convolutions of certain local sysytem of rank 1 on U. We construct certain families of Calabi-Yau manifolds whose cohomology groups of middle degree are these hypergeometric sheaves. We discuss the potential-modularity of these varieties and unit root formula. This is a joint work with Michio Tsuzuki. (trans. by the organizer of the seminar)
2010/05/12
15:30 - 17:00Room #123 (Mathematics building)
Luc Illusie (東京大学/Paris南大学)
"Independence of families of $\ell$-adic representations and uniform constructibility"
Let $k$ be a number field, $\overline{k}$ an algebraic closure of $k$, $\Gamma_k = \mathrm{Gal}(\overline{k}/k)$. A family of continuous homomorphisms $\rho_{\ell} : \Gamma_k \rightarrow G_{\ell}$, indexed by prime numbers $\ell$, where $G_{\ell}$ is a locally compact $\ell$-adic Lie group, is said to be independent if $\rho(\Gamma_k) = \prod \rho_{\ell}(\Gamma_k)$, where $\rho = (\rho_{\ell}) : \Gamma_k \rightarrow \prod G_{\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\ell$.
17:30 - 18:30Room #056 (Mathematics building)
Makoto Matsumoto (University of Tokyo)
"Differences between
Galois representations in outer-automorphisms
of the fundamental groups and those in automorphisms, implied by
topology of moduli spaces"
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number field K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:
ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).
Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are infinitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.
This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).
There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)
10:30 - 11:30Room #056 (Mathematics building)
Jean-Pierre Puel (Graduate School of Mathematical Sciences
The University of Tokyo)
"Exact controllability for incompressible fluids"
After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.
We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).
We will end up with some important open problems.
16:30 - 18:00Room #002 (Mathematics building)
Takeshi Ogita (Tokyo Woman's Christian University)
"Accurate factorizations of ill-conditioned matrices and applications"
http://www.infsup.jp/utnas/
16:30 - 18:00Room #002 (Mathematics building)
荻田 武史 (東京女子大学現代教養学部)
"悪条件行列の高精度な分解法とその応用"
http://www.infsup.jp/utnas/
2010/05/11
16:30 - 18:00Room #056 (Mathematics building)
Nariya Kawazumi (The University of Tokyo)
"The logarithms of Dehn twists"
We establish an explicit formula for the action of (non-separating and
separating) Dehn twists on the complete group ring of the fundamental group of a
surface. It generalizes the classical transvection formula on the first homology.
The proof is involved with a homological interpretation of the Goldman
Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).
16:30 - 18:00Room #126 (Mathematics building)
Hisayosi Matumoto (the University of Tokyo)
"On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module"
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.
2010/05/10
16:40 - 18:10Room #126 (Mathematics building)
Makoto Miura
(The University of Tokyo)
"Toric degenerations of Grassmannians and mirror symmetry"
I will talk about toric degenerarions of Grassmannians and
an application to the mirror constructions for complete intersection
Calabi-Yau manifolds in Grassmannians.
In particular, if we focus on toric degenerations by term orderings on
polynomial rings,
we have to choose a term ordering for which the coordinate ring has an
uniformly homogeneous sagbi basis.
We discuss this condition for some examples of ordinary Grassmannians
and a spinor variety.
10:30 - 12:00Room #128 (Mathematics building)
Yoshihiko MATSUMOTO (Univ. of Tokyo)
"Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds"
To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.
2010/05/07
16:00 - 17:30Room #056 (Mathematics building)
Luc Illusie (東京大学/Paris南大学)
"Independence of families of $\ell$-adic representations and uniform constructibility"
Let $k$ be a number field, $\overline{k}$ an algebraic closure of $k$, $\Gamma_k = \mathrm{Gal}(\overline{k}/k)$. A family of continuous homomorphisms $\rho_{\ell} : \Gamma_k \rightarrow G_{\ell}$, indexed by prime numbers $\ell$, where $G_{\ell}$ is a locally compact $\ell$-adic Lie group, is said to be independent if $\rho(\Gamma_k) = \prod \rho_{\ell}(\Gamma_k)$, where $\rho = (\rho_{\ell}) : \Gamma_k \rightarrow \prod G_{\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\ell$.
16:30 - 17:30Room #123 (Mathematics building)
Jean-Pierre Puel (The University of Tokyo, Universite de Versailles Saint-Quentin)
"Why to study controllability problems and the mathematical tools involved"
We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.
2010/05/06
16:30 - 18:00Room #128 (Mathematics building)
Makoto Yamashita (Univ. Tokyo)
"Connes-Landi Deformation of Spectral Triples"
We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic K-theoretic invariants independent of the deformation parameter.
2010/04/28
10:30 - 11:30Room #056 (Mathematics building)
Marcus Wunsch (Kyoto University
)
"GLOBAL AND SINGULAR SOLUTIONS TO SOME
HYDRODYNAMIC EVOLUTION EQUATIONS"
The two-component Hunter-Saxton system is a recently derived system of evolution equations modeling, e.g., the nonlinear dynamics of nondissipative dark matter and the propagation of orientation waves in nematic liquid crystals. It is imbedded into a parameterized family of systems called the generalized Hunter-Saxton (2HS) system [2] reducing, if one component is omitted, to the generalized Proudman-Johnson(gPJ) equation [1] modeling three-dimensional vortex dynamics.
After demonstrating, by means of Kato's semigroup theory, the local-in-time existence of classical solutions, the blow-up scenarios for the 2HS system and the gPJ equation are described. The explicit construction of weak dissipative solutions for both models is discussed in detail.
Finally, global existence in time of these weak solutions is proved.
16:00 - 17:30Room #056 (Mathematics building)
Luc Illusie (東京大学/Paris南大学)
"Independence of families of $\ell$-adic representations and uniform constructibility"
Let $k$ be a number field, $\overline{k}$ an algebraic closure of $k$, $\Gamma_k = \mathrm{Gal}(\overline{k}/k)$. A family of continuous homomorphisms $\rho_{\ell} : \Gamma_k \rightarrow G_{\ell}$, indexed by prime numbers $\ell$, where $G_{\ell}$ is a locally compact $\ell$-adic Lie group, is said to be independent if $\rho(\Gamma_k) = \prod \rho_{\ell}(\Gamma_k)$, where $\rho = (\rho_{\ell}) : \Gamma_k \rightarrow \prod G_{\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\ell$.
15:00 - 16:10Room #002 (Mathematics building)
KATO, Shogo (The Institute of Statistical Mathematics)
"A Markov process for circular data"
We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html
2010/04/27
16:30 - 18:00Room #056 (Mathematics building)
横田 佳之 (首都大学東京)
"On the complex volume of hyperbolic knots"
In this talk, we give a formula of the volume and the Chern-Simons invariant of hyperbolic knot complements, which is closely related to the volume conjecture of hyperbolic knots.
We also discuss the volumes and the Chern-Simons invariants of closed 3-manifolds
obtained by Dehn surgeries on hyperbolic knots.
16:30 - 18:00Room #126 (Mathematics building)
Yoshiki Oshima (the University of Tokyo)
"Restriction of Vogan-Zuckerman's derived functor modules to symmetric subgroups"
We study the restriction of Vogan-Zuckerman derived functor modules $A_\frak{q}(\lambda)$ to symmetric subgroups.
An algebraic condition for the discrete decomposability of
$A_\frak{q}(\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.
In this talk, when $A_\frak{q}(\lambda)$ is discretely decomposable,
we construct some of irreducible components occurring in the branching law and determine their associated variety.
2010/04/26
16:40 - 18:10Room #126 (Mathematics building)
Shouhei Ma (The University of Tokyo)
"The unirationality of the moduli spaces of 2-elementary K3
surfaces"
We prove the unirationality of the moduli spaces of K3 surfaces
with non-symplectic involution. As a by-product, we describe the
configuration spaces of 5, 6, 7, 8 points in the projective plane as
arithmetic quotients of type IV.
16:30 - 18:00Room #002 (Mathematics building)
Akishi Ikeda (The University of Tokyo)
"The correspondence between Frobenius algebra of Hurwitz numbers
and matrix models"
The number of branched coverings of closed surfaces are called Hurwitz
numbers. They constitute a Frobenius algebra structure, or
two dimensional topological field theory. On the other hand, correlation
functions of matrix models are expressed in term of ribbon graphs
(graphs embedded in closed surfaces).
In this talk, I explain how the Frobenius algebra structure of Hurwitz
numbers are described in terms of matrix models. We use the
correspondence between ribbon graphs and covering of S^2 ramified at
three points, both of which have natural symmetric group actions.
As an application I use Frobenius algebra structure to compute Hermitian
matrix models, multi-variable matrix models, and their large N
expansions. The generating function of Hurwitz numbers is also expressed
in terms of matrix models. The relation to integrable hierarchies and
random partitions is briefly discussed.
10:30 - 12:00Room #128 (Mathematics building)
Yoshihiro AIHARA (Fukushima Univ.)
"Deficiencies of holomorphic curves in projective algebraic varieties"
2010/04/23
16:30 - 17:30Room #123 (Mathematics building)
松本 眞 (東京大学大学院数理科学研究科)
"疑似乱数発生に用いられる数学:メルセンヌ・ツイスターを例に"
疑似乱数生成法とは、あたかも乱数であるかのようにふるまう数列を、計算機内で高速に、再現性があるように生成する方法の総称です。確率的事象を含む現象の計算機シミュレーションには、疑似乱数は欠かせません。たとえば、核物理シミュレーション、株価に関する商品の評価、DNA塩基配列からのたんぱく質の立体構造推定など、広い範囲で疑似乱数は利用されています。講演者と西村拓士氏が97年に開発したメルセン・ツイスタ―生成法は、生成が高速なうえ周期が$2^19937-1$で623次元空間に均等分布することが証明されており、ISO規格にも取り入れられるなど広く利用が進んでいます。ここでは、メルセンヌ・ツイスターとその後の発展において、(初等的・古典的な)純粋数学(有限体、線形代数、多項式、べき級数環、格子など)がどのように使われたかを、非専門家向けに解説します。学部1年生を含め、他学部・他専攻の方の参加を期待して講演を準備します。
http://www.ms.u-tokyo.ac.jp/~matumoto/PRESENTATION/tokyo-univ2010-4-23.pdf
2010/04/22
16:30 - 18:00Room #128 (Mathematics building)
Nigel Higson (Pennsylvania State Univ.)
"The Baum-Connes Conjecture and Group Representations"
The Baum-Connes conjecture asserts a sort of duality between the reduced unitary dual of a group and (a variant of) the classifying space of the group. The conjectured duality occurs at the level of K-theory. For example, for free abelian groups it amounts to a K-theoretic form of Fourier-Mukai duality. The conjecture has well-known applications in topology and geometry, but it also resonates in various ways with Lie groups and representation theory. I'll try to indicate how this comes about, and then focus on a fairly new aspect of the relationship that develops some early ideas of Mackey.
16:00 - 17:30Room #002 (Mathematics building)
Jens Starke (Technical University of Denmark)
"Deterministic and stochastic modelling of catalytic surface processes"
Three levels of modelling, the microscopic, the mesoscopic and the macroscopic level are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. The macroscopic description can be derived rigorously for low pressure conditions as limit of the stochastic many particle model for large particle numbers. This is in correspondence with the successful description of experiments under low pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The introduced models include a new approach for the platinum phase transition which allows for a unification of existing models for Pt(100) and Pt(110).
The rich nonlinear dynamical behaviour of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, so-called raindrop patterns which are not captured by earlier models, can be reproduced and are shown in simulations.
This is joint work with M. Eiswirth, H. Rotermund, G. Ertl,
Frith Haber Institut, Berlin, K. Oelschlaeger, University of
Heidelberg and C. Reichert, INSA, Lyon.
2010/04/21
10:30 - 11:30Room #056 (Mathematics building)
Gen Sazaki (Hokkaido University)
"Direct observation of elementary processes of crystal growth by advanced optical microscopy"
16:30 - 18:00Room #002 (Mathematics building)
Kenta Kobayashi (Kanazawa University)
"On the interpolation constant over triangular and rectangular elements"
http://www.infsup.jp/utnas/
2010/04/20
16:30 - 18:00Room #056 (Mathematics building)
Helene Eynard-Bontemps (東京大学大学院数理科学研究科, JSPS)
"Homotopy of foliations in dimension 3."
We are interested in the connectedness of the space of
codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved
the fundamental result:
Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a
foliation.
W. R. gave a new proof of (and generalized) this result in 1973 using
local constructions. It is then natural to wonder if two foliations with
homotopic tangent plane fields can be linked by a continuous path of
foliations.
A. Larcanch\'e gave a positive answer in the particular case of
"sufficiently close" taut foliations. We use the key construction of her
proof (among other tools) to show that this is actually always true,
provided one is not too picky about the regularity of the foliations of
the path:
Theorem: Two C^\infty foliations with homotopic tangent plane fields can
be linked by a path of C^1 foliations.
16:30 - 18:00Room #126 (Mathematics building)
Takayuki Okuda (the University of Tokyo)
"Proper actions of SL(2,R) on semisimple symmetric spaces"
Complex irreducible symmetric spaces which admit proper SL(2,R)-actions were classified by Katsuki Teduka.
In this talk, we generalize Teduka's method and classify semisimple symmetric spaces which admit proper SL(2,R)-actions.
2010/04/19
16:40 - 18:10Room #126 (Mathematics building)
松村 慎一 (東大数理)
"制限型体積と因子的ザリスキー分解"
豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.
(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,
多くの状況で出現する重要な概念である.
様々な部分多様体に沿った制限型体積の振る舞いと
巨大な因子のザリスキー分解可能性の関係について考察したい.
また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に
ついても触れたい.
16:00 - 17:00Room #122 (Mathematics building)
Cyrill Muratov (New Jersey Institute of Technology)
"Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions"
In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.
10:30 - 12:00Room #128 (Mathematics building)
Filippo Bracci (Universita di Roma, ``Tor Vergata'')
"Loewner's theory on complex manifolds"
Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.
http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html
16:30 - 18:00Room #056 (Mathematics building)
Horoshi HAENO (Memorial Sloan-Kettering Cancer Center)
"骨髄増殖性疾患の起源細胞に関する数理的研究"
2010/04/17
13:30 - 16:00Room #123 (Mathematics building)
MIYAZAKI Tadashi (Tokyo Univ. of agr. and indus.) 13:30 - 14:30
"Principal series Whittaker functions on $Sp(2,C)$"
Not given here.
HARASHITA Shushi (Yokohama National Univ.) 15:00 - 16:00
"A paving of the Siegel 10-fold of positive characteristic"
Not given here.
2010/04/15
16:30 - 18:00Room #056 (Mathematics building)
Uuganbayar Zunderiya (Nagoya University)
"Generalized hypergeometric systems"
A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\times l$ matrices of derivations with respect to certain variables.
In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.
16:00 - 17:30Room #002 (Mathematics building)
Alberto Tesei (University of Rome 1)
"Long-time behaviour of solutions of a forward-backward parabolic equation"
We discuss some recent results concerning the asymptotic behaviour of entropy measure-valued solutions for a class of ill-posed forward-backward parabolic equations, which arise in the theory of phase transitions.
16:00 - 17:00Room #122 (Mathematics building)
Claude Mitschi (Univ. de Strasbourg)
"The Galois group of projectively isomonodromic deformations"
Isomonodromic families of regular singular differential equations over $\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.
2010/04/14
17:30 - 18:30Room #056 (Mathematics building)
Gerard Laumon (CNRS, Universite Paris XI - Orsay)
"The cohomological weighted fundamental lemma "
Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
10:30 - 11:30Room #056 (Mathematics building)
Etsuro Yokoyama (Gakushuin University)
"Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station
--basal plane growth rate and dendritic growth velocity
"
2010/04/13
16:30 - 18:00Room #056 (Mathematics building)
Christian Kassel (CNRS, Univ. de Strasbourg)
"Torsors in non-commutative geometry"
G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.
16:30 - 18:00Room #128 (Mathematics building)
Jean-Marc Bouclet (Toulouse University, France)
"Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds"
2010/04/12
10:30 - 12:00Room #128 (Mathematics building)
千葉 優作 (東大数理)
"Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space"
http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html
2010/04/06
16:30 - 18:00Room #126 (Mathematics building)
加藤周 (京都大学)
"On the characters of tempered modules of affine Hecke
algebras of classical type"
We present an inductive algorithm to compute the characters
of tempered modules of an affine Hecke algebras of classical
types, based on a new class of representations which we call
"tempered delimits". They have some geometric origin in the
eDL correspondence.
Our new algorithm has some advantage to the Lusztig-Shoji
algorithm (which also describes the characters of tempered
modules via generalized Green functions) in the sense it
enables us to tell how the characters of tempered modules
changes as the parameters vary.
This is a joint work with Dan Ciubotaru at Utah.
2010/04/05
16:40 - 18:10Room #126 (Mathematics building)
Alexandru Dimca (Université Nice-Sophia Antipolis)
"From Lang's Conjecture to finiteness properties of Torelli groups"
First we recall one of Lang's conjectures in diophantine geometry
on the interplay between subvarieties and translated subgroups in a
commutative algebraic group
(proved by M. Laurent in the case of affine tori in 1984).
Then we present the technique of resonance and characteristic varieties,
a powerful tool in the study of fundamental groups of algebraic varieties.
Finally, using the two ingredients above, we show that the Torelli
groups $T_g$
have some surprising finiteness properties for $g>3$.
In particular, we show that for any subgroup $N$ in $T_g$ containing
the Johnson kernel $K_g$, the complex vector space $N_{ab} \otimes C$
is finite dimensional.
All the details are available in our joint preprint with S. Papadima
arXiv:1002.0673.
2010/03/30
10:00 - 15:00Room #122 (Mathematics building)
Masahiro Yamamoto (University of Tokyo) 10:00 - 10:50
"産学連携による新たな数学の課題:非整数階拡散方程式への誘い"
Shu Nakamura (University of Tokyo) 11:00 - 11:50
"量子力学のスペクトル・散乱理論における数学的手法"
Kazufumi Ito (University of Tokyo, North Carolina State University) 13:20 - 14:10
"Semismooth Newton法の理論、及び応用"
Georg Weiss (University of Tokyo) 14:10 - 15:00
"TBA"
2010/03/29
13:00 - 14:10Room #002 (Mathematics building)
Catherine Laredo (MIA, INRA)
"Inference for partially observed Markov processes and applications"
We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.
We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html
2010/03/25
17:00 - 18:00Room #370 (Mathematics building)
Dr Bangti Jin (Center for Industrial Mathematics University of Bremen, Germany)
"Heuristic Choice Rules for Convex Variational Regularization"
In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.
16:00 - 17:00Room #370 (Mathematics building)
M.M. Lavrentiev, Jr. (Sobolev Institute of Mathematics, Novosibirsk, Russia)
"Modern computer architectures for tsunami simulation"
Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.
2010/03/23
15:00 - 17:15Room #370 (Mathematics building)
Mourad Bellassoued (Univ. of Bizerte) 15:00 - 16:00
"Stability estimates for the anisotropic wave and Schrodinger equations from
the Dirichlet to Neumann map"
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.
Johannes Elschner (Weierstrass Institute Berlin, Germany) 16:15 - 17:15
"On uniqueness in inverse elastic obstacle scattering"
The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.
Our approach is essentially based on a reflection principle for the Navier equation.
2010/03/19
11:00 - 12:00Room #366 (Mathematics building)
竹内 知哉 (North Carolina State University, USA)
"A Regularization Parameter for Nonsmooth Tikhonov Regularization"
We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.
2010/03/17
16:30 - 17:30Room #128 (Mathematics building)
三角 淳 (東大数理)
"方向依存性を持つ長距離パーコレーションの臨界曲線"
2010/03/15
15:00 - 16:00Room #002 (Mathematics building)
Cecilia Mancini (University of Florence)
"BROWNIAN COVARIATION AND CO-JUMPS, GIVEN DISCRETE OBSERVATION"
We consider two processes driven by Brownian motions plus drift and possibly infinite activity jumps.
Given discrete observations we separately estimate the covariation between the two Brownian parts and the sum of the co-jumps. This allows to gain insight into the dependence structure of the processes and has important applications in finance.
Our estimator is based on a threshold principle allowing to isolate the jumps over a threshold.
The estimator of the continuous covariation is asymptotically Gaussian and converges at speed square root of n when the jump components have finite variation. In presence infinite variation jumps the speed is heavily influenced both by the small jumps dependence structure and by their jump activity indexes.
This talk is based on Mancini and Gobbi (2009), and Mancini (2010).
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/16.html
14:00 - 15:00Room #002 (Mathematics building)
Alexandre Brouste (Université du Maine)
"Statistical inference in the partial observation setting, in continuous time"
In various fields, the {\it signal} process, whose law depends on an unknown parameter $ artheta \in \Theta \subset \R^p$, can not be observed directly but only through an {\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\left( Y_t, t \geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \label{mod:modelgeneral} Y_t = Y_0 + \int_0^t h(X_s, artheta) ds + \sigma W^H_t\,, \quad t > 0 \end{equation} where the function $ h: \, \R imes \Theta \longrightarrow \R$ and the constant $\sigma>0$ are known and the noise $\left( W^H_t\,, t\geq 0 ight)$ is a fractional Brownian motion valued in $\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $ artheta \in \Theta$ given the observation of the continuous sample path $Y^T=\left( Y_t , 0 \leq t \leq T ight)$, $T>0$, naturally arises.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html
2010/03/12
15:00 - 17:30Room #050 (Mathematics building)
岡本和夫 (東京大学大学院数理科学研究科) 15:00 - 16:00
"ガルニエ系の数理"
ガルニエ系は,パンルヴェ方程式の拡張であり,完全積分可能な多時間ハミルトン系として与えられる。これは2階線型常微分方程式のホロノミック変形を与える非線型完全積分可能な偏微分方程式系であり,講演の対象である2次元系では,8つのタイプの基本形がある。ガルニエ系の研究は,初期値空間やソリトン方程式系の相似簡約などの立場から行われているが,材料が揃ってくれば,一般リーマン・ヒルベルト対応を経由して考察することが自然であるし,数学的であるだろう。パンルヴェ方程式の場合もそのような方向に進んでいる。一方,パンルヴェ方程式については,そのハミルトニアンの満足する非線型常微分方程式が,アフィンワイル群の対称性など数学的な材料を与える上で一定の役割を果たした。ガルニエ系についても,そのハミルトニアンについての非線型偏微分方程式系を具体的に書き下すことは,意味のあることと信じているが,未完である。この話題について,部分的な結果を紹介する。
森田茂之 (東京大学大学院数理科学研究科) 16:30 - 17:30
"特性類と不変量を巡る旅"
40年近くの間,さまざまな幾何構造に関する特性類と不変量の研究を続けてきた.葉層構造やリーマン面のモジュライ空間の特性類,そして3次元多様体の位相不変量等である.これらについて振り返りつつ,これからの目標をいくつかの予想を交えてお話ししたい.
2010/03/09
10:30 - 11:30Room #123 (Mathematics building)
Joachim Escher (Leibniz University of Hanover)
"Shallow water waves with singularities"
The Degasperis-Procesi equation is a recently derived shallow water wave equation, which is - similar as the Camassa-Holm equation - embedded in a family of spatially periodic third order dispersive conservation laws.
The coexistence of globally in time defined classical solutions, wave breaking solutions, and spatially periodic peakons and shock waves is evidenced in the talk, and the precise blow-up scenario, including blow-up rates and blow-up sets, is discussed in detail. Finally several conditions on the initial profile are presented, which ensure the occurence of a breaking wave.
2010/02/24
15:00 - 16:30Room #370 (Mathematics building)
Robert Penner (Aarhus University / University of Southern California)
"Protein Moduli Space"
Recent joint works with J. E. Andersen and others
provide explicit discrete and continuous models
of protein geometry. These models are inspired
by corresponding constructions in the study of moduli
spaces of flat G-connections on surfaces, in particular,
for G=PSL(2,R) and G=SO(3). These models can be used
for protein classification as well as for folding prediction,
and computer experiments towards these ends will
be discussed.
2010/02/23
14:00 - 15:00Room #122 (Mathematics building)
Bendong LOU (同済大学)
"Homogenization Limit and Singular Limit of the Allen-Cahn equation"
We consider the Allen-Cahn equation in a cylinder with periodic undulating boundaries in the plane. Our problem involves two small parameters $\delta$ and $\epsilon$, where $\delta$ appears in the equation to denote the scale of the singular limit and $\epsilon$ appears in the boundary conditions to denote the scale of the homogenization limit. We consider the following two limiting processes:
(I): taking homogenization limit first and then taking singular limit;
(II) taking singular limit first and then taking homogenization limit.
We formally show that they both result in the same mean curvature flow equation, but with different boundary conditions.
2010/02/19
16:30 - 18:00Room #126 (Mathematics building)
Yves Benoist (Orsay)
"Discrete groups acting on homogeneous spaces V"
I will focus on recent advances on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups, ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1, and such that no finite union of vector subspaces is invariant by A and B. We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
2010/02/18
10:30 - 17:00Room #126 (Mathematics building)
Yves Benoist (Pars Sud) 10:30 - 11:30
"Discrete groups acting on homogeneous spaces III"
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist (Paris Sud) 15:00 - 16:00
"Discrete groups acting on homogeneous spaces IV"
16:30 - 18:00Room #128 (Mathematics building)
Roberto Longo (University of Rome, Tor Vergata)
"Von Neumann Algebras and Boundary Quantum Field Theory"
16:00 - 17:30Room #002 (Mathematics building)
Bendong LOU (同済大学)
"Homogenization limit of a parabolic equation with nonlinear boundary conditions"
We consider a quasilinear parabolic equation with the following nonlinear Neumann boundary condition:
"the slope of the solution on the boundary is a function $g$ of the value of the solution". Here $g$ takes values near its supremum with the frequency of $\epsilon$. We show that the homogenization limit of the solution, as $\epsilon$ tends to 0, is the solution satisfying the linear Neumann boundary condition: "the slope of the solution on the boundary is the supremum of $g$".
10:10 - 11:00Room #122 (Mathematics building)
俣野 博 (数理科学)
"空間的に非一様な場における進行波"
11:00 - 11:50Room #122 (Mathematics building)
野口 潤次郎 (数理科学)
"岡の連接定理から一致の定理(点分布から分かるもの)まで"
13:20 - 14:10Room #122 (Mathematics building)
儀我 美一、大塚 岳 (数理科学、明治大学先端数理科学インスティチュート)
"結晶界面の成長と偏微分方程式"
14:10 - 14:40Room #122 (Mathematics building)
古場 一 (数理科学)
"成層の影響を考えたエクマン層の安定性について"
14:50 - 15:40Room #122 (Mathematics building)
O. Iliev (フラウンホーファー産業数学研究所、ドイツ)
"Flow and material simulation for industrial purposes"
2010/02/17
10:30 - 16:00Room #126 (Mathematics building)
Yves Benoist (Paris Sud) 10:30 - 11:30
"Discrete groups acting on homogeneous spaces I"
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.
I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:
We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist (Paris Sud) 15:00 - 16:00
"Discrete groups acting on homogeneous spaces II"
15:00 - 16:10Room #128 (Mathematics building)
清 智也 (東京大学 情報理工学系研究科)
"勾配写像で表される球面上の確率分布族"
球面上の確率分布族は、方向統計学において重要である。本講演では、コスト凸関数 (c-凸関数)と呼ばれる関数とその勾配写像を用いて、球面上の分布族を構成する。 コスト凸関数とは、最適輸送理論の分野で導入された概念であり、ユークリッド空間 における凸関数をリーマン多様体の場合へ拡張させたものである。提案する分布族の 性質をいくつか示し、簡単な方向データの解析例を示す。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/14.html
2010/02/16
17:30 - 18:30Room #056 (Mathematics building)
Dieter Kotschick (Univ. M\"unchen)
"Characteristic numbers of algebraic varieties"
The Chern numbers of n-dimensional smooth projective varieties span a vector space whose dimension is the number of partitions of n. This vector space has many natural subspaces, some of which are quite small, for example the subspace spanned by Hirzebruch--Todd numbers, the subspace of topologically invariant combinations of Chern numbers, the subspace determined by the Hodge numbers, and the subspace of Chern numbers that can be bounded in terms of Betti numbers. I shall explain the relation between these subspaces, and characterize them in several ways. This leads in particular to the solution of a long-standing open problem originally formulated by Hirzebruch in the 1950s.
2010/02/05
09:45 - 11:00Room #118 (Mathematics building)
Takahiro Tsushima (University of Tokyo)
"Elementary computation of ramified components of Jacobi sum Hecke characters"
11:00 - 12:15Room #118 (Mathematics building)
Tomoyuki Abe (University of Tokyo)
"Comparison between Swan conductors and characteristic cycles"
13:00 - 14:15Room #118 (Mathematics building)
宮﨑 直 (東京大学大学院数理科学研究科)
"The structures of generalized principal series representations of SL(3,R) and related Whittaker functions (SL(3,R)の一般主系列表現の構造と関連するWhittaker関数)
"
14:15 - 15:30Room #118 (Mathematics building)
長谷川 泰子 (東京大学大学院数理科学研究科)
"PRINCIPAL SERIES AND GENERALIZED PRINCIPAL SERIES WHITTAKER FUNCTIONS WITH PERIPHERAL K-TYPES ON THE REAL SYMPLECTIC GROUP OF RANK 2 (実二次シンプレクティック群上の主系列表現及び一般主系列表現の周辺的K-TYPEを持つWHITTAKER 関数)
"
09:45 - 11:00Room #122 (Mathematics building)
二木 昌宏 (東京大学大学院数理科学研究科)
"On the generalized suspension theorem for directed Fukaya categories (有向深谷圏の懸垂定理の一般化について)"
11:00 - 12:15Room #122 (Mathematics building)
松尾 信一郎 (東京大学大学院数理科学研究科)
"On the Runge theorem for instantons (インスタントンに対するRungeの近似定理について)"
11:00 - 12:15Room #126 (Mathematics building)
西岡 斉治 (東京大学大学院数理科学研究科)
"Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)"
13:00 - 14:15Room #126 (Mathematics building)
水田 有一 (東京大学大学院数理科学研究科)
"Weak Amenability for a Group Acting on a Finite Dimensional CAT(0) Cube Complex (有限次元CAT(0)方体複体に作用する群の弱従順性)"
14:15 - 15:30Room #126 (Mathematics building)
酒匂 宏樹 (東京大学大学院数理科学研究科)
"Stone-Čech boundaries of discrete groups and measure equivalence theory (離散群のストーン-チェック境界と測度同値理論)"
09:45 - 11:00Room #128 (Mathematics building)
西山 了允 (東京大学大学院数理科学研究科)
"CONSTRUCTION OF ISOTROPIC CELLULAR AUTOMATON AND ITS APPLICATION (等方セル・オートマトンの構成とその応用)"
2010/02/04
09:45 - 11:00Room #122 (Mathematics building)
久野 雄介 (東京大学大学院数理科学研究科)
"The Meyer functions for projective varieties and their applications to local signatures for fibered 4-manifolds (射影多様体に対するMeyer函数と,その局所符号数への応用)"
11:00 - 12:15Room #122 (Mathematics building)
服部 広大 (東京大学大学院数理科学研究科)
"On hyperkähler manifolds of type A∞ (A∞型超ケーラー多様体について)"
13:00 - 14:15Room #122 (Mathematics building)
篠原 克寿 (東京大学大学院数理科学研究科)
"On the index problem for C1-generic wild homoclinic classes (C1通有的に野性的なホモクリニック類の指数問題について)"
14:15 - 15:30Room #122 (Mathematics building)
佐藤 正寿 (東京大学大学院数理科学研究科)
"The abelianization of the level d mapping class group (レベルd写像類群のアーベル化)"
14:15 - 15:30Room #126 (Mathematics building)
毛 仕寛 (東京大学大学院数理科学研究科)
"Singularities for Solutions to Schrödinger Equations (シュレーディンガー方程式の解の特異性)"
15:45 - 17:00Room #126 (Mathematics building)
Si, Duc Quang (東京大学大学院数理科学研究科)
"Nevanlinna theory for holomorphic mappings and related problems (正則写像のネヴァンリンナ理論と関連する問題)"
11:00 - 12:15Room #128 (Mathematics building)
高岡 洋介 (東京大学大学院数理科学研究科)
"On existence of models for the logical system MPCL (単相格論理系におけるモデルの存在について)"
13:00 - 14:15Room #128 (Mathematics building)
岩尾 慎介 (東京大学大学院数理科学研究科)
"Exact Solutions of Ultradiscrete Integrable Systems (超離散可積分系の厳密解)"
14:15 - 15:30Room #128 (Mathematics building)
中田 庸一 (東京大学大学院数理科学研究科)
"Vertex operators and background solutions for ultradiscrete soliton equations (超離散ソリトン方程式における頂点作用素と背景解)"
2010/02/02
16:30 - 18:00Room #056 (Mathematics building)
Fanny Kassel (Orsay)
"Deformation of compact quotients of homogeneous spaces"
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting properly discontinuously.
16:30 - 18:00Room #056 (Mathematics building)
Fanny Kassel (Univ. Paris-Sud, Orsay)
"Deformation of compact quotients of homogeneous spaces"
Let G/H be a reductive homogeneous space. In all known examples, if
G/H admits compact Clifford-Klein forms, then it admits "standard"
ones, by uniform lattices of some reductive subgroup L of G acting
properly on G/H. In order to obtain more generic Clifford-Klein forms,
we prove that for L of real rank 1, if one slightly deforms in G a
uniform lattice of L, then its action on G/H remains properly
discontinuous. As an application, we obtain compact quotients of
SO(2,2n)/U(1,n) by Zariski-dense discrete subgroups of SO(2,2n) acting
properly discontinuously.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100202kassel
2010/02/01
10:30 - 12:00Room #128 (Mathematics building)
大沢健夫 (名古屋大学多元数理科学研究科)
"Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds"
16:40 - 18:10Room #126 (Mathematics building)
大川 新之介 (東大数理)
"Extensions of two Chow stability criteria to positive characteristics"
I will talk about two results on Chow (semi-)stability of cycles in positive characteristics, which were originally known in characteristic 0. One is on the stability of non-singular projective hypersurfaces of degree greater than 2, and the other is the criterion by Y. Lee in terms of the log canonical threshold of Chow divisor. A couple of examples will be discussed in detail.
16:30 - 18:00Room #002 (Mathematics building)
Timur Sadykov (Siberian Federal University)
"Bases in the solution space of the Mellin system"
I will present a joint work with Alicia Dickenstein.
We consider algebraic functions $z$ satisfying equations of the
form
\begin{equation}
a_0 z^m + a_1z^{m_1} + a_2 z^{m_2} + \ldots + a_n z^{m_n} +
a_{n+1} =0.
\end{equation}
Here $m > m_1 > \ldots > m_n>0,$ $m,m_i \in \N,$ and
$z=z(a_0,\ldots,a_{n+1})$ is a function of the complex variables
$a_0, \ldots, a_{n+1}.$ Solutions to such equations are
classically known to satisfy holonomic systems of linear partial
differential equations with polynomial coefficients. In the talk
I will investigate one of such systems of differential equations which
was introduced by Mellin. We compute the holonomic rank of the
Mellin system as well as the dimension of the space of its
algebraic solutions. Moreover, we construct explicit bases of
solutions in terms of the roots of initial algebraic equation and their
logarithms. We show that the monodromy of the Mellin system is
always reducible and give some factorization results in the
univariate case.
2010/01/29
16:30 - 17:30Room #002 (Mathematics building)
Charles Fefferman (Princeton University)
"Extension of Functions and Interpolation of Data"
Let $f$ be a given real-valued function defined on a subset of $\mathbb{R}^n$. We explain how to decide whether $f$ extends to a function $F$ in $C^m(\mathbb{R}^n)$. If such an $F$ exists, we show how to construct one.
2010/01/28
16:00 - 17:30Room #002 (Mathematics building)
清水扇丈 (静岡大学理学部)
"相転移を伴う非圧縮性2相流の線形化問題について"
氷が常圧で0度以上になると水になるなどの相転移を伴う非圧縮性2相流に対し,質量保存則, 運動量保存則, エネルギー保存則を界面を含む系全体に適用し, 線形化した方程式系について考察する. 本講演では, 線形化方程式系のL_p-L_q 最大正則性定理について述べる.
密度が異なる場合は, 法線方向の高さ関数は表面張力つき2相Stokes問題の高さ関数と同じ正則性をもち, 系は流速が支配するのに対し,密度が等しい場合は, Gibbs-Thomson補正された表面張力つき2相Stefan問題の高さ関数と同じ正則性をもち, 系は温度が支配する.
10:40 - 12:10Room #123 (Mathematics building)
Olivier Alvarez (Head of quantitative research, IRFX options Asia, BNP Paribas)
"Partial differential equations in Finance I"
1. Markov processes and Partial differential equations (PDE)
- Markov processes, stochastic differential equations and infinitesimal generator
- The Feynman Kac formula and the backward Kolmogorov equation
- The maximum principle
- Exit time problems and Dirichlet boundary conditions
- Optimal time problems and obstacle problems
2. Application to the pricing of exotic options
- The model equation
- The Black-Scholes equation : absence of arbitrage and dynamical hedging
- Recovering the Black-Scholes formula
- Pricing exotic options : Knock-out / knock-in, american, Asian, lookback
- Overview of affine models and semi-closed formulae
- Heston model : valuing European options
- The Hull White model for IR exotics : valuing zero-coupons, caplets and swaptions.
3. Finite difference methods in Finance
- Basic concepts for numerical schemes : consistency, stability, accuracy and
convergence; the Lax equivalence theorem
- Finite difference methods in dimension 1 : Explicit, implicit, Crank-Nicholson methods for the heat equation : overview, accuracy and convergence
Incorporating first-order derivatives : upwind derivative, stability
- Finite difference methods in dimension 2 : presentation of various schemes :explicit, implicit, alternating direction implicit (ADI), Hopscotch method
- Solving high dimensional linear systems :
LU decomposition, iterative methods
- Finite difference and Monte Carlo methods
4. Optimal control in finance
- Introduction to optimal control
- The dynamic programming principle and the Hamilton-Jacobi-Bellman equation
- The verification theorem and the determination of the optimal control policy
- Utility maximization and Merton's problem
- Pricing with uncertain parameters
- Pricing with transaction costs
- Finite difference methods for optimal control
13:00 - 14:10Room #122 (Mathematics building)
Olivier Alvarez (Head of quantitative research, IRFX options Asia, BNP Paribas)
"Partial differential equations in Finance II"
1. Markov processes and Partial differential equations (PDE)
- Markov processes, stochastic differential equations and infinitesimal generator
- The Feynman Kac formula and the backward Kolmogorov equation
- The maximum principle
- Exit time problems and Dirichlet boundary conditions
- Optimal time problems and obstacle problems
2. Application to the pricing of exotic options
- The model equation
- The Black-Scholes equation : absence of arbitrage and dynamical hedging
- Recovering the Black-Scholes formula
- Pricing exotic options : Knock-out / knock-in, american, Asian, lookback
- Overview of affine models and semi-closed formulae
- Heston model : valuing European options
- The Hull White model for IR exotics : valuing zero-coupons, caplets and swaptions.
3. Finite difference methods in Finance
- Basic concepts for numerical schemes : consistency, stability, accuracy and
convergence; the Lax equivalence theorem
- Finite difference methods in dimension 1 : Explicit, implicit, Crank-Nicholson methods for the heat equation : overview, accuracy and convergence
Incorporating first-order derivatives : upwind derivative, stability
- Finite difference methods in dimension 2 : presentation of various schemes :explicit, implicit, alternating direction implicit (ADI), Hopscotch method
- Solving high dimensional linear systems :
LU decomposition, iterative methods
- Finite difference and Monte Carlo methods
4. Optimal control in finance
- Introduction to optimal control
- The dynamic programming principle and the Hamilton-Jacobi-Bellman equation
- The verification theorem and the determination of the optimal control policy
- Utility maximization and Merton's problem
- Pricing with uncertain parameters
- Pricing with transaction costs
- Finite difference methods for optimal control
16:30 - 17:30Room #999 (Mathematics building)
Charles Fefferman (Princeton University)
"Extension of Functions and Interpolation of Data"
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.
Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?
Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?
What can be said about the above problems for function spaces other than $C^m(\mathbf{R}^n)$?
2010/01/27
14:40 - 16:10Room #002 (Mathematics building)
Charles Fefferman (Princeton University)
"Extension of Functions and Interpolation of Data"
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.
Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?
Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?
What can be said about the above problems for function spaces other than $C^m(\mathbf{R}^n)$?
2010/01/26
16:30 - 18:00Room #128 (Mathematics building)
Jacob S. Christiansen (コペンハーゲン大学)
"Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)"
17:00 - 18:00Room #056 (Mathematics building)
栗林 勝彦 (信州大学)
"On the (co)chain type levels of spaces"
Avramov, Buchweitz, Iyengar and Miller have introduced
the notion of the level for an object of a triangulated category.
The invariant measures the number of steps to build the given object
out of some fixed object with triangles.
Using this notion in the derived category of modules over a (co)chain
algebra,
we define a new topological invariant, which is called
the (co)chain type level of a space.
In this talk, after explaining fundamental properties of the invariant,
I describe the chain type level of the Borel construction
of a homogeneous space as a computational example.
I will also relate the chain type level of a space to algebraic
approximations of the L.-S. category due to Kahl and to
the original L.-S. category of a map.
16:30 - 18:00Room #118 (Mathematics building)
伊東一文 (大学院数理科学研究科)
"Fractional Evolution Equations and Applications 5"
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
2010/01/25
14:40 - 16:10Room #002 (Mathematics building)
Charles Fefferman (Princeton University)
"Extension of Functions and Interpolation of Data"
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.
Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?
Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?
What can be said about the above problems for function spaces other than $C^m(\mathbf{R}^n)$?
16:30 - 18:00Room #056 (Mathematics building)
伊東一文 (大学院数理科学研究科)
"Fractional Evolution Equations and Applications 4"
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
10:30 - 12:00Room #128 (Mathematics building)
Colin Guillarmou (Ecole Normale Superieure)
"Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds"
16:40 - 18:10Room #126 (Mathematics building)
權業 善範 (東大数理)
"On weak Fano varieties with log canonical singularities"
We prove that the anti-canonical divisors of weak Fano
3-folds with log canonical singularities are semiample. Moreover, we consider
semiampleness of the anti-log canonical divisor of any weak log Fano pair
with log canonical singularities. We show semiampleness dose not hold in
general by constructing several examples. Based on those examples, we propose
sufficient conditions which seem to be the best possible and we prove
semiampleness under such conditions. In particular we derive semiampleness of the
anti-canonical divisors of log canonical weak Fano 4-folds whose lc centers
are at most 1-dimensional. We also investigate the Kleiman-Mori cones of
weak log Fano pairs with log canonical singularities.
2010/01/22
16:20 - 17:50Room #117 (Mathematics building)
中川淳一 (新日本製鐵(株)技術開発本部)
"数学者と企業研究者との連携"
16:30 - 18:00Room #118 (Mathematics building)
伊東一文 (大学院数理科学研究科)
"Fractional Evolution Equations and Applications 3"
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Nonlinear evolution equations, Crandall-Ligget theory,
Locally quasi-dissipative operators approach
2010/01/21
16:30 - 18:00Room #128 (Mathematics building)
山下真 (東大数理)
"On Subfactors Arising from Asymptotic Representations of Symmetric Groups"
16:00 - 17:30Room #122 (Mathematics building)
Danielle Hilhorst (パリ南大学 / CNRS)
"A finite volume method on general meshes for a degenerate parabolic convection-reaction-diffusion equation"
We propose a finite volume method on general meshes for degenerate parabolic convection-reaction-diffusion equations. Such equations arise for instance in the modeling of contaminant transport in groundwater. After giving a convergence proof, we present the results of numerical tests.
2010/01/20
17:00 - 18:30Room #122 (Mathematics building)
Craig Van Coevering (MIT)
"Asymptotically conical manifolds and the Monge-Ampere equation"
Some analysis is considered on manifolds with a conical end. Then we show that in the Kahler case the complex Monge-Ampere equation can be solved with the same regularity as is known in the ALE case. By considering resolutions of toric singularities and hypersurface singularities this can easily be used to produce many Calabi-Yau manifolds with a conical end.
16:30 - 18:00Room #118 (Mathematics building)
伊東一文 (大学院数理科学研究科)
"Fractional Evolution Equations and Applications 2"
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Existence and Uniqueness by C_0 semigroup theory, dissipative linear
operator
and Hille-Yoshida, Trotter-Kato theory.
14:40 - 16:10Room #052 (Mathematics building)
江島啓介 (東京大学情報理工学研究科数理情報専攻修士課程)
"東京都市圏パーソントリップ調査に基づく新型インフルエンザ感染拡大シミュレーション"
新型インフルエンザの感染拡大に対する対応策として,学校施設等の閉鎖など外
出時の感染機会を減らすための措置が考えられるが,その効果は十分に明らかで
はない.そこで本研究では,individual based modelに東京都市圏パーソント
リップ調査を組み合わせることにより感染拡大モデルを構築し,数値シミュレー
ションによって外出規制および施設閉鎖の効果を検討した.外出規制に関して
は,規制日数が12日以上と長い場合には効果が大きいことがわかった.また,施
設閉鎖に関しては,閉鎖期間・閉鎖基準を厳しくすると,ピークまでの日数は変
わらないものの,累積罹患率は低下することがわかった.
2010/01/19
16:30 - 18:00Room #128 (Mathematics building)
岡田 靖則 (千葉大・理)
"超函数の有界性と Massera 型定理について"
16:30 - 18:00Room #126 (Mathematics building)
高井博司 (首都大学東京)
"Entire Cyclic Cohomology of Noncommutative Spheres"
17:00 - 18:00Room #056 (Mathematics building)
小林 亮一 (名古屋大学)
"Localization via group action and its application to
the period condition of algebraic minimal surfaces"
The optimal estimate for the number of exceptional
values of the Gauss map of algebraic minimal surfaces is a long
standing problem. In this lecture, I will introduce new ideas
toward the solution of this problem. The ``collective Cohn-Vossen
inequality" is the key idea. From this we have effective
Nevanlinna's lemma on logarithmic derivative for a certain class
of meromorphic functions on the disk. On the other hand, we can
construct a family holomorphic functions on the disk from the
Weierstrass data of the algebraic minimal surface under
consideration, which encodes the period condition.
Applying effective Lemma on logarithmic derivative to these
functions, we can extract an intriguing inequality.
16:30 - 18:00Room #118 (Mathematics building)
伊東一文 (大学院数理科学研究科)
"Fractional Evolution Equations and Applications 1"
In recent years increasing interests and considerable
researches have been given to the fractional differential equations both
in time and space variables.
These are due to the applications of the fractional calculus
to problems in a wide areas of physics and engineering science and a rapid
development of the corresponding theory. A motivating example includes
the so-called continuous time random walk process
and the Levy process model for the mathematical finance.
In this lecture we develop solution techniques based on the linear and
nonlinear semigroup theory and apply it to solve the associated inverse
and optimal control problems. The property and stability of the solutions
as well as numerical integration methods
are discussed. The lecture also covers the basis and application of the
so-called Crandall-Ligget theory and the locally quasi-dissipative
operator method developed by Kobayashi-Kobayashi-Oharu.
Motivation: Continuous time random walk (CTRW) process
Fractional differential equations in time and Mittag-Leffler functions
2010/01/18
10:30 - 12:00Room #128 (Mathematics building)
奥間智弘 (山形大学地域教育文化学部)
"スプライス商特異点について"
16:40 - 18:10Room #126 (Mathematics building)
Anne-Sophie Kaloghiros (RIMS)
"The divisor class group of terminal Gorenstein Fano 3-folds and rationality questions"
Let Y be a quartic hypersurface in CP^4 with mild singularities, e.g. no worse than ordinary double points.
If Y contains a surface that is not a hyperplane section, Y is not Q-factorial and the divisor class group of Y, Cl Y, contains divisors that are not Cartier. However, the rank of Cl Y is bounded.
In this talk, I will show that in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, the generators of Cl Y/ Pic Y are ``topological traces " of K-negative extremal contractions on X.
This has surprising consequences: it is possible to conclude that a number of families of non-factorial quartic 3-folds are rational.
In particular, I give some examples of rational quartic hypersurfaces Y_4\subset CP^4 with rk Cl Y=2 and show that when the divisor class group of Y has sufficiently high rank, Y is always rational.
2010/01/15
16:20 - 17:50Room #117 (Mathematics building)
中川淳一 (新日本製鐵(株)技術開発本部)
"製鐵プロセスにおける数学"
2010/01/14
16:30 - 18:00Room #128 (Mathematics building)
Marius Junge (Univ. Illinois, Urbana-Champaign)
"Applications of operator algebras in Quantum information theory"
2010/01/13
16:45 - 17:45Room #128 (Mathematics building)
Felix Rubin (Zurich 大学)
"Scaled limit for the largest eigenvalue from the generalized Cauchy ensemble"
15:30 - 16:30Room #128 (Mathematics building)
Michael Allman (Warwick 大学)
"Breaking the chain: slow versus fast pulling"
2010/01/12
16:30 - 18:00Room #126 (Mathematics building)
西岡斉治 (東京大学大学院数理科学研究科博士課程)
"代数的差分方程式の可解性と既約性"
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20100112nishioka
16:30 - 18:30Room #056 (Mathematics building)
篠原 克寿 (東京大学大学院数理科学研究科) 16:30 - 17:30
"Index problem for generically-wild homoclinic classes in dimension three"
In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.
二木 昌宏 (東京大学大学院数理科学研究科) 17:30 - 18:30
"On a generalized suspension theorem for directed Fukaya categories"
The directed Fukaya category $\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \to \mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\infty$-category $\mathrm{Fuk} W = \mathrm{Fuk}^\to
\mathbb{V}$ generated by a distinguished basis $\mathbb{V}$ of
vanishing cycles.
Recently Seidel has proved that this is stable under the suspension $W
+ u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\mathrm{Fuk} W \otimes'
\mathcal{A}_{d-1}$, where $\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.
2010/01/08
16:30 - 17:30Room #123 (Mathematics building)
大島利雄 (東京大学大学院数理科学研究科)
"特殊関数とFuchs型常微分方程式"
岩波全書の数学公式集III「特殊関数」の大部分はGaussの超幾何関数とその特殊化のBessel関数やLegendre多項式などで占められている。この超幾何関数についての最も重要な基本結果は1での値を与えるGaussの和公式とRiemann schemeによる特徴付けとであろう。この関数は一般超幾何関数やJordan-Pochhammer方程式へ、またHeun方程式からPainleve方程式へという解析、さらにAppell,Gelfand-青本,Heckman-Opdamによる多変数化という3つの方向の発展がある。講演ではこれらを含む統一的な理解、Riemann schemeの一般化とuniversal modelの存在定理(Deligne-Katz-Simpson問題)、接続公式(Gaussの和公式の一般化)、無限次元Kac-Moody Weyl群の作用について解説し、特異点の合流、積分表示、ベキ級数表示などについても述べたい。結果は構成的 でコンピュータ・プログラムで実現できる。
2010/01/07
16:30 - 18:00Room #128 (Mathematics building)
Luc Rey-Bellet (Univ. Massachusetts)
"Large deviations, Billiards, and Non-equilibrium Statistical Mechanics "
16:30 - 18:00Room #128 (Mathematics building)
LucRey-Bellet (Univ. Massachusetts)
"Large deviations, Billiards, and Non-equilibrium Statistical Mechanics "
Large deviations have applications in many aspects of statistical mechanics. New applications for the steady states of non-equilibrium statistical mechanics have emerged during the past ten years and these applications deal with the fluctuations of the entropy production. After discussing some general aspects of entropy production we turn to concrete examples, in particular billiards with and without external forces and discuss large deviations theorems for such systems.
2010/01/05
16:30 - 18:30Room #056 (Mathematics building)
服部 広大 (東京大学大学院数理科学研究科) 16:30 - 17:30
"The volume growth of hyperkaehler manifolds of type $A_{\infty}$"
Hyperkaehler manifolds of type $A_{\infty}$ were constructed due to Anderson-Kronheimer-LeBrun and Goto. These manifolds are 4-demensional, noncompact and their homology groups are infinitely generated. We focus on the volume growth of these hyperkaehler metrics. Here, the volume growth is asymptotic behavior of the volume of a ball of radius $r0$ with the center fixed. There are known examples of hyperkaehler manifolds whose volume growth is $r^4$ (ALE space) or $r^3$ (Taub-NUT space). In this talk we show that there exists a hyperkaehler manifold of type $A_{\infty}$ whose volume growth is $r^c$ for a given $3
松尾 信一郎 (東京大学大学院数理科学研究科) 17:30 - 18:30
"On the Runge theorem for instantons"
A classical theorem of Runge in complex analysis asserts that a
meromorphic function on a domain in the Riemann sphere can be
approximated, over compact subsets, by rational functions, that is,
meromorphic functions on the Riemann sphere.
This theorem can be paraphrased by saying that any solution of the
Cauchy-Riemann equations on a domain in the Riemann sphere can be
approximated, over compact subsets, by global solutions.
In this talk we will present an analogous result in which the
Cauchy-Riemann equations on Riemann surfaces are replaced by the
Yang-Mills instanton equations on oriented 4-manifolds.
We will also mention that the Runge theorem for instantons can be
applied to develop Yang-Mills gauge theory on open 4-manifolds.
2009/12/25
17:00 - 18:00Room #370 (Mathematics building)
Academician T. Sh. Kalmenov (Research Centre of Physics and Mathematics Almaty, Kazakhstan)
"A criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation"
2009/12/24
16:00 - 17:30Room #123 (Mathematics building)
堀内 四郎 (The City University of New York, Hunter College)
"Decomposition分析:趨勢データ分析の新しい枠組とアプローチ "
A demographic measure is often expressed as a deterministic or stochastic function of multiple variables (covariates), and a general problem (the decomposition problem) is to assess contributions of individual covariates to a difference in the demographic measure (dependent variable) between two populations.
We propose a method of decomposition analysis based on an assumption that covariates change continuously along an actual or hypothetical dimension. This assumption leads to a general model that logically justifi es the additivity of covariate effects and the elimination of interaction terms, even if the dependent variable itself is a nonadditive function.
A comparison with earlier methods illustrates other practical advantages of the method: in addition to an absence of residuals or interaction terms, the method can easily handle a large number of covariates and does not require a logically meaningful ordering of covariates. Two empirical examples show that the method can be applied fl exibly to a wide variety of decomposition problems.
http://shiro_horiuchi.homestead.com/homepage.html
2009/12/22
16:30 - 18:00Room #126 (Mathematics building)
西山享 (青山学院大学)
"既約表現の隨伴多様体は余次元1で連結か?--- 証明の破綻とその背景
"
既約 Harish-Chandra $ (g, K) $ 加群の原始イデアルの隨伴多様体が既約であって、ただ一つの冪零隨伴軌道 $ O^G $ の閉包になることはよく知られている(Joseph, Borho)。
一方、HC加群の隨伴多様体は必ずしも既約でないが、その既約成分は $ O^G $ の $ K $-等質ラグランジュ部分多様体の閉包になる。
それらの既約成分は余次元1で連結であることをいくつかの集会で報告したが、その証明には初等的な誤りがあった。セミナーでは、証明の元になった Vogan の定理の紹介(もちろん間違っていない)と、それを拡張する際になぜ証明が破綻するかについてお話しする。(今のところ証明修復の目処は立っていない。)
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
14:40 - 18:00Room #128 (Mathematics building)
谷本溶 (Univ. Roma ``Tor Vergata'') 14:40 - 16:10
" Symmetric representations of the group of diffeomorphisms of $\mathbb R$"
David Kerr (Texas A&M Univ.) 16:30 - 18:00
"Topological entropy for actions of sofic groups"
16:30 - 18:00Room #056 (Mathematics building)
寺杣 友秀 (東京大学大学院数理科学研究科)
"Relative DG-category, mixed elliptic motives and elliptic polylog"
We consider a full subcategory of
mixed motives generated by an elliptic curve
over a field, which is called the category of
mixed elliptic motives. We introduce a DG
Hopf algebra such that the categroy of
mixed elliptic motives is equal to that of
comodules over it. For the construction, we
use the notion of relative DG-category with
respect to GL(2). As an application, we construct
an mixed elliptic motif associated to
the elliptic polylog. It is a joint work with
Kenichiro Kimura.
10:00 - 14:00Room #056 (Mathematics building)
岩尾 慎介 (東大数理) 10:00 - 11:00
"離散周期KP方程式の簡約と、初期値問題の解の構成"
様々に簡約された離散周期KP方程式に対して、スペクトル曲線を用いた逆散乱解法を考える。 このとき、簡約の種類によっては、超楕円とは限らない代数曲線が多数あらわれてくる。 本講演では、簡約周期KP方程式の初期値問題の解を構成する方法を紹介する。この方法はFayの恒等式を用いない構成的なもので、わかりやすいものである。
Y. Avishai (Ben Gurion University) 13:00 - 14:00
"Laplacian on graphs: Examples from physics"
When the Laplacian operator is written as a second order difference operator the physicists refer to it as a tight-binding model. In two dimensions the eigenvalue problem connects the function at a given point to the sum of its values on its nearest neighbors. In numerous physical problems, some of the coefficients are multiplied by phase factors. This problem is amazingly rich and the pattern of eigenvalues E(φ) has a fractal nature known as the Hofstadter butterfly.
I will discuss some of these models and especially concentrate on two problems, which I solved recently, where the vertices of the graphs are located on the sphere S2. The first one corresponds to the famous problem of the Dirac magnetic monopole, while in the second one, the eigenfunctions are two component vectors and the phase factors are replaced by unitary 2x2 matrices. This is relevant to the spin-orbit problem in Physics. In both cases the solutions can be obtained in closed form, and exhibit a beautiful symmetry pattern. Their elucidation requires some special techniques in graph theory. Quite surprisingly, the spectra of the two systems coincide at one symmetry point.
2009/12/21
16:40 - 18:10Room #126 (Mathematics building)
源 泰幸 (京都大学理学部数学教室)
"Ampleness of two-sided tilting complexes"
From the view point of noncommutative algebraic geometry (NCAG),
a two-sided tilting complex is an analog of a line bundle.
In this talk we introduce the notion of ampleness for two-sided
tilting complexes over finite dimensional algebras.
From the view point of NCAG, the Serre functors are considered to be
shifted canonical bundles. We show by examples that the property
of shifted canonical bundle captures some representation theoretic
property of algebras.
15:00 - 16:10Room #128 (Mathematics building)
Thomas Simon (Universite de Lille 1)
"Absolute continuity of Ornstein-Uhlenbeck processes"
Let X be a multidimensional Ornstein-Uhlenbeck process, solution to the S.D.E.
dX = AX + dB
where A is a real nxn matrix and B a Lévy process. We show that when A is non-singular, the law of X_1 is absolutely continuous if and only if the jumping measure of B fulfils a certain geometric condition with respect to A and the Gaussian part of B, which we call the exhaustion property. This optimal criterion is much weaker than for B, which might be very singular and genuinely one-dimensional. The proof uses a certain time derivation procedure and basic arguments from controllability theory.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/13.html
2009/12/18
16:20 - 17:50Room #117 (Mathematics building)
山下 浩 (数理システム代表取締役)
"数理科学をビジネスに - 最適化とデータマイニングの周辺でⅡ"
16:30 - 17:30Room #002 (Mathematics building)
小澤登高 (東京大学大学院数理科学研究科)
"Dixmierの相似問題"
群のユニタリ表現に関しては美しい理論があるが, ユニタリでない無限次元表現はまったくとらえがたい対象である. そこで, 群のヒルベルト空間上の表現がいつユニタリ表現と相似(共役ともいう)になるかを問うのがDixmierの相似問題である. この問題は従順性という概念と深い関わりを持ち, 従って群の従順性の代数的な特徴づけを問うたvon Neumannの問題とも関わっている. von Neumannの問題は, 1980年代に否定的に解かれたものの, 近年の測度論的群論の発展により予想外の展開を見た. 講演では, これらのストーリ ーと測度論的群論の相似問題への応用(Monod氏との共同研究)を話す予定である. 予備知識はほとんど仮定しないので, 学部生にも聞きに来てもらいたい.
2009/12/17
16:30 - 18:00Room #128 (Mathematics building)
佐藤康彦 (北海道大理)
"Almost commuting unitaries and ${\mathbb{Z}}^2$-action"
16:30 - 18:00Room #126 (Mathematics building)
Alan Huckleberry (Ruhr-Universität Bochum)
"Hyperbolicity of cycle spaces and automorphism groups of flag domains"
16:00 - 17:30Room #002 (Mathematics building)
Hatem Zaag (CNRS / パリ北大学)
"A Liouville theorem for a semilinear heat equation with no gradient structure"
We prove a Liouville Theorem for entire solutions of a vector
valued semilinear heat equation with no gradient structure. Classical tools such as the maximum principle or energy techniques break down and have to be replaced by a new approach. These tools involve a very good understanding of the dynamical system formulation of the equation in the selfsimilar setting. Using the Liouville Theorem, we derive uniform estimates for blow-up solutions of the same equation.
2009/12/16
15:00 - 16:10Room #128 (Mathematics building)
Stefano Maria Iacus (Department of Economics, Business and Statistics, University of Milan, Italy)
"ecent results on volatility change point analysis for discretely sampled stochastic differential equations"
In this seminar we review recent advances on change point analysis for the volatility component of stochastic differential equations under different discrete sampling schemes. We consider both ergodic and high frequency and non ergodic cases. Results have been obtained by means of least squares, CUSUM tests and quasi-maximum likelihood approach. We show an application to the recent financial crisis and finally present a Monte Carlo study to compare the three methods under different setups.
Join work with Prof. Nakahiro Yoshida.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/12.html
2009/12/15
17:00 - 18:00Room #056 (Mathematics building)
砂田利一氏 (明治大学理工学部)
"Open Problems in Discrete Geometric Analysis"
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20091215sunada
17:00 - 18:00Room #056 (Mathematics building)
砂田 利一 (明治大学)
"Open Problems in Discrete Geometric Analysis"
Discrete geometric analysis is a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability. This field concerns solely analysis on graphs, a synonym of "1-dimensional cell complex". In this talk, I shall discuss several open problems related to the discrete Laplacian, a "protagonist" in discrete geometric analysis. Topics dealt with are 1. Ramanujan graphs, 2. Spectra of covering graphs, 3. Zeta functions of finitely generated groups.
2009/12/14
14:00 - 15:10Room #128 (Mathematics building)
L. VOSTRIKOVA (LAREMA, Departement de Mathematiques, Universite d’Angers, FRANCE)
"On the stability of contingent claimes in incomplet models under statistical estimations."
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure P and corresponding martingale measure Q change to tilde{P} and tilde{Q} respectively. Then, we estimate L1 distance of option’s prices for corresponding parametric models with known and estimated parameters. The results are applied to exponential Levy models with special choise of martingale measure as Esscher measure, minimal entropy measure and f^q -minimal martingale measure. We illustrate our results by considering GMY and CGMY models.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/11.html
14:40 - 16:10Room #126 (Mathematics building)
Sergey Galkin (IPMU)
"Invariants of Fano varieties via quantum D-module"
We will introduce and compute Apery characteristic
class and Frobenius genera - invariants of Fano variety derived from
it's Gromov-Witten invariants. Then we will show how to compute them
and relate with other invariants.
2009/12/11
16:20 - 17:50Room #117 (Mathematics building)
山下 浩 (数理システム代表取締役 )
"数理科学をビジネスに - 最適化とデータマイニングの周辺でⅠ"
2009/12/10
10:40 - 12:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (9)"
16:30 - 18:00Room #128 (Mathematics building)
張欽 (東大数理)
"Symmetric norms and spaces of operators modelled on a semifinite von Neumann algebra"
2009/12/09
14:40 - 16:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (8)"
15:00 - 16:10Room #002 (Mathematics building)
佐藤 整尚 (統計数理研究所)
"分離情報最尤法を使った高頻度金融データにおける実現分散、共分散の推定について"
近年、金融データを使った分析の中で、高頻度データを用いるものが多くなってきている。 しかしながら、通常のヒストリカルな推定法で求めた分散、共分散ではバイアスが発生することが知られており、その一致推定量を求めることがこの分野で盛んに研究されてきている。 本報告では新たに開発された分離情報最尤法(SIML)を用いた推定法を紹介するとともにその性質に関して議論していきたい。さらに、非常に広範囲な応用可能性についても紹介する。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/10.html
2009/12/08
14:40 - 16:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (7)"
17:30 - 19:00Room #002 (Mathematics building)
Giovanni Felder (ETH Zurich)
"Gaudin subalgebras and stable rational curves."
We show that Abelian subalgebras of maximal dimensions spanned by generators of the n-th Kohno-Drinfeld Lie algebra are classified by the Grothendieck-Knudsen moduli space of stable rational curves with n+1 marked points. I will explain the relation with Gaudin integrable systems of statistical mechanics and the representation theory of the symmetric group in the formulation of Vershik and Okounkov. The talk is based on joint work with Leonardo Aguirre and Alexander Veselov.
2009/12/07
17:30 - 19:00Room #002 (Mathematics building)
Weiping Zhang (Chern Institute of Mathematics, Nankai University)
"Geometric quantization on noncompact manifolds"
We will describe our analytic approach with Youlinag Tian to the Guillemin-Sternberg geometric quantization conjecture which can be summarized as "quantization commutes with reduction". We will aslo describe a recent extension to the case of noncompact symplectic manifolds. This is a joint work with Xiaonan Ma in which we solve a conjecture of Vergne mentioned in her ICM2006 plenary lecture.
2009/12/03
16:30 - 18:00Room #128 (Mathematics building)
見村万佐人 (東大数理)
"Vanishing of quasi-homomorphisms and the stable commutator
lengths on special linear groups over euclidean rings"
2009/12/02
10:30 - 11:30Room #056 (Mathematics building)
Juergen Saal (University of Konstanz)
"A hyperbolic fluid model based on Cattaneo's law"
In various applications a delay of the propagation speed of a fluid (temperature, ...) has been observed. Such phenomena cannot be described by standard parabolic models, whose derivation relies on Fourier's law (Paradoxon of infinite propagation speed).
One way to give account to these observations and which was successfully applied to several models, is to replace Fourier's law by the law of Cattaneo. In the case of a fluid, this leads to a hyperbolicly perturbed quasilinear Navier-Stokes system for which existence and uniqueness results will be presented.
2009/12/01
16:30 - 18:00Room #056 (Mathematics building)
Andrei Pajitnov (Univ. de Nantes)
"Non-Abelian Novikov homology"
Classical construction of S.P. Novikov
associates to each circle-valued Morse map
a chain complex defined over a ring
of Laurent power series in one variable.
In this survey talk we shall explain several
results related to the construction and
properties of non-Abelian generalizations of the
Novikov complex.
2009/11/30
10:30 - 12:00Room #128 (Mathematics building)
奥山裕介 (京都工芸繊維大学)
"Equidistribution and Nevanlinna theory"
16:30 - 18:00Room #002 (Mathematics building)
Junya Yagi (Rutgers University)
"Chiral Algebras of (0,2) Models: Beyond Perturbation Theory"
The chiral algebras of two-dimensional sigma models with (0,2)
supersymmetry are infinite-dimensional generalizations of the chiral
rings of (2,2) models. Perturbatively, they enjoy rich mathematical
structures described by sheaves of chiral differential operators.
Nonperturbatively, however, they vanish completely for certain (0,2)
models with no left-moving fermions. In this talk, I will explain how
this vanishing phenomenon takes places. The vanishing of the chiral
algebra of a (0, 2) model implies that supersymmetry is spontaneously
broken in the model, which in turn suggests that no harmonic spinors
exist on the loop space of the target space. In particular, the
elliptic genus of the model vanishes, thereby providing a physics
proof of a special case of the Hoelhn-Stolz conjecture.
2009/11/27
16:20 - 17:50Room #117 (Mathematics building)
池森俊文氏(高野 康 氏) (みずほ第一フィナンシャルテクノロジー(株))
"金融リスク管理と数理(実践)"
13:40 - 14:50Room #128 (Mathematics building)
加藤 賢悟 (広島大学大学院理学研究科数学専攻)
"非線形時系列モデルのイノベーション密度の推定"
In this talk, we consider the problem of estimating the innovation density in nonlinear autoregressive models. Specifically, we establish the convergence rate of the supremum distance between the residual-based kernel density estimator and the kernel density estimator using the unobservable actual innovation variables. The proof of the main theorem relies on empirical process theory instead of the conventional Taylor expansion approach. As applications, we obtain the exact rate of weak uniform consistency on the whole line, pointwise asymptotic normality of the residual-based kernel density estimator and the asymptotic distribution of a Bickel-Rosenblatt type global measure statistic related to it. We also examine the conditions of the main theorem for some specic time series model.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/09.html
2009/11/26
16:00 - 17:30Room #002 (Mathematics building)
小池 茂昭 (埼玉大学・理学部数学科)
"L^p 粘性解の弱ハルナック不等式の最近の進展"
Caffarelli による粘性解の regularity 研究 (1989 年) を基に, 1996 年に Caffarelli- Crandall-Kocan-Swiech によって L^p 粘性解の概念が導入された. L^p 粘性解とは, 通 常の粘性解理論では扱えなかった, 非有界非斉次項を持つ (非発散型) 偏微分方程 式にも適用可能な弱解である.
しかしながら, 係数に関しては有界係数しか研究されていなかった. その後, Swiech との共同研究により, 係数が非有界だが適当なべき乗可積分性を仮定して Aleksandrov-Bakelman-Pucci 型の最大値原理を導くことが可能になった.
本講演では, 非有界係数・非斉事項を持った, 完全非線形 2 階一様楕円型方程式 の L^p 粘性解の弱ハルナック不等式に関する最近のSwiech との共同研究の結果を紹 介する.
2009/11/25
10:30 - 11:30Room #056 (Mathematics building)
Hermann Sohr (University Paderborn)
"Recent results on weak and strong solutions of the Navier-Stokes equations"
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.
This condition is not only sufficient
- there are several well-known sufficient conditions in this context
- but also necessary, and yields therefore the largest possible class of such strong solutions.
As an application we obtain several extensions of Serrin's regularity condition. A restricted result also holds for completely general domains. Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.
2009/11/24
16:30 - 18:00Room #128 (Mathematics building)
吉野 邦生 (東京都市大学)
"Analytic Properties of Eigen Values of Daubechies Localization Operator"
1)ドーベシー局在化作用素の固有値の解析的性質、積分表示式、
(2)ドーベシー局在化作用素のシンボルの再現公式、
(3)ドーベシー局在化作用素のバーグマンーフォック空間での表示
等について述べる。
16:30 - 18:00Room #056 (Mathematics building)
Adam Clay (University of British Columbia)
"A topological approach to left orderable groups"
A group G is said to be left orderable if there is a strict
total ordering of its elements such that g
in G. Left orderable groups have been useful in solving many problems in topology, and now we find that topology is returning the favour: the set of all left orderings of a group is denoted by LO(G), and it admits a natural topology, under which LO(G) becomes a compact topological
space. In general, the structure of the space LO(G) is not well understood, although there are surprising results in a few special cases.
For example, the space of left orderings of the braid group B_n for n>2
contains isolated points (yet it is uncountable), while the space of left
orderings of the fundamental group of the Klein bottle is finite.
Twice in recent years, the space of left orderings has been used very
successfully to solve difficult open problems from the field of left
orderable groups, even though the connection between the topology of LO(G) and the algebraic properties of G was still unclear. I will explain the
newest understanding of this connection, and highlight some potential
applications of further advances.
2009/11/20
16:20 - 17:50Room #117 (Mathematics building)
池森俊文 (みずほ第一フィナンシャルテクノロジー(株)取締役社長)
"金融リスク管理と数理(概論)"
16:30 - 17:30Room #002 (Mathematics building)
Louis Nirenberg
(New York University)
"On solving fully nonlinear elliptic Partial Differential Equations
"
The talk will present some results in recent work by R.Harvey and B. Lawson: Dirichlet duality and the nonlinear Dirichlet problem, Comm. Pure Appl. Math. 62 (2009), 396-443. It concerns solving boundary value problems for elliptic equations of the form F(D'2u) = 0. They find generalized solutions which are merely continuous . The talk will be expository. No knowledge of Partial Differential Equations will be necessary.
2009/11/19
15:00 - 16:00Room #123 (Mathematics building)
阿部知行 (東京大学大学院数理科学研究科)
"数論的D加群の特性サイクルと分岐理論
"
2009/11/18
15:30 - 17:00Room #128 (Mathematics building)
Herbert Spohn (ミュンヘン工科大学・九州大学)
"The stochastic Burgers equation and its discretization"
16:30 - 18:45Room #056 (Mathematics building)
津嶋 貴弘 (東京大学大学院数理科学研究科) 16:30 - 17:30
"Elementary computation of ramified component of the Jacobi sum"
R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.
Christopher Deninger (Universität Münster) 17:45 - 18:45
"P-divisible groups and the p-adic Corona problem"
2009/11/17
16:30 - 18:00Room #056 (Mathematics building)
高田 敏恵 (新潟大学)
"On the $SO(N)$ and $Sp(N)$ free energy of a closed oriented 3-manifold"
We give an explicit formula of the $SO(N)$ and $Sp(N)$ free energy
of a lens space and show that the genus $g$ terms of it are analytic
in a neighborhood at zero, where we can choose the neighborhood
independently of $g$.
Moreover, it is proved that for any closed oriented 3-manifold $M$
and any $g$, the genus $g$ terms of $SO(N)$ and $Sp(N)$ free energy
of $M$ coincide up to sign.
2009/11/16
10:30 - 12:00Room #128 (Mathematics building)
上野康平 (京都大学大学院理学研究科)
"Weighted Green functions of polynomial skew products on C^2"
16:40 - 18:10Room #126 (Mathematics building)
Colin Ingalls (University of New Brunswick and RIMS)
"Rationality of the Brauer-Severi Varieties of Skylanin algebras"
Iskovskih's conjecture states that a conic bundle over
a surface is rational if and only if the surface has a pencil of
rational curves which meet the discriminant in 3 or fewer points,
(with one exceptional case). We generalize Iskovskih's proof that
such conic bundles are rational, to the case of projective space
bundles of higher dimension. The proof involves maximal orders
and toric geometry. As a corollary we show that the Brauer-Severi
variety of a Sklyanin algebra is rational.
2009/11/14
13:30 - 16:00Room #117 (Mathematics building)
岡崎武生 (京都大学) 13:30 - 14:30
"On weak endoscopic lift (117号室)"
rank 2のsymplectic 群の保型表現$\pi$の spinor L-関数(4次)が殆どの素点で楕円保型形式のL-関数の積になっているものをweak ndoscopic liftと呼びます. $\pi$がtemperedならば, 全てのweak endoscopic liftはrank 4のtheta関数(theta lift)でかける事がBrooks Roberts氏により知られています.
本公演では, このtheta liftの明示的な構成法やその周辺に関する話題(Siegel 三次多様体など)についてお話したいと思います.
井原健太郎 (POSTEC) 15:00 - 16:00
"Derivations and Automorphisms on the noncommutative algebra of power series.
"
We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim is the explicit description of the
automorphisms which are corresponding to the derivations via exponential map.
2009/11/12
10:40 - 12:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (6)"
16:30 - 18:00Room #128 (Mathematics building)
酒匂宏樹 (東大数理)
"Recent results for amalgamated free products of type II$_1$ factors"
2009/11/11
14:40 - 16:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (5)"
2009/11/10
14:40 - 16:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (4)"
16:30 - 18:00Room #056 (Mathematics building)
Alexander Getmanenko (IPMU)
"Resurgent analysis of the Witten Laplacian in one dimension"
I will recall Witten's approach to the Morse theory through properties of a certain differential operator. Then I will introduce resurgent analysis -- an asymptotic method used, in particular, for studying quantum-mechanical tunneling. In conclusion I will discuss how the methods of resurgent analysis can help us "see" pseudoholomorphic discs in the eigenfunctions of the Witten Laplacian.
2009/11/09
16:30 - 18:00Room #002 (Mathematics building)
Makoto Sakurai (東京大学大学院数理科学研究科)
"Differential Graded Categories and heterotic string theory"
The saying "category theory is an abstract nonsense" is even physically not true.
The schematic language of triangulated category presents a new stage of string theory.
To illuminate this idea, I will draw your attention to the blow-up minimal model
of complex algebraic surfaces. This is done under the hypothetical assumptions
of "generalized complex structure" of cotangent bundle due to Hitchin school.
The coordinate transformation Jacobian matrices of the measure of sigma model
with spin structures cause one part of the gravitational "anomaly cancellation"
of smooth Kahler manifold $X$ and Weyl anomaly of compact Riemann surface $\Sigma$.
$Anom = c_1 (X) c_1 (\Sigma) \oplus ch_2 (X)$,
in terms of 1st and 2nd Chern characters. Note that when $\Sigma$ is a puctured disk
with flat metric, the chiral algebra is nothing but the ordinary vertex algebra.
Note that I do not explain the complex differential geometry,
but essentially more recent works with the category of DGA (Diffenreial Graded Algebra),
which is behind the super conformal field theory of chiral algebras.
My result of "vanishing tachyon" (nil-radical part of vertex algebras)
and "causality resortation" in compactified non-critical heterotic sigma model
is physically a promising idea of new solution to unitary representation of operator algebras.
This idea is realized in the formalism of BRST cohomology and its generalization
in $\mathcal{N} = (0,2)$ supersymmetry, that is, non-commutative geometry
with non-linear constraint condition of pure spinors for covariant quantization.
2009/11/07
13:30 - 16:00Room #117 (Mathematics building)
Andrei Marshakov (Lebedev Physical Institute) 13:30 - 14:30
"Tau-functions of Toda theories, partitions and conformal blocks"
I discuss the class of tau-functions,
corresponding to special solutions of integrable systems,
related to Hurwitz numbers and supersymmetric Yang-Mills
theories. Their natural generalization turn to coincide with
the conformal blocks of two-dimensional conformal
field theories. In special case these conformal
blocks turn into the scalar products of certain ``coherent
states'' in the highest-weight module of the Virasoro
algebra, generalizing the matrix elements
for the well-known coherent states in Fock spaces.
TBA (TBA) 15:00 - 16:00
"TBA"
TBA
2009/11/05
16:20 - 17:50Room #056 (Mathematics building)
藤原 洋 (インターネット総合研究所代表取締役所長)
"社会における学位取得者の役割Ⅱ"
16:00 - 17:30Room #002 (Mathematics building)
大西 勇 (広島大学大学院理学研究科)
"A Mathematical Aspect of the One-Dimensional Keller and Rubinow Model for Liesegang Bands"
In 1896, colloid-chemist R.E. Liesegang [4] observed strikingly
regular patterns in precipitation-reaction processes, which are referred to as Liesegang bands or rings, according to their shape. In this talk I introduce an attempt to understand from a mathematical viewpoint the experiments in which regularized structures with spatially distinct bands of precipitated material are exhibited, with clearly visible scaling properties. This study is a result [1] of a collaboration with Professors D. Hilhorst, R. van der Hout, and M. Mimura.
References:
[1] Hilhorst, D., van der Hout, R., Mimura, M., and Ohnishi, I.: A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands. J. Stat Phys 135: 107-132 (2009)
[2] Kai, S., Muller, S.C.: Spatial and temporal macroscopic structures in chemical reaction system: precipitation patterns and interfacial motion. Sci. Form 1, 8-38 (1985)
[3] Keller, J.B., Rubinow, S.I.: Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, 5000-5007 (1981)
[4] Liesegang, R.E.: Chemische Fernwirkung. Photo. Archiv 800, 305-309 (1896)
[5] Mimura, M., Ohnishi, I., Ueyama, D.: A mathematical aspect of Liesegang phenomena in two space dimensions. Res. Rep. Res. Inst. Math. Sci. 1499, 185-201 (2006)
[6] Ohnishi, I.,Mimura, M.: A mathematical aspect of Liesegang phenomena. In: Proceedings of Equadiff-11, pp. 343-352 (2005).
2009/11/04
16:30 - 18:00Room #128 (Mathematics building)
Gert Heckman (IMAPP, Faculty of Science, Radboud University Nijmegen)
"Birational Hyperbolic Geometry"
We study compactifications for complex ball quotients.
We first recall the Satake-Bailey-Borel compactification and the Mumford resolution.
Then we discuss compactifications of ball quotients minus a totally geodesic divisor.
These compactifications turn up for a suitable class of period maps.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009/11/02
16:40 - 18:10Room #126 (Mathematics building)
Gerard van der Geer (Universiteit van Amsterdam)
"Cohomology of moduli spaces of curves and modular forms"
The Eichler-Shimura theorem expresses cohomology of local systems
on the moduli of elliptic curves in terms of modular forms. The
cohomology of local systems can be succesfully explored by counting
points over finite fields. We show how this can be applied to
obtain a lot of information about the cohomology of other moduli spaces
of low genera and also about Siegel modular forms of genus 2 and 3.
This is joint work with Jonas Bergstroem and Carel Faber.
2009/10/30
16:20 - 17:50Room #117 (Mathematics building)
辻 芳彦 ((社)日本アクチュアリー会事務局事務局長)
"アクチュアリーの役割Ⅱ"
15:00 - 16:00Room #370 (Mathematics building)
Shuai Lu (Johann Radon Institute)
"Regularized total least squares: computational aspects and error bounds"
For solving linear ill-posed problems, regularization methods are required when the right hand side and/or the operator are corrupted by some noise. In the present talk, regularized solutions are constructed using regularized total least squares and dual regularized total least squares. We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, dual RTLS and the standard Tikhonov regularization.
2009/10/29
16:30 - 18:00Room #128 (Mathematics building)
Robert Coquereaux (CNRS/CPT, Marseille)
"Fusion graphs for Lie groups at level k and quantum symmetries"
16:30 - 17:30Room #270 (Mathematics building)
Michael I. Tribelsky (MIREA (Technical University), Moscow, Russia)
"Spectral properties of Nikolaevskiy chaos"
2009/10/28
16:30 - 17:30Room #370 (Mathematics building)
Michael Ruzhansky (Imperial College, London)
"Dispersive and Strichartz estimates for hyperbolic equations of general form"
2009/10/27
16:30 - 18:00Room #056 (Mathematics building)
Alex Bene (IPMU)
"A new appearance of the Morita-Penner cocycle"
In this talk, I will recall the Morita-Penner cocycle on the dual fatgraph complex for a surface with one boundary component. This cocycle, when restricted to paths representing elements of the mapping class group, represents the extended first Johnson homomorphism \tau_1, thus can be viewed as a (in some specific sense canonical) "groupoid extension" of \tau_1. There are now several different contexts in which this cocycle can be constructed, and in this talk I will briefly review several of them, including one discovered in the context of finite type invariants of homology cylinders in joint work with J.E. Andersen, J-B. Meilhan, and R.C. Penner.
2009/10/26
10:30 - 12:00Room #128 (Mathematics building)
Pietro Corvaja (Università di Udine)
"On Vojta's conjecture in the split function field case"
2009/10/23
16:20 - 17:50Room #117 (Mathematics building)
辻 芳彦 ((社)日本アクチュアリー会事務局事務局長)
"アクチュアリーの役割Ⅰ"
16:30 - 17:30Room #002 (Mathematics building)
辻 雄 (東京大学大学院数理科学研究科)
"p進エタール層のp進Hodge理論"
複素や実の多様体の特異コホモロジーを微分形式の言葉で記述する理論として、de Rhamの定理やHodge理論が良く知られている。p進Hodge理論は、これらの類似をp進体上の代数多様体のp進エタール・コホモロジーで考える理論である。p進エタール・コホモロジーにはp進体の絶対ガロア群が非常に複雑に作用しており、この作用を分かりやすい別の言葉で記述する理論の構築が、p進Hodge理論における大きな課題となっている。前半でp進Hodge理論の研究の歴史や背景について概観した後、後半ではp進体の絶対ガロア群のp進表現の相対版である、p進体上定義された代数多様体上のp進エタール層についての最近の研究を紹介する。
15:00 - 16:10Room #128 (Mathematics building)
Vladimir Bogachev (Moscow State University)
"On invariant measures of diffusion processes with unbounded drifts"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/08.html
2009/10/22
16:30 - 18:00Room #128 (Mathematics building)
Adam Skalski (Lancaster University)
"On some questions related to Voiculescu's noncommutative topological entropy"
10:40 - 12:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (3)"
16:30 - 17:40Room #122 (Mathematics building)
深澤 正彰 (大阪大学 金融・保険教育研究センター)
"ASYMPTOTICALLY EFFICIENT DISCRETE HEDGING"
The notion of asymptotic efficiency for discrete hedging is introduced and a discretizing strategy which is asymptotically efficient is given explicitly. A lower bound for asymptotic risk of discrete hedging is given, which is attained by a simple discretization scheme. Numerical results for delta hedging in the Black-Scholes model are also presented.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/07.html
13:00 - 14:15Room #122 (Mathematics building)
深澤 正彰 (大阪大学 金融・保険教育研究センター)
"Asymptotic Analysis for Stochastic Volatility (確率的ボラティティの漸近解析)"
2009/10/21
15:30 - 17:00Room #122 (Mathematics building)
Jean-Dominique Deuschel (TU Berlin)
"Mini course on the gradient models, Ⅲ: Non convex potentials at high temperature"
In the non convex case, the situation is much more complicated. In fact Biskup and Kotecky describe a non convex model with several ergodic components. We investigate a model with non convex interaction for which unicity of the ergodic component, scaling limits and large deviations can be proved at sufficiently high temperature. We show how integration can generate strictly convex potential, more precisely that marginal measure of the even sites satisfies the random walk representation. This is a joint work with Codina Cotar and Nicolas Petrelis.
16:30 - 17:30Room #056 (Mathematics building)
Bernard Le Stum (Université de Rennes 1)
"The local Simpson correspondence in positive characteristic"
A Simpson correspondance should relate Higgs bundles to differential modules (or local systems). We stick here to positive characteristic and recall some old and recent results : Cartier isomorphism, Van der Put's classification, Kaneda's theorem and Ogus-Vologodsky local theory. We'll try to explain how the notion of Azumaya algebra is a convenient tool to unify these results. Our main theorem is the equivalence between quasi-nilpotent differential modules of level m and quasi-nilpotent Higgs Bundles (depending on a lifting of Frobenius mod p-squared). This result is a direct generalization of the previous ones. The main point is to understand the Azumaya nature of the ring of differential operators of level m. Following Berthelot, we actually use the dual theory and study the partial divided power neighborhood of the diagonal.
14:40 - 16:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (2)"
15:00 - 16:10Room #002 (Mathematics building)
田中 冬彦 (科学技術振興機構さきがけ)
"AR過程の優調和事前分布と偏自己相関係数による表示"
Tanaka and Komaki(2008)では時系列データが2次の自己回帰過程(AR過程)に従う 時のスペクトル密度の推定を考え、優調和事前分布に基づいたベイズスペクトル 密度の方がジェフリーズ事前分布に基づいたベイズスペクトル密度よりも精度よ く推定できることを示している。高次のAR過程での優調和事前分布はTanaka( 2009)によって初めて与えられたが、特性方程式の根を用いた表示のため、数値 実験を行う上では取り扱いづらかった。本発表では高次のAR過程への応用を念頭 において偏自己相関係数(PAC)によるパラメータ表示を導入し数値実験した結 果を紹介する。 また、PACパラメータによる表示は解析的な取扱いをする上でも利点があり、AR 過程の優調和事前分布に関して新しく得られた結果も幾つか紹介したい。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/06.html
2009/10/20
16:30 - 18:00Room #056 (Mathematics building)
吉田 尚彦 (明治大学大学院理工学研究科)
"Torus fibrations and localization of index"
I will describe a localization of index of a Dirac type operator.
We make use of a structure of torus fibration, but the mechanism
of the localization does not rely on any group action. In the case of
Lagrangian fibration, we show that the index is described as a sum of
the contributions from Bohr-Sommerfeld fibers and singular fibers.
To show the localization we introduce a deformation of a Dirac type
operator for a manifold equipped with a fiber bundle structure which
satisfies a kind of acyclic condition. The deformation allows an
interpretation as an adiabatic limit or an infinite dimensional analogue
of Witten deformation.
Joint work with Hajime Fujita and Mikio Furuta.
14:40 - 16:10Room #128 (Mathematics building)
竹崎正道 (UCLA)
"冨田竹崎理論とその応用 (1)"
2009/10/19
10:30 - 12:00Room #128 (Mathematics building)
濱野佐知子 (松江高専)
"Variation formulas for principal functions (II)"
16:40 - 18:10Room #126 (Mathematics building)
渡辺 究 (早稲田大学基幹理工学研究科)
"ファノ多様体上の有理曲線の鎖の長さについて"
ピカール数1のファノ多様体に対し、一般の二点を結ぶために必要な
極小有理曲線の本数を「長さ」と呼び、それについて考える。特に、5次元以下の
ファノ多様体や余指数が3以下のファノ多様体などに対し、長さを求める。
2009/10/15
16:20 - 17:50Room #056 (Mathematics building)
藤原 洋 (インターネット総合研究所代表取締役所長)
"社会における学位取得者の役割Ⅰ"
16:30 - 18:00Room #122 (Mathematics building)
土岡俊介 (RIMS, Kyoto University)
"Hecke-Clifford superalgebras and crystals of type $D^{(2)}_{l}$"
It is known that we can sometimes describe the representation theory of ``Hecke algebra'' by ``Lie theory''. Famous examples that involve the Lie theory of type $A^{(1)}_n$ are Lascoux-Leclerc-Thibon's interpretation of Kleshchev's modular branching rule for the symmetric groups and Ariki's theorem generalizing Lascoux-Leclerc-Thibon's conjecture for the Iwahori-Hecke algebras of type A.
Brundan and Kleshchev showed that some parts of the representation theory of the affine Hecke-Clifford superalgebras and its finite-dimensional ``cyclotomic'' quotients are controlled by the Lie theory of type $A^{(2)}_{2l}$ when the quantum parameter $q$ is a primitive $(2l+1)$-th root of unity.
In this talk, we show that similar theorems hold when $q$ is a primitive $4l$-th root of unity by replacing the Lie theory of type $A^{(2)}_{2l}$ with that of type $D^{(2)}_{l}$.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009/10/14
15:30 - 17:00Room #128 (Mathematics building)
Claudio Landim (IMPA, Brazil)
"Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅳ"
13:30 - 15:00Room #128 (Mathematics building)
Jean-Dominique Deuschel (TU Berlin)
"Mini course on the gradient models, Ⅱ: Convex interaction potential"
Much is known for strictly convex interactions, which under rescaling behave much like the harmonic model. In particular the unicity of the ergodic component have been established by Funaki and Spohn, and the scaling limit to the gradient of the continuous gaussian free field by Naddaf and Spencer. The results are based on special analytical and probabilistic tools such as the Brascamp-Lieb inequality and the Hellfer-Sj\"osstrand random walk representation. These techniques rely on the strict convexity of the interaction potential.
14:45 - 18:00Room #056 (Mathematics building)
近藤剛史 (Kondo Takefumi) (神戸大学大学院理学研究科) 14:45 - 16:15
"Fixed point theorems for non-positively curved spaces and random groups"
It is not easy to construct a finitely generated group with a fixed point property for non-positively curved spaces. However, if we randomly choose relators, then we can get examples of such groups. To show this, we need a criterion for deducing a fixed point property from a local property of a group. In this talk, we will introduce one such criterion, and our approach is via a scaling limit argument.
赤穂まなぶ (Akaho Manabu) (首都大学東京大学院理工学研究科) 16:30 - 18:00
"Lagrangian mean curvature flow and symplectic area"
In this talk, we consider symplectic area of smooth maps from a Riemann surface with boundary on embedded Lagrangian mean curvature flow in Kahler-Einstein manifolds. As an application, we observe a relation between embedded Lagrangian mean curvature flow and Floer theory of monotone Lagrangian submanifolds in Kahler-Einstein manifolds; in this case non-trivial holomorphic discs turn out to be an obstruction to the existence of long time solution of the flow.
16:30 - 17:30Room #370 (Mathematics building)
O. Emanouilov (Colorado State University)
"Partial Cauchy data for general second order elliptic operators in two dimensions"
We consider the problem of determining the coefficients of a first-order perturbation of the Laplacian in two dimensions by measuring the corresponding Cauchy data on an arbitrary open subset of the boundary. From this information we obtained a coupled PDE system of first order which the coefficients satisfy. As a corollary we show for the magnetic Schr"odinger equation that the magnetic field and the electric potential are uniquely determined by measuring the partial Cauchy data on an arbitrary part of the boundary. We also show that the coefficients of any real vector field perturbation of the Laplacian, the convection terms, are uniquely determined by their partial Cauchy data.
2009/10/13
16:30 - 18:00Room #056 (Mathematics building)
笹平 裕史 (東京大学大学院数理科学研究科)
"Instanton Floer homology for lens spaces"
Let Y be an oriented closed 3-manifold and P be an SU(2)-bundle on Y. Under a certain condition, instanton Floer homology for Y can be defined as the Morse homology of the Chern-Simons functional. The condition is that all flat connections on P are irreducible. When there is a reducible flat connection on P, instanton Floer homology is not defined in general.
Since the fundamental group of a lens sapce is commutative, all flat connections on the lens space are reducible. In this talk I will introduce instanton Floer homology for lens spaces. I also show calculations for some lens spaces.
16:30 - 18:00Room #126 (Mathematics building)
小寺諒介 (東京大学)
"Extensions between finite-dimensional simple modules over a generalized current Lie algebra
"
$\mathfrak{g}$を$\mathbb{C}$上の有限次元半単純Lie代数,$A$を有限生成可換$\mathbb {C}$代数とする.
テンソル積$A \otimes \mathfrak{g}$に自然にLie代数の構造を与えたものを一般化されたカレントLie代数と呼ぶ.
一般化されたカレントLie代数の任意の2つの有限次元既約表現に対して,その1次のExt群を完全に決定することができたので,その結果について発表する.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009/10/09
16:20 - 17:50Room #117 (Mathematics building)
岡本龍明 (NTT 情報流通プラットフォーム研究所 岡本特別研究室長)
"暗号の実践編"
16:30 - 17:30Room #128 (Mathematics building)
Michel Duflo (Paris 7)
"Associated varieties for Representations of classical Lie
super-algebras"
In this lecture, I'll discuss the notion of "Associated
varieties for Representations of classical Lie super-algebras (joint work with Vera Serganova)" and the relation with the degree of atypicality. This is related to a conjecture of Kac and Wakimoto.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009/10/07
10:30 - 11:30Room #056 (Mathematics building)
劉和平(Liu Heping) (Beijing University)
"Wiener measure and Feynman-Kac formula on the Heisenberg group"
It is well known that the Feynman-Kac formula on the Euclidean space gives the solution of Schrodinger equation by the Wiener integral. We will discuss the Wiener measure and Feynman-Kac formula on the Heisenberg group. The results hold on the H-type groups.
16:30 - 17:30Room #128 (Mathematics building)
Michel Duflo (Paris 7)
"Representations of classical Lie super-algebras
"
In this lecture, I'll survey classical topics on finite dimensional representations of classical Lie super-algebras, in particular the notion of the degree of atypicality.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
16:30 - 17:30Room #056 (Mathematics building)
Ahmed Abbes (Université de Rennes 1)
"On GAGA theorems for the rigide-étale topology"
Last year, I finished my course in Todai on "Rigide Geometry following M. Raynaud" by stating a GAGA theorem for the rigide-étale topology, due to Gabber and Fujiwara. I will give a new proof of this theorem, inspired by another theorem of Gabber, namely the Affine analog of the proper base change theorem.
2009/10/05
15:30 - 17:00Room #128 (Mathematics building)
Claudio Landim (IMPA, Brazil)
"Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅲ"
13:30 - 15:00Room #128 (Mathematics building)
Jean-Dominique Deuschel (TU Berlin)
"Mini course on the gradient models, I: Effective gradient models, definitions and examples"
We describe a phase separation in $R^{d+1}$ by an effective interface model with basis in $Z^d$ and height in $R$. We assume that the interaction potential depends only on the discrete gradient and that the a priori measure is the product Lebesgue measure. Note that this is an unbounded massless model with continuous symmetry and this implies that the interface is delocalized for the infinite model in lower lattice dimensions $d=1,2$. Instead of looking at the distribution of the height of the interface itself, we consider the measure on the height differences the so called gradient Gibbs measure, which exists in any dimensions. The gradient field must satisfy the loop condition, that is the sum of the gradient along any closed loop is zero, this implies a long range interaction with a slow decay of the correlations. We are interested in characterizing the ergodic components of this gradient field, in the decay of correlations, large deviations and continuous scaling limits. As an example we consider the harmonic or discrete gaussian free field with quadratic interactions.
16:40 - 18:10Room #126 (Mathematics building)
伊藤 敦 (東大数理)
"代数曲面上の随伴束の基底点集合について"
偏極付き代数多様体上(X,L)は、Lに数値的な条件を付け加えると
その随伴束が自由になったり、基底点集合が具体的にかけることがある。しかし
、曲線の場合は簡単であるが高次元の場合は難しい。今回の講演では主に代数曲
面の場合について解説する。
2009/10/02
16:20 - 17:50Room #117 (Mathematics building)
岡本龍明 (NTT 情報流通プラットフォーム研究所 岡本特別研究室長)
"暗号の基礎編"
2009/09/30
15:30 - 17:00Room #123 (Mathematics building)
Claudio Landim (IMPA, Brazil)
"Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅱ"
15:00 - 16:10Room #128 (Mathematics building)
矢田 和善 (筑波大学大学院数理物質科学研究科)
"HDLSSデータにおけるPCAについて"
マイクロアレイデータなどに見られるように,データの次元数dが標本数nよりも遥かに大きな高次元小標本(HDLSS)データが,解析対象になる場面が増えてきている.
HDLSSデータに対して従来の統計手法を用いると,次元の呪いによって解析が上手くいかない.解決策の一つとして次元縮約法があり, その一つにPCAがある.高次元における従来型のPCAの漸近的性質は,正規性もしくは同等な仮定のもとで,先行研究が多数存在する. しかしながら,これら仮定は,HDLSSを研究する上で,厳しい制約にもなっている. Yata and Aoshimaの一連の研究は,この制約条件の枠を外すことから始まった.HDLSSにおける従来型PCAの限界は何か?推測が一致性をもつための標本数nと 次元数dの関係が,オーダー条件として明らかにされる.従来型PCAの限界を超える手法は何か?一つの実用的な方法として,クロス行列と呼ばれるデータの変換行列が導入され, この行列の特異値分解に基づいた新しいPCAが提案される.
当日は,マイクロアレイデータによる実例と,シミュレーション結果も交えながら,お話します.本研究は,筑波大学数理物質科学研究科の青嶋誠先生との共同研究です.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/05.html
2009/09/29
16:30 - 18:00Room #056 (Mathematics building)
Sergei Duzhin (Steklov Mathematical Institute, Petersburg Division)
"Symbol of the Conway polynomial and Drinfeld associator"
The Magnus expansion is a universal finite type invariant of pure braids
with values in the space of horizontal chord diagrams. The Conway polynomial
composed with the short circuit map from braids to knots gives rise to a
series of finite type invariants of pure braids and thus factors through
the Magnus map. We describe explicitly the resulting mapping from horizontal
chord diagrams on 3 strands to univariante polynomials and evaluate it on
the Drinfeld associator obtaining a beautiful generating function whose
coefficients are integer combinations of multple zeta values.
2009/09/28
15:30 - 17:00Room #123 (Mathematics building)
Claudio Landim (IMPA, Brazil)
"Macroscopic fluctuation theory for nonequilibrium stationary states, I"
We present a review of recent work on the statistical mechanics of nonequilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.
2009/09/17
16:00 - 17:30Room #002 (Mathematics building)
Norayr MATEVOSYAN (ケンブリッジ大学・数理)
"On a parabolic free boundary problem modelling price formation"
We will discuss existence and uniqueness of solutions for a one dimensional parabolic evolution equation with a free boundary. This problem was introduced by J.-M. Lasry and P.-L. Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in time-extension of the local solution which is intimately connected to the regularity of the free boundary.
We also present numerical results.
2009/09/15
16:30 - 18:00Room #128 (Mathematics building)
打越 敬祐 (防衛大学校数学教育室)
"渦層の超局所解析"
渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,
界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.
2009/09/14
11:00 - 12:00Room #123 (Mathematics building)
Dinakar Ramakrishnan (カリフォルニア工科大学)
"Modular forms and Calabi-Yau varieties"
2009/09/10
16:00 - 17:30Room #002 (Mathematics building)
Henrik SHAHGHOLIAN (王立工科大学・ストックホルム)
"A two phase free boundary problem with applications in potential theory"
In this talk I will present some recent directions, still to be developed, in potential theory, that are connected to a two-phase free boundary problems. The potential theoretic topic that I will discuss is the so called Quadrature Domains.
The most simple free boundary/potential problem that we can present is the following. Given constants $a_\pm, \lambda_\pm >0$ and two points $x^\pm$ in ${\bf R}^n$. Find a function $u$ such that
$$\Delta u = \left( \lambda_+ \chi_{\{u>0 \}} - a_+\delta_{x^+}\right) - \left( \lambda_- \chi_{\{u<0 \}} - a_-\delta_{x^-}\right),$$
where $\delta$ is the Dirac mass.
In general this problem is solvable for two Dirac masses. The requirement, somehow implicit in the above equation, is that the support of the measures (in this case the Dirac masses) is to be in included in the positivity and the negativity set (respectively).
In general this problem does not have a solution, and there some strong restrictions on the measures, in order to have some partial results.
2009/09/08
15:00 - 16:00Room #123 (Mathematics building)
H.R.Thieme (Arizona State University)
"Global compact attractors and their tripartition under persistence"
The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.
Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.
Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)
16:15 - 17:15Room #123 (Mathematics building)
Glenn Webb (Vanderbilt University)
"Analysis of a Model for Transfer Phenomena in Biological Populations"
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
2009/09/07
17:00 - 18:30Room #056 (Mathematics building)
Marek Bozejko (University of Wroclaw)
"Generalized Gaussian field, theta function of Jacobi and functor of second quantization"
2009/09/01
16:30 - 18:00Room #002 (Mathematics building)
Matthias Schuett (Leibniz University Hannover)
"Arithmetic of K3 surfaces"
This talk aims to review recent developments in the arithmetic of K3 surfaces, with emphasis on singular K3 surfaces.
We will consider in particular modularity, Galois action on Neron-Severi groups and behaviour in families.
2009/08/12
10:00 - 16:30Room #002 (Mathematics building)
Sigurdur Helgason (MIT) 10:00 - 11:00
"Radon Transform and some Applications"
Fulton G. Gonzalez (Tufts University) 11:20 - 12:20
"Multitemporal Wave Equations: Mean Value Solutins"
Angela Pasquale (Universite Metz) 14:00 - 15:00
"Analytic continuation of the resolvent of the Laplacian in the Euclidean settings"
We discuss the analytic continuation of the resolvent of the Laplace operator on symmetric spaces of the Euclidean type and some generalizations to the rational Dunkl setting.
Henrik Schlichtkrull (University of Copenhagen) 15:30 - 16:30
"Decay of smooth vectors for regular representations"
Let $G/H$ be a homogeneous space of a Lie group, and consider the regular representation $L$ of $G$ on $E=L^p(G/H)$. A smooth vector for $L$ is a function $f$ in $E$ such that $g$ mapsto $L(g)f$ is smooth, $G$ to $E$. We investigate circumstances under which all such functions decay at infinity (jt with B. Krotz)
2009/08/07
16:30 - 17:30Room #117 (Mathematics building)
Fabien Trihan (Nottingham大学)
"On the $p$-parity conjecture in the function field case"
Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).
2009/07/30
11:00 - 15:45Room #002 (Mathematics building)
水町 徹 (九州大学) 11:00 - 12:00
"長波長近似モデルと孤立波の安定性Ⅱ"
Frank Merle (Cergy Pontoise 大学/IHES) 13:30 - 14:30
"Dynamics of solitons in non-integrable systemsⅤ"
Frank Merle (Cergy Pontoise 大学/IHES) 14:45 - 15:45
"Dynamics of solitons in non-integrable systemsⅥ"
http://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
2009/07/29
11:00 - 17:15Room #002 (Mathematics building)
水町 徹 (京都大学) 11:00 - 12:00
"長波長近似モデルと孤立波の安定性Ⅰ"
KdV方程式をはじめとする長波長近似の非線形分散型方程式は,水面波の運動やプラズマ中のイオンの運動を記述することで知られている. KdV方程式のソリトン解は安定的に伝播することが知られていたが,近年変分法に基づいたアプローチで非可積分系のモデルの場合にもソリトン解とよく似た解が安定的に存在することが証明された.第1回目の講演ではに変分原理に基づいた安定性の結果について概説し,次にFermi-Pasta-Ulam格子やある種の流体のbidirectional modelなど変分原理から安定性がうまく説明できないモデルの場合について述べる.
Frank Merle (Cergy Pontoise 大学/IHES) 13:30 - 14:30
" Dynamics of solitons in non-integrable systemsⅢ"
Frank Merle (Cergy Pontoise 大学/IHES) 14:45 - 15:45
"Dynamics of solitons in non-integrable systemsⅣ"
中西 賢次 (九州大学) 16:15 - 17:15
"シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅡ"
http://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
2009/07/28
13:30 - 17:15Room #002 (Mathematics building)
Frank Merle (Cergy Pontoise 大学/IHES) 13:30 - 14:30
"Dynamics of solitons in non-integrable systemsⅠ"
完全可積分系であるKdV方程式においては,多重ソリトン解の構造はすでに詳しく解明されており,ソリトンどうしが衝突した後,各ソリトンの形状がすぐに元通りに復元するなどの性質もよく知られている.しかし方程式中の指数を変えて得られる一般化KdV方程式の場合は,非可積分系であるため,多重ソリトン解の便利な表示式は存在せず,ソリトンどうしの衝突後に何が起こるのか,理論的には未解明であった.Merle氏は,最近Yvon Martel氏と共同でこの問題を解決し,衝突後にわずかな欠損が生じるもののソリトンの形状が見事に復元することを証明するとともに,大きなソリトンが微小なソリトンと衝突した際に生じる位相(phase)のズレに関して, KdV方程式の場合と全く違う現象が起こることも明らかにした.
Frank Merle (Cergy Pontoise 大学/IHES) 14:45 - 15:45
"Dynamics of solitons in non-integrable systemsⅡ"
中西 賢次 (京都大学) 16:15 - 17:15
"シュレディンガー写像及び熱流における調和写像の漸近安定性と振動現象についてⅠ"
平面から球面への調和写像をシュレディンガーや熱流で時間発展させたときの漸近安定性を回転対称下で調べる.この問題は,調和写像の写像度が低いほど摂動部との空間遠方相互作用が大きくなる所が難しく,実際写像度2の熱流では初期摂動に応じて非自明な時間漸近挙動が現れる.この講演では,非線形シュディンガー方程式の場合をモデルとして比較しながら、漸近安定性を示す一般的な手続きとそこからの変更点,必要となる線形評価などについて解説する.
http://www.ms.u-tokyo.ac.jp/gcoe/index_001.html
2009/07/27
14:00 - 15:15Room #123 (Mathematics building)
野澤 啓 (東京大学大学院数理科学研究科)
"『Five dimensional K-contact Manifolds of rank 2(階数2の5次元K接触多様体について)』"
17:00 - 18:30Room #002 (Mathematics building)
Misha Verbitsky (ITEP Moscow/IPMU)
"Mapping class group for hyperkaehler manifolds"
A mapping class group is a group of orientation-preserving
diffeomorphisms up to isotopy. I explain how to compute a
mapping class group of a hyperkaehler manifold. It is
commensurable to an arithmetic lattice in a Lie group
$SO(n-3,3)$. This makes it possible to state and prove a
new version of Torelli theorem.
2009/07/24
16:30 - 17:30Room #123 (Mathematics building)
Carlos Simpson (CNRS, University of Nice)
"Differential equations and the topology of algebraic varieties"
The study of the topology of complex algebraic varieties makes use of differential equations in several different ways. The classical notion of variation of Hodge structure contains, on the one hand, the Gauss-Manin differential equations, on the other hand Hodge metric data which satisfy harmonic bundle equations. These two aspects persist in the study of arbitrary representations of the fundamental group. Combining them leads to a notion of ``Hodge structure'' on the space of representations. This can be extended to the higher homotopical structure of a variety, by using ideas of ``shape'' and nonabelian cohomology.
13:00 - 15:30Room #056 (Mathematics building)
武部尚志 (Faculty of Math, Higher School of Economics, Moscow) 13:00 - 14:00
"On recursion relation of the KP hierarchy"
This talk is based on an ongoing project in collaboration with Takasaki and Tsuchiya. Our goal is to reconstruct and generalise results by Eynard et al. from the standpoint of the integrable systems. Eynard, Orantin and their collaborators found "topological recursion formulae" to describe partition functions and correlation functions of the matrix models, topological string theories etc., using simple algebro-geometric data called "spectral curves". On the other hand, it is well known that the partition functions of those theories are tau functions of integrable hierarchies.
We have found that any solution of the KP hierarchy (with an asymptotic expansion parameter h) can be recovered by recursion relations from its "dispersionless" part (which corresponds to the genus zero part in topological theories) and a quantised contact transformation (which corresponds to the string equations) specifying the solution.
高崎金久 (京大人間) 14:30 - 15:30
"球面のフルビッツ数とKP・戸田階層の特殊解"
球面の1点を指定し、その上方で任意被覆型の分岐点
をもち、それ以外では単純分岐点のみもつような n 次分岐被覆を考える。
このような分岐被覆の位相的同型類の個数は単純フルビッツ数と呼ばれる。
1点の代わりに2点を指定して同様に定義されるものは2重フルビッツ数である。
これらのフルビッツ数にシューア函数を乗じて総和したものはそれぞれ
KP階層および戸田階層のτ函数になることが知られている。この講演では
これらの特殊解においてラックス作用素とオルロフ・シュルマン作用素が
満たす関係式 (拘束条件) を紹介し、そこから導かれる帰結を探る。
2009/07/23
16:30 - 18:00Room #056 (Mathematics building)
Catherine Oikonomides (慶応大理工)
"Cyclic cohomology and the Novikov conjecture"
2009/07/21
16:30 - 18:00Room #128 (Mathematics building)
Georgi Raikov (PUC, Chile)
"Low Energy Asymptotics of the SSF for Pauli Operators with Non-Constant Magnetic Fields"
In my talk, I will consider the 3D Pauli operator with non-constant magnetic field of constant direction,
perturbed by a matrix-valued electric potential which decays fast enough at infinity. I will discuss
the low-energy asymptotics of the associated spectral shift function which is proportional to the eigenvalue
counting function at negative energies, and to the scattering phase at positive energies.
2009/07/18
13:30 - 16:00Room #123 (Mathematics building)
大石亮子 (高エネルギー加速器研究機構(KEK)) 13:30 - 14:30
"On some algebraic properties of CM-types of CM-fileds and their reflexs"
織田孝幸 (東京大学数理科学研究科) 15:00 - 16:00
"仮題:GL(n)のWhittaker関数に関連する今後の問題"
今回は、普段から言及している、未解決の問題をできればなるべくきちんと定式化したい。「GL(n)上の保型形式論は終わった」という愚かな愚かな人たちもいるが、実は彼らにも新たな研究手法が必要であることを指摘したい。実際、現状ではカスプ形式の存在論に関しては、ほとんど何も分かっていない。
2009/07/17
16:30 - 17:30Room #002 (Mathematics building)
Nessim Sibony (Universite Paris-Sud)
"Holomorphic dynamics in several variables: equidistribution problems and statistical properties"
The main problem in the dynamical study of a map is to understand the long term behavior of orbits. The abstract theory of non uniformly hyperbolic systems is well understood but it is very difficult to decide when a given system is non uniformly hyperbolic and to study it's sharp ergodic properties.
Holomorphic dynamics in several variables provide large classes of examples of non uniformly hyperbolic systems. One can compute the entropy, construct a measure of maximal entropy and study the sharp statistical properties: central limit theorem, large deviations and exponential decay of correlations. It is also possible to prove sharp equidistribution results for preimages of analytic sets of arbitrary dimension. The main tools are: pluripotential theory, analytic geometry, and good estimates from PDE.
These systems appear naturally if we apply Newton's method to localise the common zeros of of polynomial equations in several variables. In the study of polynomial automorphisms of complex Euclidean spaces, or automorphisms of compact K\"ahler manifolds.
13:45 - 14:45Room #128 (Mathematics building)
Karl Oeljeklaus (University of Provence)
"Logarthmic
Moduli Spaces for Surfaces of Class VII (joint work with M. TOMA)"
15:00 - 16:00Room #128 (Mathematics building)
Andrei Iordan (Univ. Paris VI)
"Boundary Regularity of d-bar Operator and Non Existence of Smooth Levi Flat Hypersurfaces in Compact K¥"ahler Manifolds"
16:30 - 17:30Room #002 (Mathematics building)
Nessim Sibony (Univ. Paris Sud)
"Holomorphic Dynamics In Several
Variables: equidistribution properties and statistical behavior"
2009/07/16
16:30 - 18:00Room #056 (Mathematics building)
Ingo Runkel (King's College London)
"Algebraic structures in conformal field theory"
It turned out to be fruitful to isolate questions in CFT which can be formulated in a purely categorical fashion. The way left and right moving degrees of freedom can be combined to a consistent theory is an example of this, the relevant structure being a commutative symmetric Frobenius algebra. This is true independently of whether CFT is formulated via sewing of surfaces or nets of operator algebras. Another example is modular invariance, which has a surprising alternative formulation as a certain maximality condition.
15:00 - 16:20Room #056 (Mathematics building)
Odo Diekmann (Mathematical Institute, Utrecht University)
"The delay equation formulation of physiologically structured population models"
Traditionally, physiologically structured population models are formulated in terms of first order partial differential equations with non-local boundary conditions and/or transformed arguments. The stability and bifurcation theory for such equations is, in the quasi-linear case, still very immature.
The aim of this lecture is to explain that, alternatively, one can formulate such models in terms of delay equations (more precisely : renewal equations coupled to delay differential equations) without losing essential information and that for delay equations there is a well-developed local stability and bifurcation theory. As a motivating example we consider the interaction between a size-structured consumer and an unstructured resource. The lecture is based on joint work with Mats Gyllenberg and Hans Metz.
2009/07/14
17:00 - 18:00Room #056 (Mathematics building)
作間 誠 (広島大学)
"The Cannon-Thurston maps and the canonical decompositions
of punctured-torus bundles over the circle."
To each once-punctured-torus bundle over the circle
with pseudo-Anosov monodromy, there are associated two tessellations of the complex plane:
one is the triangulation of a horosphere induced by the canonical decomposition into ideal
tetrahedra, and the other is a fractal tessellation
given by the Cannon-Thurston map of the fiber group.
In this talk, I will explain the relation between these two tessellations
(joint work with Warren Dicks).
I will also explain the relation of the fractal tessellation and
the "circle chains" of double cusp groups converging to the fiber group
(joint work with Caroline Series).
If time permits, I would like to discuss possible generalization of these results
to higher-genus punctured surface bundles.
2009/07/13
16:30 - 18:00Room #126 (Mathematics building)
佐野 太郎 (東大数理)
"Seshadri constants on rational surfaces with anticanonical pencils
"
射影多様体上の豊富線束の$k$-jet ample性を測る不変量として
Seshadri定数と呼ばれる正の実数がある。
この不変量を調べることでしばしば幾何的な情報が得られる。
今回、1次元以上の反標準線形系をもつ有理曲面上のSeshadri定数を計算する公式
が得られた。
その公式を使うと、対数del Pezzo曲面の特異点の情報をSeshadri定数の値から
復元できる。
2009/07/09
16:30 - 18:00Room #056 (Mathematics building)
Mikael Pichot (東大数物連携宇宙研究機構)
"Examples of groups of intermediate rank "
2009/07/06
10:30 - 12:00Room #126 (Mathematics building)
赤堀隆夫 (兵庫県立大学)
"On the CR Hamiltonian flows"
The deformation theory of CR structures was initiated by Kuranishi and the versal family of CR structures were constructed by Garfied, Lee and myself "in the sense of Kuranishi". Miyajima also discussed the versal family by the completely different method. While, our method relies on the contact geometry(this suggest that there is a deep relation between Hamiltonian geometry and CR structures). Today, I report that our family is also versal "in the sense of CR Hamiltonian flows".
16:30 - 18:00Room #126 (Mathematics building)
柳田 伸太郎 (神戸大学理学研究科)
"アーベル曲面上の安定層とフーリエ向井変換について"
今回の講演は吉岡康太との共同研究に基づくものである. 研究の発端は, 向井茂が1980年前後(フーリエ向井変換の発見前後)に考察し, 当時の講演記録に書き残した主張や予想の解読にある.
本研究は, 大まかに言うと, 半等質層とフーリエ向井変換を用いて, アーベル曲面上の安定層のモジュライ空間の構造を調べるというものである.
アーベル曲面上には半等質層と呼ばれる半安定層があり, その分類, 構成方法やコホモロジーが完全に知られている. アーベル曲面のフーリエ向井対は半等質層のモジュライ空間であることも知られている.
今回の研究はこの半等質層をbulding blockとして一般の安定層を構成することを考える. その際に"semi-homogeneous presentation"という概念が必要になる. これはアーベル曲面上の安定層の半等質層によるある種の分解のことである. 曲面のピカール数が1の時, この種の分解の存在が安定層のチャーン指標のみを用いて判定できる.
また安定層のフーリエ変換における振舞いの記述において, 算術群や整数係数2次形式が重要な役割を果たすことも分かる. この事と先に述べた表示の存在から, 安定層のモジュライとアーベル曲面上の点のヒルベルトスキームとの間の双有理変換が明示的に構成できる.
アーベル曲面のフーリエ向井変換のフォーマリズムはK3曲面の変換と共通する部分も少なくない. 講演ではそうした点にも触れつつ, 今回の結果とその証明の概要を解説したい.
2009/07/02
17:00 - 18:00Room #056 (Mathematics building)
小沢登高 (東大数理)
"Dixmier's Similarity Problem ---Littlewood and Forests--- (一般の数学者向け)"
2009/07/01
15:30 - 17:00Room #470 (Mathematics building)
金井 政宏 (東大数理)
"ASEPおよびzero-range processの分配関数"
2009/06/30
16:30 - 18:00Room #056 (Mathematics building)
北山 貴裕 (東京大学大学院数理科学研究科)
"Torsion volume forms and twisted Alexander functions on
character varieties of knots
"
Using non-acyclic Reidemeister torsion, we can canonically
construct a complex volume form on each component of the
lowest dimension of the $SL_2(\mathbb{C})$-character
variety of a link group.
This volume form enjoys a certain compatibility with the
following natural transformations on the variety.
Two of them are involutions which come from the algebraic
structure of $SL_2(\mathbb{C})$ and the other is the
action by the outer automorphism group of the link group.
Moreover, in the case of knots these results deduce a kind
of symmetry of the $SU_2$-twisted Alexander functions
which are globally described via the volume form.
16:30 - 18:00Room #128 (Mathematics building)
Ivana Alexandrova (東京大数理)
"The Structure of the Scattering Amplitude for Schrodinger Operators with a Strong Magnetic Field"
We study the microlocal structure of the semi-classical scattering amplitude for Schrodinger operators with a strong magnetic field at non-trapping energies. We prove that, up to any order, the scattering amplitude can be approximated by a semi-classical pseudodifferential-operator-valued Fourier integral operator.
2009/06/29
10:30 - 12:00Room #126 (Mathematics building)
藤木 明 (大阪大学)
"VII型曲面上の反自己双対双エルミート構造の存在について"
16:30 - 18:00Room #126 (Mathematics building)
大川 領 (東京工業大学)
"Moduli on the projective plane and the wall-crossing"
射影平面上の半安定層のモジュライ空間を、Bridgeland 安定性条件
を用いることにより、ある有限次元代数の半安定表現のモジュライ空間
として構成する。階数が2以下の場合、表現の安定性条件を変化させること
により、壁越え現象としてのflip の記述を得る。
応用として、flip のBetti 数などが計算できる。
2009/06/25
16:30 - 18:00Room #056 (Mathematics building)
鈴木章斗 (九州大学数理学研究院)
"Infrared divergence of scalar quantum field model on pseudo Riemann manifold
"
2009/06/24
16:30 - 18:45Room #056 (Mathematics building)
Vincent Maillot (Paris第7大学) 16:30 - 17:30
"New algebraicity results for analytic torsion"
Richard Hain (Duke大学) 17:45 - 18:45
"On the Section Conjecture for the universal curve over function fields"
10:30 - 11:30Room #056 (Mathematics building)
Winston Ou (Scripps College / currently visiting assistant professor at Keio University)
"Monge-Ampere equations, the Bellman Function Technique, and Muckenhoupt weights"
In the last few years several classical results in harmonic analysis (in particular, the study of $A_\infty$ weights have been sharpened with the use of a version of the Bellman function method (promulgated by Nazarov, Treil, and Volberg in the 90's) that involves recognizing the Bellman function as the solution of a Monge-Ampere PDE (the method was introduced by Vasyunin in 2003). We will give a sketch of the modified technique, outline some recent work-in-progress (with Slavin and Wall) using the technique in $A_\infty$, and then present a few related problems.
15:30 - 17:00Room #122 (Mathematics building)
柳尾 朋洋 (早大 基幹理工)
"原子・分子集合体の集団運動における動的秩序と階層性"
小さな気体分子の化学反応から、結晶成長、さらにはDNAやタンパク質のような生体高分子の機能発現に至るまで、原子・分子集合体の集団運動と自己組織化の一般原理を明らかにすることは、現代科学の大変興味深い課題である。近年の実験技術の進歩により、これら原子分子系の集団運動の多くは、平衡状態から大きく離れた非平衡状態において発生し、動的な秩序を内包していることが明らかになってきている。本発表では、一例として原子クラスターの構造変化の集団運動を取り上げ、これらの集団運動が、「遅い自由度」と「速い自由度」の間の動的結合によって系統的に生み出される仕組みについて紹介する。あわせて、このような非平衡過程を記述する新たな反応速度論の試みについても紹介する。続いて、より複雑な分子系の例として、生物のDNAをとりあげ、ランジュバン動力学に基づく粗視化モデルを導入することによって、DNAが細胞中で階層的な秩序構造を形成するメカニズムの一端を明らかにする。
2009/06/23
16:30 - 18:00Room #056 (Mathematics building)
久野 雄介 (東京大学大学院数理科学研究科)
"The Meyer functions for projective varieties and their applications"
Meyer function is a kind of secondary invariant related to the signature
of surface bundles over surfaces. In this talk I will show there exist uniquely the Meyer function
for each smooth projective variety.
Our function is a class function on the fundamental group of some open algebraic variety.
I will also talk about its application to local signature for fibered 4-manifolds
16:30 - 18:00Room #126 (Mathematics building)
岸本崇氏 (埼玉大学理工学研究科)
"Group actions on affine cones "
The action of the additive group scheme C_+ on normal affine varieties is one of main subjects in affine algebraic geometry for a long time. In this talk, we shall mainly consider the problem about the existence of C_+-actions on affine cones, more precisely, the question:
"Determine the affine cones over smooth projective varieties admitting a (non-trivial) C_+-action ".
This question has an interest from a point of view of singularities. Indeed, a normal Cohen-Macaulay affine variety admitting an action by C_+ has at most rational singularities due to the result of H. Flenner and M. Zaidenberg. In the case of dimension 2, any affine cone over the projective line P^1 has a cyclic quotient singularity, and we can see that it admits, in fact, a C_+-action. Meanwhile, in case of dimension 3, i.e., affine cones over rational surfaces, the situation becomes more subtle.
One of the main results is concerned with a criterion for the existence of a C_+-action on affine cones (of any dimension) in terms of a cylinderlike open subset on the base variety. By making use of it, it is shown that, for any rational surface Y, we can take a suitable embedding of Y in such a way that the associated affine cone admits an action of C_+. Furthermore we are able to confirm that an affine cone over an anticanonically embedded del Pezzo surface of degree greater than or equal to 4 also admits such an action.
Nevertheless, our final purpose to decide whether or not there does exist a C_+-action on the fermat cubic: x^3+y^3+z^3+u^3 =0 in C^4, which is the affine cone over an anticanonically embedded cubic surface, say Y_3, is not yet accomplished. But, we can obtain certain informations about a linear pencil of rational curves on Y_3 arising from a C_+-action which seem to be useful in order to deny an existence of an action of C_+.
2009/06/22
10:30 - 12:00Room #126 (Mathematics building)
早乙女飛成 (筑波大学)
"強疑凸多様体間の擬正則写像の楕円型作用素に関する性質について"
2009/06/20
13:30 - 16:00Room #123 (Mathematics building)
小池 健二 (山梨大学教育人間科学部) 13:30 - 14:30
"射影直線上の6点とI型領域上のテータ関数
射影直線上の6点とI型領域上のテータ関数"
成田宏秋 (熊本大学理学部) 15:00 - 16:00
"Fourier coefficients of Arakawa lifting and some degree eight L-function
"
次数2のシンプレクティック群ないしはその非コンパクトな内部形式上のヘッケ同時固有的保型形式のフーリエ係数は、保型L関数の中心値と密接に関係すると考えられている。
この講演では「荒川リフト」という内部形式上のカスプ形式に対し、そのフーリエ係数とある次数8の保型L関数の中心値との明示的な関係について最近得られた結果を紹介する。(村瀬篤氏との共同研究)
11:00 - 12:00Room #117 (Mathematics building)
有田親史 (九大数理)
"多成分排他過程の固有値が満たす双対性"
非対称単純排他過程(asymmetric simple exclusion process, ASEP)と呼ばれ
る1次元格子上の確率過程がある。今回はその多成分の場合を考える。系の時間
発展を特徴付けるジェネレータ行列(マルコフ行列)は,Heisenberg模型を含む
Perk-Schultz模型のハミルトニアンの特殊な場合と等価である。講演者らは各粒
子セクターを超立方体の頂点と対応させ固有値の構造を調べた。超立方体上で双
対点を成す2つのセクターの固有値が満たす関係を示した。国場敦夫氏,堺和光
氏,沢辺剛氏との共同研究。
2009/06/18
16:30 - 18:00Room #056 (Mathematics building)
河東泰之 (東大数理)
"The super Virasoro algebra and noncommutative geometry"
2009/06/17
10:30 - 11:30Room #056 (Mathematics building)
小磯深幸 (奈良女子大学理学部/JSTさきがけ)
"Variational problems for anisotropic surface energies"
A surface energy is anisotropic if it depends on the direction of the surface. The minimizer of an anisotropic surface energy among all closed surfaces enclosing a fixed volume is called the Wulff shape. We will discuss the characterization of the Wulff shape, the uniqueness and stability of solutions to variational problems for anisotropic surface energy with several boundary conditions.
2009/06/16
16:30 - 18:00Room #056 (Mathematics building)
佐藤 正寿 (東京大学大学院数理科学研究科)
"The abelianization of the level 2 mapping class group"
The level d mapping class group is a finite index subgroup of the mapping class group of an orientable closed surface. For d greater than or equal to 3, the abelianization of this group is equal to the first homology group of the moduli space of nonsingular curves with level d structure.
In this talk, we determine the abelianization of the level d mapping class group for d=2 and odd d. For even d greater than 2, we also determine it up to a cyclic group of order 2.
2009/06/15
10:30 - 12:00Room #126 (Mathematics building)
野口潤次郎 (東京大学)
"A unicity theorem and Erd\"os' problem for polarized semi-abelian varieties (joint with P. Corvaja)"
16:30 - 18:00Room #126 (Mathematics building)
Vladimir P. Kostov (Nice大学)
"On the Schur-Szeg\"o composition of polynomials"
The Schur-Szeg\"o composition of the degree $n$ polynomials $P:=\sum_{j=0}^na_jx^j$ and $Q:=\sum_{j=0}^nb_jx^j$ is defined by the formula $P*Q:=\sum_{j=0}^na_jb_jx^j/C_n^j$ where $C_n^j=n!/j!(n-j)!$. Every degree $n$ polynomial having one of its roots at $-1$ (i.e. $P=(x+1)(x^{n-1}+c_1x^{n-2}+\cdots +c_{n-1})$) is representable as a Schur-Szeg\"o composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$ where the numbers $a_i$ are uniquely defined up to permutation. Denote the elementary symmetric polynomials of the numbers $a_i$ by $\sigma_1$, $\ldots$, $\sigma_{n-1}$. The talk will focus on some properties of the affine mapping
$$(c_1,\ldots ,c_{n-1})\mapsto (\sigma_1,\ldots ,\sigma_{n-1})$$
16:30 - 18:00Room #128 (Mathematics building)
馬 昭平氏 (東大数理)
"アーベル曲面の分解と2次形式
"
複素Abel曲面が楕円曲線の積に分解可能である時、分解の仕方は一般に何通りも
ありうる。いくつかの場合に分解の個数公式が求められてきた(林田、塩田-三谷
)。本講演では、すべての分解可能な複素Abel曲面に対して、2次形式論の技法
を用いて分解数の公式を与える。関連して次のことも話す:合同モジュラー曲線
上のAtkin-Lehner対合の幾何学的意味;正定値2元2次形式の類数と判別式形式
の等長群の関係。
2009/06/11
16:30 - 18:00Room #056 (Mathematics building)
Chris Heunen (Radboud Universiteit Nijmegen)
"A topos for algebraic quantum theory"
2009/06/10
16:30 - 18:30Room #056 (Mathematics building)
Bruno Kahn (Paris第7大学)
"On the classifying space of a linear algebraic group"
15:30 - 17:00Room #470 (Mathematics building)
永幡幸生 (阪大基礎工)
"格子気体のスペクトルギャップについて"
2009/06/09
16:30 - 18:00Room #056 (Mathematics building)
五味 清紀 (京都大学大学院理学研究科)
"A finite-dimensional construction of the Chern character for
twisted K-theory"
Twisted K-theory is a variant of topological K-theory, and
is attracting much interest due to applications to physics recently.
Usually, twisted K-theory is formulated infinite-dimensionally, and
hence known constructions of its Chern character are more or less
abstract. The aim of my talk is to explain a purely finite-dimensional
construction of the Chern character for twisted K-theory, which allows
us to compute examples concretely. The construction is based on
twisted version of Furuta's generalized vector bundle, and Quillen's
superconnection.
This is a joint work with Yuji Terashima.
2009/06/08
10:30 - 12:00Room #126 (Mathematics building)
大沢健夫 (名古屋大学)
"正因子の正値性について"
17:00 - 18:30Room #002 (Mathematics building)
Kiyonori Gomi (Kyoto University)
"Multiplication in differential cohomology and cohomology operation"
The notion of differential cohomology refines generalized
cohomology theory so as to incorporate information of differential
forms. The differential version of the ordinary cohomology has been
known as the Cheeger-Simons cohomology or the smooth Deligne
cohomology, while the general case was introduced by Hopkins and
Singer around 2002.
The theme of my talk is the cohomology operation induced from the
squaring map in the differential ordinary cohomology and the
differential K-cohomology: I will relate these operations to the
Steenrod operation and the Adams operation. I will also explain the
roles that the squaring maps play in 5-dimensional Chern-Simons theory
for pairs of B-fields and Hamiltonian quantization of generalized
abelian gauge fields.
2009/06/04
16:30 - 18:00Room #056 (Mathematics building)
中神祥臣 (日本女子大)
"Determinant for rectangular martices"
2009/06/03
10:30 - 11:30Room #056 (Mathematics building)
須藤孝一 (大阪大学)
"Evolution of microstructures on crystal surfaces by surface diffusion"
We have studied the shape evolution of microstructures fabricated on silicon surfaces by surface diffusion during annealing. Various interesting phenomena, such as corner rounding, facet growth, and void formation, have been experimentally observed. We discuss these observations both from macroscopic and mesoscopic viewpoints. The evolution of macroscopic surface profiles is discussed using evolution equations based on the continuum surface picture. We analyze the mesoscopic scale aspects of the shape evolution using a step-flow model.
15:00 - 16:10Room #128 (Mathematics building)
山田 亮 (東京大学医科学研究所 ヒトゲノム解析センター ゲノム機能解析分野)
"遺伝的多様性を捉える"
遺伝統計学は、遺伝子の多様性と生物個体の特徴(形質)の多様性との間の関係を検出するための方法を提供する学問分野である。
遺伝情報はDNAの塩基配列にその多くが刻まれているが、昨今、このDNA配列に関する実験技法が急速に発展し、同一種内のDNA配列が、非常に多様かつ不均一な集団を構成していることが明らかになってきた。
DNA配列多様性と形質多様性との関係を検出するにあたり、このDNA配列集団の多様性と不均一性は、遺伝因子間の非独立性として、関係検出過程に大きな影響を与えることから、DNA配列集団の多様性の把握そのものが、遺伝統計学の課題となっている。
ヒトDNA配列は4種類の塩基が長さ30億であるため、『生命体として成立しうる』という制約の下、非常に多様な配列を取り得る。このDNA配列が取り得る範囲をDNA配列の空間とみなしたとき、DNA配列集団の多様性は、その空間におけるDNA配列集団の分布状態となる。
本セミナーでは、DNA配列集団の分布状態を捉える方法について検討する。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/04.html
16:30 - 18:30Room #056 (Mathematics building)
Bruno Kahn (Paris第7大学)
"Motives and adjoints"
2009/06/02
16:30 - 18:00Room #056 (Mathematics building)
Alexander Voronov (University of Minnesota)
"Graph homology: Koszul duality = Verdier duality"
Graph cohomology appears in computation of the cohomology of the moduli space of Riemann surfaces and the outer automorphism group of a free group. In the former case, it is graph cohomology of the commutative and Lie types, in the latter it is ribbon graph cohomology, that is to say, graph cohomology of the associative type. The presence of these three basic types of algebraic structures hints at a relation between Koszul duality for operads and Poincare-Lefschetz duality for manifolds. I will show how the more general Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This is a joint work with Andrey Lazarev.
16:30 - 18:00Room #128 (Mathematics building)
神本 晋吾 (東京大数理)
"無限階擬微分作用素の形式核関数について"
2009/05/28
16:30 - 18:00Room #056 (Mathematics building)
佐藤康彦 (北大理)
"The Rohlin property for automorphisms of the Jiang-Su algebra"
2009/05/27
16:30 - 17:30Room #056 (Mathematics building)
Gombodorj Bayarmagnai (東京大学大学院数理科学研究科)
"The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)"
2009/05/26
16:30 - 18:00Room #128 (Mathematics building)
Myriam Ounaies (Strasbourg大学数学科)
"Intrepolation problems in H￥"ormander algebras"
We call Hörmander algebras the spaces $A_p(\mathbb C)$ of entire functions $f$ such that, for all $z$ in $\mathbb C$, \[|f(z)|\le Ae^{Bp(z)},\] where $A$ and $B$ are some positive constants (depending on $f$) and $p$ is a subharmonic weight. We consider the following interpolation problem : Given a discrete sequence $\{a_j\}$ of complex numbers and a sequence of complex values $\{b_j\}$, under what conditions does there exist a function $f\in A_p(\mathbb C)$ such that $f(a_j)=b_j$ for all $j$ ? In other words, what is the trace of $A_p(\mathbb C)$ on $\{a_j\}$ ?
We say that $\{a_j\}$ is an interpolating sequence if the trace is defined by the space of all $\{b_j\}$ satisfying $|b_j|\le A'e^{B'p(a_j)}$, for some constants $A',B'>0$.
We use Hörmander's $L^2$-estimates for the $\bar\partial$-equation to describe the trace when the weight $p$ is radial and doubling and to characterize the interpolating sequences for more general weights.
16:30 - 18:00Room #056 (Mathematics building)
境 圭一 (東京大学大学院数理科学研究科)
"Configuration space integrals and the cohomology of the space of long embeddings
"
It is known that some non-trivial cohomology classes, such as finite type invariants for (long) 1-knots (Bott-Taubes, Kohno, ...) and invariants for codimension two, odd dimensional long embeddings (Bott, Cattaneo-Rossi, Watanabe) are given as configuration space integrals associated with trivalent graphs.
In this talk, I will describe more cohomology classes by means of configuration space integral, in particular those arising from non-trivalent graphs and a new formulation of the Haefliger invariant for long 3-embeddings in 6-space, in relation to Budney's little balls operad action and Roseman-Takase's deform-spinning.
This is in part a joint work with Tadayuki Watanabe.
2009/05/25
10:30 - 12:00Room #126 (Mathematics building)
塚本真輝 (京都大学)
"Brody曲線の空間の幾何と平均次元"
2009/05/22
16:30 - 17:30Room #002 (Mathematics building)
緒方芳子 (東京大学大学院数理科学研究科)
"量子スピン系における大偏差原理について"
量子スピン系における大偏差原理の研究について紹介する。特に、Gibbs State, Finitely Correlated State と呼ばれる状態についてお話しする。一次元量子スピン系の大偏差原理、Gibbs State の大偏差原理のレート関数の特徴づけ、さらに統計力学における分布の同値性の問題との関連について述べる。
15:00 - 16:30Room #128 (Mathematics building)
Prof. Steven Zucker (Johns Hopkins University)
"The RBS compactification: a real stratified space in
algebraic geometry"
2009/05/20
10:30 - 11:30Room #056 (Mathematics building)
前川泰則 (神戸大学)
"Stability of the Burgers vortex"
The Burgers vortex is an exact vortex solution to the three dimensional stationary Navier-Stokes equations for viscous incompressible fluids in the presence of an axisymmetric background straining flow. In this talk we discuss the stability of the Burgers vortex with respect to two or three dimensional perturbation flows.
17:30 - 19:00Room #122 (Mathematics building)
鍛冶 俊輔 (大阪大)
"Financial inverse problem and reconstruction of infinitely divisible distributions with Gaussian component (小谷真一氏(関西学院大)との共同研究)
"
16:30 - 17:30Room #056 (Mathematics building)
廣江 一希 (東京大学大学院数理科学研究科)
"Generalized Whittaker functions for degenerate principal series of GL(4,R)
"
2009/05/19
16:30 - 18:00Room #056 (Mathematics building)
Mark Hamilton (東京大学大学院数理科学研究科, JSPS)
"Geometric quantization of integrable systems"
The theory of geometric quantization is one way of producing a "quantum system" from a "classical system," and has been studied a great deal over the past several decades. It also has surprising ties to representation theory. However, despite this, there still does not exist a satisfactory theory of quantization for systems with singularities.
Geometric quantization requires the choice of a polarization; when using a real polarization to quantize a regular enough manifold, a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld fibres. However, there are many types of systems to which this result does not apply. One such type is the class of completely integrable systems, which are examples coming from mechanics that have many nice properties, but which are nontheless too singular for Sniatycki's theorem to apply.
In this talk we will explore one approach to the quantization of integrable systems, and show a Sniatycki-type relationship to Bohr-Sommerfeld fibres. However, some surprising features appear, including infinite-dimensional contributions and strong dependence on the polarization.
This is joint work with Eva Miranda.
2009/05/18
10:30 - 12:00Room #126 (Mathematics building)
本多宣博 (東京工業大学)
"Conformal symmetries of self-dual hyperbolic monopole metrics (joint work with Jeff Viaclovsky)"
2009/05/16
13:30 - 16:00Room #123 (Mathematics building)
水野 義紀 (徳島大学工学部) 13:30 - 14:30
"3次元上半空間のスペクトル理論とエルミート保型形式"
3次元上半空間のスペクトル理論のエルミート保型形式への応用につい
て述べます。内容はジーゲル保型形式に対して2次元上半空間のスペクトル理論を応用す
るという今井氏による発見、及びその実際的応用のエルミート版への類似です。具体的に
は小嶋氏により発見されたエルミート版斉藤・黒川リフトに逆定理による解析的証明を与
えること、レベル付エルミート・アイゼンシュタイン級数のフーリエ係数の決定、それを
用いたp進エルミート・アイゼンシュタイン級数のエルミート・アイゼンシュタイン級数
による記述、についてです。これらにおいて必要となる「3次元上半空間のマース形式の
特殊値のある平均が、2次元上半空間のマース形式のフーリエ係数になる」というカトッ
ク・サルナック型の結果についても述べます。(p進エルミート・アイゼンシュタイン級
数については菊田俊之氏との共同研究、その他はRoland Matthes氏との共同研究です。)
宮崎 直 (東京大学数理科学研究科) 15:00 - 16:00
"The Eisenstein series for $GL(3,Z)$ induced from cusp forms"
GL(3,Z)$に関するEisenstein級数のFourier-Whittaker展開は,
指標から誘導された場合については,Bump氏とFriedberg氏によって
明示的な表示が与えられている.ここでは,それらの類似として,
尖点形式から誘導された場合について,Fourier-Whittaker展開の
明示的な表示を与える.
2009/05/14
16:00 - 17:30Room #002 (Mathematics building)
東海林 まゆみ (日本女子大学・理学部・数物科学科)
"Particle trajectories around a running cylinder in Brinkman's porous-media flow"
Motion of fluid particles provides us with interesting problems of dynamical
systems. We consider here the movement of particles around a running cylinder.
Classically J. C. Maxwell (1870) considered the problem in irrotational flow of
inviscid fluid. He showed that the complete solution is given by the elliptic
functions and the trajectory forms one of the elastica curves. C. Darwin ('53)
considered a similar problem for a moving sphere. In this case, the solution
cannot be written in terms of elliptic functions but can be expressed by a
simple definite integral.
We consider a similar problem in Brinkman's porous-media flow which is proposed
by Brinkman ('49). Our numerical examinations reveals some new interesting
features of the particle trajectories which are not observed in the case of
irrotational flow. We will report them.
16:30 - 18:00Room #056 (Mathematics building)
Raphael Ponge (東大数理)
"Noncommutative geometry and lower dimensional volumes in Riemannian and CR geometry"
16:00 - 17:30Room #123 (Mathematics building)
岩見真吾 (静岡大学創造科学技術大学院)
"AIDSワクチン開発への理論的介入-SHIV感染実験と数理モデル-"
慢性感染症であるという特性を有するHIV感染症の拡大を阻止するためには、予防・治療AIDSワクチンの開発が不可欠である。しかし、1998年にヒトでは初めての国際的な臨床試験が始まったバックスジェン社のAIDSワクチンは、2003年に失敗だと発表された。また、2004年メルク社の最も有望だったワクチン候補も大規模な臨床試験にまで進んだが、効果がないどころか悪影響がある可能性が判明し、2007年に打ち切られた。HIV単離からすでに25年たった今でも、まだ効果的なワクチンは開発されていない。このように、HIVに対して従来のワクチン製造法では有効なワクチンを作れなかったとなれば、何かこれまでとは違う革新的な治療戦略が必要である。そこで、本研究では、HIVとその体内での振る舞いに関する基本的な疑問と取り組み、HIVを無力化する新しい方法を見つけ出すこと目指す。まず身体に備わった免疫応答が通常どのように機能するのかを知るために、HIVとよく似たSHIVの感染実験と数理モデルを用いて、SHIVの性状、病原性、免疫反応性を明らかにする。今回のセミナーでは、培養細胞での実験データから推定可能であるウイルスの増殖率と感染力によって特徴づけられるSHIVの病原性評価理論を紹介する。
2009/05/13
16:30 - 18:45Room #056 (Mathematics building)
大久保 俊 (東京大学大学院数理科学研究科) 16:30 - 17:30
"剰余体が非完全な場合のB_dR^+のGalois理論"
斎藤 秀司 (東京大学大学院数理科学研究科) 17:45 - 18:45
"A counterexample of Bloch-Kato conjecture over a local field and infinite torsion in algebraic cycles of codimension two"
2009/05/12
16:30 - 18:00Room #056 (Mathematics building)
松田 能文 (東京大学大学院数理科学研究科)
"Discrete subgroups of the group of circle diffeomorphisms"
Typical examples of discrete subgroups of the group of circle diffeomorphisms
are Fuchsian groups.
In this talk, we construct discrete subgroups of the group of
orientation-preserving
real analytic cirlcle diffeomorphisms
which are not topologically conjugate to finite coverings of Fuchsian groups.
16:20 - 17:30Room #126 (Mathematics building)
塩濱 敬之 (東京理科大学, 工学部)
"Asymptitically efficient estimation of multiple change points in GARCH types models"
Instability of volatility parameters in GARCH models in an important issue for analyzing financial time series. In this paper we investigate the asymptotic theory for multiple change point estimators of GARCH$(p,q)$ models. When the parameters of a GARCH models have changed within an observed realization, two types estimators, Maximum likelihood estimator (MLE) and Bayesian estimator (BE), are proposed. Then we derive the asymptotic distributions for these estimators. The MLE and BE have different limit laws, and the BE is asymptotically efficient. Monte Carlo studies on the finite sample behaviors are conducted. Applications to Nikkei 225 index are discussed.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/03.html
2009/05/11
10:30 - 12:00Room #126 (Mathematics building)
林本厚志 (長野高専)
"CR幾何学でのドラーム分解型定理"
2009/05/07
16:30 - 18:00Room #056 (Mathematics building)
見村万佐人 (東大数理)
"A fixed point property and the Kazhdan property of
$SL(n, \mathbb{Z} [X_1, \ldots , X_k])$ for Banach spaces"
2009/04/30
16:00 - 17:30Room #002 (Mathematics building)
池田 幸太 (明治大 研究・知財戦略機構)
"ギーラー・マインハルト方程式に対するシャドウ系おける多重スポットの不安定性"
生物の形態形成に関するモデル方程式である、ギーラー・マインハルト方程式に対するシャドウ系を考える。
この系にはスポットパターンと呼ばれる定常解が存在することが知られており、この解は、その値が非常に大きい点(スポット)を持つこととその近傍の外側では急激に値が減少することにより特徴付けされる。
実は、パラメータと領域を固定しても、単一のスポットだけからなるものや、2つ以上のスポットを持つ定常解、多重スポットが同時に存在しうるが、多重スポットは常に不安定であると予想されている。
本講演では、この予想を数学的に保証するために、多重スポットが適当な条件を満たせば不安定であることを示したい。
16:30 - 18:00Room #056 (Mathematics building)
酒匂宏樹 (東大数理)
"Measure Equivalence Rigidity and Bi-exactness of Groups"
2009/04/28
16:30 - 18:00Room #056 (Mathematics building)
平地 健吾 (東京大学大学院数理科学研究科)
"The ambient metric in conformal geometry"
In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.
16:30 - 18:00Room #128 (Mathematics building)
下村 明洋 (首都大学東京)
"非線型消散項を伴うシュレディンガー方程式の任意の大きさの初期データに対する解の漸近挙動(北直泰氏との共同研究)"
2009/04/27
15:30 - 18:00Room #122 (Mathematics building)
Prof. Alessandra Sarti (Universite de Poitier) 15:30 - 16:30
"Automorphism groups of K3 surfaces"
I will present recent progress in the study of prime order automorphisms of K3 surfaces.
An automorphism is called (non-) symplectic if the induced
operation on the global nowhere vanishing holomorphic two form
is (non-) trivial. After a short survey on the topic, I will
describe the topological structure of the fixed locus, the
geometry of these K3 surfaces and their moduli spaces.
Prof. Samuel Boissier (Universite de Nice
) 17:00 - 18:00
"The cohomological crepant resolution conjecture
"
The cohomological crepant resolution conjecture is one
form of Ruan's conjecture concerning the relation between the
geometry of a quotient singularity X/G - where X is a smooth
complex variety and G a finite group of automorphisms - and the
geometry of a crepant resolution of singularities of X/G ; it
generalizes the classical McKay correspondence. Following the
examples of the Hilbert schemes of points on surfaces and the
weighted projective spaces, I will present some of the recents
developments of the subject.
2009/04/23
16:30 - 18:00Room #128 (Mathematics building)
内藤克利 (首都大)
"Entire Cyclic Cohomology of Noncommutative 2-Tori"
2009/04/22
10:30 - 11:30Room #128 (Mathematics building)
Wilhelm Klingenberg (University of Durham)
"From Codazzi-Mainardi to Cauchy-Riemann"
In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.
14:45 - 18:00Room #122 (Mathematics building)
中田文憲 (東京工業大学理工学研究科) 14:45 - 16:15
"Einstein-Weyl structures on 3-dimensional Severi varieties"
The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)
Tamas Hausel (Oxford University) 16:30 - 18:00
"Toric non-Abelian Hodge theory"
First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.
15:00 - 16:10Room #128 (Mathematics building)
Arnaud DOUCET (統計数理研究所)
"Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations"
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html
2009/04/21
16:30 - 18:00Room #056 (Mathematics building)
Ivan Marin (Univ. Paris VII)
"Some algebraic aspects of KZ systems"
Knizhnik-Zamolodchikov (KZ) systems enables one
to construct representations of (generalized)
braid groups. While this geometric construction is
now very well understood, it still brings to
attention, or helps constructing, new algebraic objects.
In this talk, we will present some of them, including an
infinitesimal version of Iwahori-Hecke algebras and a
generalization of the Krammer representations of the usual
braid groups.
2009/04/20
10:30 - 12:00Room #126 (Mathematics building)
鎌田博行 (宮城教育大学)
"Indefinite K\"ahler surfaces of constant scalar curvature"
2009/04/18
11:00 - 14:30Room #117 (Mathematics building)
Vladimir Dobrev (Institute for Nuclear Reserch and Nuclear Energy, Sofia, Bulgaria) 11:00 - 12:00
"Invariant Differential Operators for Non-Compact Lie Groups"
We present a canonical procedure for the explicit construction of
invariant differential operators. The exposition is for semi-simple
Lie algebras, but is easily generalized to the supersymmetric and
quantum group settings. Especially important is a narrow class of
algebras, which we call 'conformal Lie algebras', which have very
similar properties to the conformal algebras of n-dimensional
Minkowski space-time. Examples are given in detail, including diagrams of
intertwining operators, or equivalently, multiplets of elementary
representations (generalized Verma modules).
笠谷昌弘 (東大数理) 13:30 - 14:30
"TBA"
TBA
2009/04/16
16:30 - 18:00Room #128 (Mathematics building)
緒方芳子 (東大数理)
"Large Deviations in Quantum Spin Chains"
2009/04/15
15:30 - 17:00Room #470 (Mathematics building)
Wilhelm Stannat (Darmstadt 工科大学)
"Invariant measures for stochastic partial differential equations: new a priori estimates and applications "
16:20 - 17:30Room #128 (Mathematics building)
Jean JACOD (Universite Paris VI)
"Estimating the successive Blumenthal-Getoor indices for a discretely observed process"
Letting F be a Levy measure whose "tail" $F ([-x, x])$ admits an expansion $\sigma_{i\ge 1} a_i/x^\beta$ as $x \rightarrow 0$, we call $\beta_1 > \beta_2 >...$ the successive Blumenthal-Getoor indices, since $\beta_1$ is in this case the usual Blumenthal-Getoor index. This notion may be extended to more general semimartingale. We propose here a method to estimate the $\beta_i$'s and the coefficients $a_i$'s, or rather their extension for semimartingales, when the underlying semimartingale $X$ is observed at discrete times, on fixed time interval. The asymptotic is when the time-lag goes to $0$. It is then possible to construct consistent estimators for $\beta_i$ and $a_i$ for those $i$'s such that $\beta_i > \beta_1 /2$, whereas it is impossible to do so (even when $X$ is a Levy process) for those $i$'s such that $\beta_i < \beta_1 /2$. On the other hand, a central limit theorem for $\beta_1$ is available only when $\beta_i < \beta_1 /2$: consequently, when we can actually consistently estimate some $\beta_i$'s besides $\beta_1$ , then no central limit theorem can hold, and correlatively the rates of convergence become quite slow (although one know them explicitly): so the results have some theoretical interest in the sense that they set up bounds on what is actually possible to achieve, but the practical applications are probably quite thin.
(joint with Yacine Ait-Sahalia)
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
15:00 - 16:10Room #128 (Mathematics building)
Jean JACOD (Universite Paris VI)
"A survey on realized p-variations for semimartingales"
Let $X$ be a process which is observed at the times $i\Delta_n$ for $i=0,1,\ldots,$. If $p>0$ the realized $p$-variation over the time interval $[0, t]$ is
V^n(p)_t=\sum_{i=1}^{[t/\Delta_n]}|X_{i\Delta_n}-X_{(i-1)\Delta_n}|^p.
The behavior of these $p$-variations when $\Delta_n ightarrow 0$ (and t is fixed) is now well understood, from the point of view of limits in probability (these are basically old results due to Lepingle) and also for the associated central limit theorem.
The aim of this talk is to review those results, as well as a few extensions (multipower variations, truncated variations). We will put some emphasis on the assumptions on $X$ which are needed, depending on the value of $p$.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/00.html
2009/04/14
16:30 - 18:00Room #056 (Mathematics building)
Klaus Niederkruger (Ecole normale superieure de Lyon)
"Resolution of symplectic orbifolds obtained from reduction"
We present a method to obtain resolutions of symplectic orbifolds arising from symplectic reduction of a Hamiltonian S1-manifold at a regular value. As an application, we show that all isolated cyclic singularities of a symplectic orbifold admit a resolution and that pre-quantizations of symplectic orbifolds are symplectically fillable by a smooth manifold.
2009/04/13
10:30 - 12:00Room #126 (Mathematics building)
千葉優作 (東大数理)
"A new method to generalize the Nevanlinna theory to several complex variables"
2009/04/09
16:30 - 18:00Room #128 (Mathematics building)
Dietmar Bisch (Vanderbilt University)
"Bimodules, planarity and freeness"
2009/04/08
10:30 - 11:30Room #056 (Mathematics building)
横山悦郎 (学習院大学)
"Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station"
We present a model of the time evolution of a disk crystal of ice with radius $R$ and thickness $h$ growing from supercooled water and discuss its morphological stability. Disk thickening, {\it i.e.}, growth along the $c$ axis of ice, is governed by slow molecular rearrangements on the basal faces. Growth of the radius, {\it i.e.}, growth parallel to the basal plane, is controlled by transport of latent heat. Our analysis is used to understand the symmetry breaking obtained experimentally by Shimada and Furukawa under the one-G condition. We also introduce that the space experiment of the morphological instability on the ice growing in supercooled water, which was carried out on the Japanese Experiment Module "Kibo" of International Space Station from December 2008 and February 2009.
http://kibo.jaxa.jp/experiment/theme/first/ice_crystal_end.html
We show the experimental results under the micro-G condition and discuss the feature on the "Kibo" experoments.
2009/03/25
16:00 - 17:30Room #128 (Mathematics building)
Mark Gross (University of California, San Diego)
"The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations II"
The second half of the lecture.
2009/03/24
16:00 - 17:30Room #128 (Mathematics building)
Mark Gross (University of California, San Diego)
"The Strominger-Yau-Zaslow conjecture and mirror symmetry via degenerations I"
I will discuss the SYZ conjecture which attempts to explain mirror symmetry via the existence of dual torus fibrations on mirror pairs of Calabi-Yau manifolds. After reviewing some older work on this subject, I will explain how it leads to an algebro-geometric version of this conjecture and will discuss recent work with Bernd Siebert. This recent work gives a mirror construction along with far more detailed information about the B-model side of mirror symmetry, leading to new mirror symmetry predictions.
2009/03/21
11:00 - 14:30Room #117 (Mathematics building)
梶原 康史 (神戸理) 11:00 - 12:00
"On classes of transformations for bilinear sum of
(basic) hypergeometric series and multivariate generalizations."
In this talk, I will present classes of bilinear transformation
formulas for basic hypergeometric series and Milne's multivariate
basic hypergeometric series associated with the root system of
type $A$. Our construction is similar to one of elementary
proof of Sears-Whipple transformation formula for terminating
balanced ${}_4 \phi_3$ series while we use multiple Euler
transformation formula with different dimensions which has
obtained in our previous work.
石井 卓 (成蹊大理工) 13:30 - 14:30
"On explicit formulas for Whittaker functions on real semisimple Lie groups"
will report explicit formulas
for Whittaker functions related to principal series
reprensetations on real semisimple Lie groups $G$ of
classical type.
Our explicit formulas are recursive formulas with
respect to the real rank of $G$, and in some lower rank
cases they are related to generalized
hypergeometric series $ {}_3F_2(1) $ and $ {}_4F_3(1) $.
2009/03/17
10:00 - 17:30Room #123 (Mathematics building)
Roger Zierau (Oklahoma State University) 11:00 - 12:00
"Dirac Cohomology"
Salah Mehdi (Metz University) 13:30 - 14:30
"Enright-Varadarajan modules and harmonic spinors "
Bernhard Krötz
(Max Planck Institute) 15:00 - 16:00
"Harish-Chandra modules "
Peter Trapa (Utah) 16:30 - 17:30
"Special unipotent representations of real reductive groups "
2009/03/16
10:00 - 16:20Room #123 (Mathematics building)
Bernhard Krötz
(Max Planck Institute) 10:00 - 11:00
"Harish-Chandra modules "
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:
1.Topological representation theory on various types of locally convex vector spaces.
2.Basic algebraic theory of Harish-Chandra modules
3. Unique globalization versus lower bounds for matrix coefficients
4. Dirac type sequences for representations
5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
http://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#kroetz
Peter Trapa (Utah) 11:15 - 12:15
"Special unipotent representations of real reductive groups "
These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:
1.Algebraic definition of special unipotent representations and examples.
2.Localization and duality for Harish-Chandra modules.
3. Geometric definition of special unipotent representations.
http://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#trapa
Roger Zierau (Oklahoma State University) 13:30 - 14:30
"Dirac Cohomology"
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\mathfrak g = \mathfrak h + \mathfrak q$. Let S\mathfrak q be the restriction of the spin representation of SO(\mathfrak q) to H ⊂ SO(\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \mathcal D: V \otimes S\mathfrak q → V \otimes S\mathfrak q, where V is an $\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\mathfrak n$-cohomology. The lectures will roughly contain the following.
1.Construction of the spin representations of \widetilde{SO}(n).
2.The algebraic cubic Dirac operator \mathcal D: V \otimes S\mathfrak q → V \otimes S\mathfrak q will be defined and some properties, including a formula for the square, will be given.
3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\mathfrak g,K)$-module. This case will be discussed.
4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\mathfrak n$-cohomology of V.
5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.
The lectures will be fairly elementary.
http://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#zierau
Salah Mehdi (Metz University) 15:20 - 16:20
"Enright-Varadarajan modules and harmonic spinors "
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory.
Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
http://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#mehdi
2009/03/14
09:00 - 14:00Room #123 (Mathematics building)
Roger Zierau (Oklahoma State University) 09:00 - 10:00
"Dirac cohomology"
Salah Mehdi (Metz University) 10:15 - 11:15
"Enright-Varadarajan modules and harmonic spinors"
Bernhard Krötz (Max Planck Institute) 11:45 - 12:45
"Harish-Chandra modules"
Peter Trapa (Utah University) 13:00 - 14:00
"Special unipotent representations of real reductive groups"
2009/03/13
09:30 - 16:30Room #123 (Mathematics building)
Salah Mehdi (Metz) 09:30 - 10:30
"Enright-Varadarajan modules and harmonic spinors"
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory. Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
Peter Trapa (Utah) 11:00 - 12:00
"Special unipotent representations of real reductive groups"
Bernhard Krötz
(Max Planck Institute) 13:30 - 14:30
"Harish-Chandra modules "
Roger Zierau (Oklahoma State University) 15:00 - 16:00
"Dirac Cohomology"
2009/03/12
15:00 - 17:30Room #050 (Mathematics building)
菊地文雄 (東京大学大学院数理科学研究科) 15:00 - 16:00
"数値解析:得られた成果と残された課題"
有限要素法を中心とする偏微分方程式の数値計算と数値解析に従事して長い歳月を経た。その間に偏微分方程式としては、Poisson方程式、弾性論のCauchy-Navierの方程式、非圧縮流体のStokes方程式、平板の曲げに対する重調和方程式やReissner-Mindlinの方程式、電磁気学のMaxwell方程式、プラズマ平衡のGrad-Shafranov方程式などを扱ってきたが、得られた成果もかなりある反面、残された課題も多いと思う。定年退職にあたり、少々整理と総括をしておきたい。
桂 利行 (東京大学大学院数理科学研究科) 16:30 - 17:30
"正標数の世界に40年"
正標数における代数幾何学には、標数0の場合とは異なる特有の現象がある。1950年代には、これらは病理的現象として捉えられ、研究している人の数も少なかった。現在では、特有の現象を扱うための手段がかなり整備され、正標数の様々な対象に対して興味ある現象が解析されている。代数多様体の単有理性、野性的ファイバーの問題、正標数特有のサイクルの構造等、これまで正標数の世界で行ってきた研究を中心に思い出を交えてお話ししたい。
09:30 - 14:30Room #123 (Mathematics building)
Roger Zierau (Oklahoma State University) 09:30 - 10:30
"Dirac Cohomology"
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\mathfrak g = \mathfrak h + \mathfrak q$. Let S\mathfrak q be the restriction of the spin representation of SO(\mathfrak q) to H ⊂ SO(\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \mathcal D: V \otimes S\mathfrak q → V \otimes S\mathfrak q, where V is an $\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\mathfrak n$-cohomology. The lectures will roughly contain the following.
1.Construction of the spin representations of \widetilde{SO}(n).
2.The algebraic cubic Dirac operator \mathcal D: V \otimes S\mathfrak q → V \otimes S\mathfrak q will be defined and some properties, including a formula for the square, will be given.
3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\mathfrak g,K)$-module. This case will be discussed.
4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\mathfrak n$-cohomology of V.
5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.
The lectures will be fairly elementary.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Bernhard Krötz (Max Planck) 11:00 - 12:00
"Harish-Chandra modules"
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:
1.Topological representation theory on various types of locally convex vector spaces.
2.Basic algebraic theory of Harish-Chandra modules
3. Unique globalization versus lower bounds for matrix coefficients
4. Dirac type sequences for representations
5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
Peter Trapa (Utah大学) 13:30 - 14:30
"Special unipotent representations of real reductive groups"
These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:
1.Algebraic definition of special unipotent representations and examples.
2.Localization and duality for Harish-Chandra modules.
3. Geometric definition of special unipotent representations.
2009/03/05
16:30 - 18:00Room #056 (Mathematics building)
Shicheng Wang (Peking University)
"Extending surface automorphisms over 4-space"
Let $e: M^p\to R^{p+2}$ be a co-dimensional 2 smooth embedding
from a closed orientable manifold to the Euclidean space and $E_e$ be the subgroup of ${\cal M}_M$, the mapping class group
of $M$, whose elements extend over $R^{p+2}$ as self-diffeomorphisms. Then there is a spin structure
on $M$ derived from the embedding which is preserved by each $\tau \in E_e$.
Some applications: (1) the index $[{\cal M}_{F_g}:E_e]\geq 2^{2g-1}+2^{g-1}$ for any embedding $e:F_g\to R^4$, where $F_g$
is the surface of genus $g$. (2) $[{\cal M}_{T^p}:E_e]\geq 2^p-1$ for any unknotted embedding
$e:T^p\to R^{p+2}$, where $T^p$ is the $p$-dimensional torus. Those two lower bounds are known to be sharp.
This is a joint work of Ding-Liu-Wang-Yao.
10:15 - 11:15Room #270 (Mathematics building)
V. Isakov (Wichita State Univ.)
"Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress"
We give Carleman estimates with two large parameters for general second order partial differential operators with real-valued coefficients.
We outline proofs based on differential quadratic forms and Fourier analysis. As an application, we give Carleman estimates for (anisotropic)elasticity system with residual stress and discuss applications to control theory and inverse problems.
11:15 - 12:15Room #270 (Mathematics building)
J. Ralston (UCLA)
"Determining moving boundaries from Cauchy data on remote surfaces"
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.
2009/03/04
15:00 - 16:00Room #270 (Mathematics building)
P. Gaitan (with H. Isozaki and O. Poisson) (Univ. Marseille)
"Probing for inclusions for the heat equation with complex
spherical waves"
16:15 - 17:15Room #270 (Mathematics building)
M. Cristofol (Univ. Marseille)
"Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type"
http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf
2009/03/03
16:15 - 17:15Room #270 (Mathematics building)
O. Poisson (Univ. Marseille)
"Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications"
We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.
15:00 - 16:00Room #270 (Mathematics building)
Y. Dermenjian (Univ. Marseille)
"Controllability of the heat equation in a stratified media : a consequence of its spectral structure.
"
http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf
2009/03/02
15:00 - 16:00Room #270 (Mathematics building)
Bernd Hofmann (Chemnitz University of Technology)
"Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions"
Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization
http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf
2009/02/26
17:00 - 18:30Room #270 (Mathematics building)
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
"Introduction to Coherent Risk Measure"
15:00 - 16:00Room #470 (Mathematics building)
Jijun Liu (Southeast University, P.R.China)
" Reconstruction of biological tissue conductivity by MREIT technique"
Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT)model, MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. In this talk, we will give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm and nonlinear integral equation algorithm. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.
2009/02/24
16:00 - 17:00Room #002 (Mathematics building)
神保道夫 (東京大学大学院数理科学研究科)
"相関関数の構成要素"
2次元の可積分な格子模型や、それと等価な1次元量子スピンチェインは、ベーテ、オンサーガー以来多くの研究が重ねられ、詳細に調べられている。ハミルトニアンのスペクトルと並ぶ重要な物理量に相関関数がある。イジング模型や共形場理論では相関関数自身が微分方程式で特徴づけられるがこのような簡明な結果はそれ以外の場合には知られていない。イジング模型を超える代表的な例として1次元のXXZ模型がある。相関関数は多重積分であらわされ、その長距離漸近挙動の研究が近年フランスのグループにより大きく進展している。
講演の前半では、相関関数に焦点をあててこれまでの研究の歴史を概観する。結合定数や温度などのパラメータの関数として見た場合、相関関数は2つの要素的超越関数から原理的には有理的に決まっていることがわかる。後半ではこの話題を紹介したい。
2009/02/23
13:30 - 14:30Room #123 (Mathematics building)
長田 博文 (九大数理)
"TBA"
14:40 - 16:10Room #123 (Mathematics building)
Herbert Spohn (ミュンヘン工科大学)
"Some problems from Statistical Mechanics linked to matrix-valued
Brownian motion"
16:20 - 17:50Room #123 (Mathematics building)
Stefano Olla (パリ第9大学)
"Macroscopic energy transport: a weak coupling approach"
2009/02/19
17:00 - 18:30Room #056 (Mathematics building)
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
"Introduction to Coherent Risk Measure"
15:50 - 18:00Room #128 (Mathematics building)
O. F. Pasarescu (Romanian Academy)
"・Linear Systems on Rational Surfaces; Applications (15:50--16: 50)
・Some Applications of Model Theory in Algebraic Geometry (17:00 --18:00)"
2009/02/18
10:30 - 11:30Room #056 (Mathematics building)
野原勉 (武蔵工業大学)
"Non-existence theorem of periodic solutions except out-of-phase
and in-phase solutions in the coupled van der Pol equation system"
We consider the periodic solutions of the coupled van der Pol equation system $\Sigma$, which is quite different from the ordinary van der Pol equation. We show the necessary and sufficient condition for the periodic solutions of $\Sigma$. Non-existence theorem of periodic solutions except out-of-phase and in-phase solutions in $\Sigma$ is presented.
17:00 - 18:10Room #122 (Mathematics building)
清野和彦 (東京大学大学院数理科学研究科)
"Finite group actions on spin 4-manifolds(四次元スピン多様体への有限群作用)"
2009/02/14
10:30 - 14:00Room #117 (Mathematics building)
藤健太 (神戸理) 10:30 - 11:30
"野海・山田系におけるタウ関数の関係式"
野海・山田系は, A型のドリンフェルト・ソコロフ階層の相似簡約から得られる高階
の常微分方程式系である.
本講演では, ドリンフェルト・ソコロフ階層を波動作用素を用いて考察することによっ
て, 野海・山田系のタウ関数の双線形方程式を求める.
鈴木貴雄 (神戸理) 13:00 - 14:00
"ワイル群の regular な共役類に付随するドリンフェルト・ソコロフ階層とパンルヴェ型微分方程式"
ドリンフェルト・ソコロフ階層はKdV階層のアフィン・リー代数への一般化で, ワイ
ル群の共役類(またはハイゼンベルグ部分代数)によって特徴付けられる可積分系で
ある.
本講演では, ワイル群の共役類のうち特に regular と呼ばれるものに注目し, それ
に対応するドリンフェルト・ソコロフ階層の定式化について, F.Kroode-J.Leur, Kik
uchi-Ikeda-Kakei 等の仕事を紹介しつつ解説する.
また, パンルヴェ型微分方程式との関連についても述べる.
2009/02/13
15:00 - 16:00Room #370 (Mathematics building)
Vladimir Romanov (Sobolev Instutite of Mathematics)
" ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第3講"
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.
14:00 - 14:45Room #270 (Mathematics building)
Johannes Elschner (Weierstrass Institute)
"Direct and inverse problems in fluid-solid interaction"
We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The direct problem is to determine the scattered pressure field in the fluid domain as well as the displacement field in the elastic body, while the inverse problem is to reconstruct the shape of the elastic body from the far field pattern of the fluid pressure. We present a variational approach to the direct problem and two reconstruction methods for the inverse problem, which are based on nonlinear optimization and regularization.
16:15 - 17:00Room #270 (Mathematics building)
Wenbin Chen (Fudan University)
"New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations"
In this talk, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.
2009/02/12
17:00 - 18:30Room #056 (Mathematics building)
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
"Introduction to Coherent Risk Measure"
2009/02/10
15:00 - 16:00Room #270 (Mathematics building)
Piermarco Cannarsa (Univ. degli Studi Roma "Tor Vergata")
"Carleman estimates for degenerate parabolic operators with application to null controllability "
From the controllability viewpoint, the behavior of uniformly parabolic equations is by now well understood. On the contrary, fewer results are known for degenerate parabolic equations, even though such a class of operators arise in many applied, as well as theoretical, problems.
A fairly complete analysis of the null controllability properties of degenerate parabolic equations in one space dimension was completed in a series of recent works by the speaker and coauthors. The aim of this talk is to review the above theory and present some recent results obtained in collaboration with P. Martinez and J.Vancostenoble for higher dimensional problems. Essential tools of such an approach are adapted Carleman estimates and Hardy type inequalities.
16:15 - 17:15Room #270 (Mathematics building)
Yurii Anikonov (Sobolev Institute of Mathematics)
"Constructive methods in inverse problems"
New representations for solutions and coefficients of evolutionary equations are presented. On the basic of these representations theorems of solvability for inverse problems are obtained. This direction develops constructibility in the theory and applications of inverse problems to differential equations
2009/02/07
13:30 - 16:00Room #123 (Mathematics building)
河村隆 (成蹊大学) 13:30 - 14:30
"次数2のモジュラー群の基本領域における行列式の最小値"
早田孝博 (山形大学・工学部) 15:00 - 16:00
"Siegel's fundamental domain of degree 2 and Groebner method
"
2009/02/06
15:00 - 16:00Room #370 (Mathematics building)
Vladimir Romanov (Sobolev Instutite of Mathematics)
"ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第2講 "
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.
09:45 - 11:00Room #118 (Mathematics building)
中岡 宏行 (東京大学大学院数理科学研究科)
"Brauer Groups,Mackey and Tambara functors on profinite groups,and 2-dimensional homological algebra(Brauer群、プロ有限群上のMackey及び丹原関手と2次元ホモロジー代数)"
11:00 - 12:15Room #118 (Mathematics building)
廣惠 一希 (東京大学大学院数理科学研究科)
"Generalized Whittaker functions for degenerate principal series of GL(4,R)(GL(4,R)の退化主系列表現の一般Whittaker関数)"
13:00 - 14:15Room #118 (Mathematics building)
阿部 紀行 (東京大学大学院数理科学研究科)
"On the existence of homomorphisms between principal series of complex semisimple Lie groups(複素半単純リー群の主系列表現の間の準同型の存在について)"
11:00 - 12:15Room #122 (Mathematics building)
中村 伊南沙 (東京大学大学院数理科学研究科)
"Surface links which are coverings of a trivial torus knot(自明なトーラスの被覆の形をした曲面結び目の研究)"
13:00 - 14:15Room #122 (Mathematics building)
山下 温 (東京大学大学院数理科学研究科)
"Compactification of the homeomorphism group of a graph(グラフの同相群のコンパクト化について)"
09:45 - 11:00Room #126 (Mathematics building)
乙部 達志 (東京大学大学院数理科学研究科)
"Large deviations and theorems of law of large numbers' type for the processes related to the interface models(
界面モデルに関連した確率過程に対する大偏差原理と大数の法則型極限定理)
"
13:00 - 14:15Room #126 (Mathematics building)
米田 剛 (東京大学大学院数理科学研究科)
"On the Navier-Stokes equations in a rotating frame and the functional-differential equations of advanced type - a Fourier analysis approach(フーリエ解析的手法による回転場内の流体方程式と進み型関数微分方程式の考察)
"
11:00 - 12:15Room #128 (Mathematics building)
野田 秀明 (東京大学大学院数理科学研究科)
"Short time asymptotic behavior and large deviations for Brownian motion on scale irregular Sierpinski gaskets(非正規なシェルピンスキーガスケット上のブラウン運動に対する熱核の短時間漸近挙動と大偏差原理)"
13:00 - 14:15Room #128 (Mathematics building)
河内 一樹 (東京大学大学院数理科学研究科)
"Rumor Transmission Models and Persistence Analysis(流言伝播モデルとパーシステンス解析)"
14:15 - 15:30Room #128 (Mathematics building)
川上 拓志 (東京大学大学院数理科学研究科)
"Generalized Okubo systems and the middle convolution(一般大久保型方程式とミドルコンボルーション)"
16:15 - 17:00Room #370 (Mathematics building)
G. Yuan (Northeast Normal Univ.)
"Inverse problems and observability inequalities for plate equations and Schrodinger equations."
In this talk, we will present some results on inverse problems and observability inequalities for some plate and Schrodinger equaions by using several kinds of Carleman estimates.
2009/02/05
17:00 - 18:30Room #117 (Mathematics building)
Freddy DELBAEN (チューリッヒ工科大学名誉教授)
"Introduction to Coherent Risk Measure"
16:00 - 17:30Room #002 (Mathematics building)
Jin CHENG (程 晋) (復旦大学)
"Heat transfer in composite materials with Stenfen-Boltzmann conditions and related inverse problems"
In this talk, we will present our recent results on the mathematical model of the heat transfer in the composite materials. The related inverse problems are discussed. The numerical results show our methods are effective.
15:45 - 17:00Room #118 (Mathematics building)
GOMBODORJ BAYARMAGNAI (東京大学大学院数理科学研究科)
"THE(g,K)-MODULE STRUCTURE OF PRINCIPAL SERIES AND RELATED WHITTAKER FUNCTIONS OF SU(2,2)(SU(2,2)の主系列の(g,K)-加群構造と関連するWHITTAKER関数)"
11:00 - 12:15Room #126 (Mathematics building)
関 行宏 (東京大学大学院数理科学研究科)
"On behavior of solutions near singularities for nonlinear diffusion equations(非線形拡散方程式の特異点近くでの解の挙動)"
13:00 - 14:15Room #126 (Mathematics building)
山﨑 智裕 (東京大学大学院数理科学研究科)
"Inverse Problems Related with Non-symmetric Operators and Inverse Problem for One-dimensional Fractional Partial Differential Equation(非対称作用素に関する逆問題と1次元非整数階偏微分方程式に関する逆問題)"
14:15 - 15:30Room #126 (Mathematics building)
坂本 健一 (東京大学大学院数理科学研究科)
"Inverse Source Problems for diffusion Equations and Fractional Diffusion Equations(拡散方程式及び非整数階拡散方程式に対するソース項決定逆問題)"
13:00 - 14:15Room #128 (Mathematics building)
劉 雪峰 (東京大学大学院数理科学研究科)
"Analysis of error constants for linear conforming and nonconforming finite elements(適合および非適合1次有限要素の誤差定数の解析)"
2009/02/04
15:00 - 16:10Room #128 (Mathematics building)
三浦 良造 (一橋大学国際企業戦略研究科)
"Non-Parametric Statistics for a partial sums of iid observations: New Trials"
I would lke to review Alpha- quantiles and Ranks with "Empirical Distributions" defined on partial sums of iid. observations discussed in the time continuous version (Brownian Motion).. Then revisiting the formulation of classical estimand and estimators for iid observations , described for example in Fillipova's paper, I would lik,e to discuss on what we could do for our partial sums of iid observations in orde to define our non-parametric estimators and estimands. I will be talking only on the ideas, but mathematical proofs will not be provided.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/13.html
16:20 - 17:30Room #128 (Mathematics building)
深澤 正彰 (大阪大学 金融・保険教育研究センター)
"Black-Scholes 周りの摂動展開について(前半)/ 確率積分の離散化誤差について(後半)"
(前半)確率ボラティリティモデルに対して知られている, Black-Scholes モデル周りでの各種摂動展開が統一的にマルチンゲール展開の理論によって 厳密に正当化かつ一般化されることを示す. またとくに拡散過程モデルに 対しては再生法を用いてより精密な結果を与える.
(後半)確率積分の近似として, 増大停止時刻列による区間分割 Riemann 和 をとったとき, その近似誤差の漸近分布を与える. ファイナンスへの応用とし てデルタヘッジエラーを解析し, 取引費用を考慮した上で漸近的に平均2乗誤 差を最小化する戦略を定義する.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/14.html
16:00 - 17:30Room #002 (Mathematics building)
Bendong LOU (婁 本東) (同済大学)
"Traveling waves of a curvature flow in almost periodic media"
In a plane media with almost periodic vertical striations, we study a curvature flow and construct two kinds of traveling waves, one having a straight line like profile and the other having a V shaped profile. For each of the first kind of traveling waves, its profile is the graph of a function whose derivative is almost periodic. For each of the second kind of traveling waves, its profile is like a pulsating cone, with tails asymptotically approach the first kind of traveling waves.
Also we consider a homogenization problem and provide an explicit formula for the homogenized traveling speed.
This is joint work with Xinfu Chen.
13:40 - 14:50Room #128 (Mathematics building)
Stefano Maria Iacus (Universita degli Studi di Milano)
"Applications of Iterated Function Systems to Inference and Simulation"
The Iterated Function Systems (IFSs) were born in mid eighties as applications of the theory of discrete dynamical systems and as useful tools for buildings fractals and other similar sets or to produce image compression algorithms. The fundamental result on which the IFS method is based is the Banach contraction theorem because IFSs are defined as operators with some contractive property. In practical applications the crucial point is to solve the inverse problem: given an element f in some metric space (S,d), find a contraction T:S -> S that admits a unique fixed point p such that d(f,p)< eps. When eps=0 the inverse problem is solved exactly and the fixed point p can be identified with the operator T, but in most cases T is an approximation of the target f and T takes linear forms. We present applications of the IFS technique to the problem of estimation of distribution and density functions and to the simulation of L2 stochastic processes.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/12.html
2009/02/03
16:30 - 18:00Room #126 (Mathematics building)
Gombodorj Bayarmagnai (東京大学数理科学研究科)
"The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)"
In this talk the basic object will be the principal series representataion of $SU(2, 2)$,
parabolically induced by the minimal parabolic subgroup. We discuss about the $(\mathfrak g,K)$-module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain $K$-types.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2009/02/02
16:30 - 17:30Room #123 (Mathematics building)
Erwin Bolthausen (University of Zurich)
"On a perceptron version of the Generalized Random Energy Model "
2009/01/30
16:15 - 17:15Room #370 (Mathematics building)
F. Cakoni (University of Delaware)
"Faber-Krahn Type Inequalities in Inverse Scattering Theory"
We first consider the scattering of time harmonic plane waves by a perfectly conducting infinite cylinder of cross section D. We observe that the Dirichlet eigenvalues for the Laplacian in D can be determined from the far field pattern of the scattered wave and hence from the Faber-Krahn inequality we can obtain a lower bound for the area of D. We then consider the corresponding problem for a dielectric medium. Here we observe that a relatively new type of spectra called transmission eigenvalues can be determined from the far field pattern of the scattered wave and show that transmission eigenvalues exist and form a discrete set. We then obtain a Faber-Krahn type inequality for transmission eigenvalues which, if D is known, provide a lower bound on the index of refraction n(x). Of special interest is the case when cavities may be present,i.e. regions where n(x)=1.We consider both isotropic and anisotropic materials.
15:10 - 16:10Room #370 (Mathematics building)
Lucie Baudouin (LAAS-CNRS groupe MAC)
" Use of Carleman estimates for stability in some inverse problems"
In this presentation, we shall present how global Carleman inequalities can be used to prove the well-posedness of inverse problems related to various partial differential equations. This lecture will gather joint works with J.-P. Puel, A. Osses and A. Mercado. We focus here on stability results for the determination of potential from Neumann boundary measurements by using the Bukhgeim-Klibanov method. We will begin with the simplest models: the Schrodinger and wave equations, and then present some more recent results for transmission problems (same equations with discontinuous main coefficient).
2009/01/29
16:00 - 17:30Room #002 (Mathematics building)
千葉 逸人 (京都大学 情報学研究科)
"Extension and Unification of Singular Perturbation Methods for ODE's Based on the Renormalization Gourp Method"
くりこみ群の方法は微分方程式に対する特異摂動法の一種であり,多重尺度法、平均化法、normal forms, 中心多様体縮約、位相縮約、WKB解析などの古くから知られる摂動法を統一的に扱うことができる.ここではくりこみ群の方法を数学的定式化を与え,結合振動子系などへのいくつかの応用も紹介したい.
2009/01/28
16:20 - 17:50Room #122 (Mathematics building)
吉野 伸 (東京電力)
"電場による配管損傷評価法について"
16:30 - 17:30Room #056 (Mathematics building)
Pierre Colmez (École polytechnique)
"On the p-adic local Langlands correspondence"
2009/01/27
17:00 - 18:00Room #056 (Mathematics building)
深谷 賢治 (京都大学大学院理学研究科)
"Lagrangian Floer homology and quasi homomorphism
from the group of Hamiltonian diffeomorphism
"
Entov-Polterovich constructed quasi homomorphism
from the group of Hamiltonian diffeomorphisms using
spectral invariant due to Oh etc.
In this talk I will explain a way to study this
quasi homomorphism by using Lagrangian Floer homology.
I will also explain its generalization to use quantum
cohomology with bulk deformation.
When applied to the case of toric manifold, it
gives an example where (infinitely) many quasi homomorphism
exists.
(Joint work with Oh-Ohta-Ono).
2009/01/26
10:30 - 12:00Room #128 (Mathematics building)
高山 茂晴 (東大数理)
"高次順像層のホッジ計量の正値性"
17:15 - 18:15Room #470 (Mathematics building)
Vladimir Romanov (Sobolev Instutite of Mathematics)
"ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講"
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.
16:00 - 17:00Room #470 (Mathematics building)
Vilmos Komornik (University of Strasbourg)
"Ingham-Beurling type inequalities"
We present a self-contained constructive proof for a multidimensional generalization of Beurling's optimal condition for the validity of Ingham type estimates. We illustrate the usefulness of the result on a particular observability problem.
2009/01/24
11:00 - 16:00Room #117 (Mathematics building)
仲田 研登 (京大数研) 11:00 - 12:00
"一般化されたヤング図形の q-Hook formula"
Young図形における hook formula は、組合せ論的には、その Young 図形の standar
d tableau の総数を数え上げる公式である。R. P. Stanley は reverse plane parti
tion のなす母関数を考えることにより、この公式をq-hook formula に拡張し、E. R
. Gansner はそれをさらに多変数に一般化した。
本講演では、この(多変数)q-Hook formula が(D. Peterson、R. A. Proctor の意
味の)一般化されたYoung図形においても成り立つこと紹介する。特にこれはPeterso
n の hook formula の証明も与える。
土岡 俊介 (京大数研) 13:30 - 14:30
"Catalan numbers and level 2 weight structures of $A^{(1)}_{p-1}$"
Motivated by a connection between representation theory of
the degenerate affine Hecke algebra of type A and
Lie theory associated with $A^{(1)}_{p-1}$, we determine the complete
set of representatives of the orbits for the Weyl group action on
the set of weights of level 2 integrable highest weight representations of $\widehat{\mathfrak{sl}}_p$.
Applying a crystal technique, we show that Catalan numbers appear in their weight multiplicities.
Here "a crystal technique" means a result based on a joint work with S.Ariki and V.Kreiman,
which (as an application of the Littelmann's path model) combinatorially characterize
the connected component (usually called Kleshchev bipartition in the representation theoretic context)
$B(\Lambda_0+\Lambda_s)\subseteq B(\Lambda_0)\otimes B(\Lambda_s)$ in the tensor product.
中野 史彦 (高知大理学部数学) 15:00 - 16:00
"On a dimer model with impurities"
We consider the dimer problem on a non-bipartite graph $G$, where there are two types of dimers one of which we regard impurities. Results of simulations using Markov chain seem to indicate that impurities are tend to distribute on the boundary, which we set as a conjecture. We first show that there is a bijection between the set of dimer coverings on
$G$ and the set of spanning forests on two graphs which are made from $G$, with configuration of impurities satisfying a pairing condition, and this bijection can be regarded as a extension of the Temperley bijection. We consider local move consisting of two operations, and by using the bijection mentioned above, we prove local move connectedness. Finally, we prove that the above conjecture is true,
in some spacial cases.
2009/01/23
16:20 - 17:50Room #128 (Mathematics building)
渡辺 秀明 (防衛省技術研究本部電子装備研究所)
"防衛電子技術についてⅡ"
17:00 - 18:00Room #370 (Mathematics building)
Eric Opdam (University of Amsterdam )
"The spectral category of Hecke algebras and applications 第4講 Example: Lusztig's unipotent representations for classical groups."
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
2009/01/22
16:30 - 18:00Room #128 (Mathematics building)
関根良紹 (東大数理)
"On the electron-phonon interacting system"
17:00 - 18:00Room #370 (Mathematics building)
Eric Opdam (University of Amsterdam)
" The spectral category of Hecke algebras and applications 第3講 The spectral category and correspondences of tempered representations.
"
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
2009/01/21
16:50 - 17:50Room #123 (Mathematics building)
Erwin Bolthausen (University of Zurich)
"The quenched critical point of a diluted disordered polymer model and the related question for the random copolymer "
2009/01/20
16:30 - 18:00Room #128 (Mathematics building)
吉野 邦生 (武蔵工業大学)
"Generating function of eigenvalues of Daubechies Localization Operator"
Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について
16:30 - 17:30Room #002 (Mathematics building)
野澤 啓 (東京大学大学院数理科学研究科)
"Five dimensional $K$-contact manifolds of rank 2"
A $K$-contact manifold is an odd dimensional manifold $M$ with a contact form $\alpha$ whose Reeb flow preserves a Riemannian metric on $M$. For examples, the underlying manifold with the underlying contact form of a Sasakian manifold is $K$-contact. In this talk, we will state our results on classification up to surgeries, the existence of compatible Sasakian metrics and a sufficient condition to be toric for closed $5$-dimensional $K$-contact manifolds with a $T^2$ action given by the closure of the Reeb flow, which are obtained by the application of Morse theory to the contact moment map for the $T^2$ action.
17:30 - 18:30Room #002 (Mathematics building)
中村 伊南沙 (東京大学大学院数理科学研究科)
"Surface links which are coverings of a trivial torus knot"
We consider surface links which are in the form of coverings of a
trivial torus knot, which we will call torus-covering-links.
By definition, torus-covering-links include
spun $T^2$-knots, turned spun $T^2$-knots, and symmetry-spun tori.
We see some properties of torus-covering-links.
2009/01/19
10:30 - 12:00Room #128 (Mathematics building)
金子 宏 (東京理科大理)
"確率論的視点による単位円周の双対としてのp進整数環の考察"
2009/01/16
16:20 - 17:50Room #128 (Mathematics building)
渡辺 秀明 (防衛省技術研究本部電子装備研究所)
"防衛電子技術についてⅠ"
2009/01/15
16:30 - 18:00Room #126 (Mathematics building)
Alin Ciuperca (Univ. Toronto)
"Isomorphism of Hilbert modules over stably finite $C^*$-algebras"
16:00 - 17:30Room #002 (Mathematics building)
木村 正人 (九州大学・大学院数理学研究院)
"On a phase field model for mode III crack growth"
2次元弾性体の面外変形による亀裂の進展を記述する,ある
フェイズ・フィールド・モデルについて考える.モデルの
導出は,Francfort-Marigoによる拡張された意味での
Griffithの破壊基準をもとに,Ambrosio-Tortorelliに
よるエネルギー正則化のアイデアを用いてなされる.
現状で得られている数学的な結果と,適合型メッシュを
用いた有限要素シミュレーション例についての紹介も行う.
本研究は高石武史(広島国際学院大学)との共同研究である.
16:30 - 18:00Room #126 (Mathematics building)
Alin Ciuperca (Univ. Toronto)
"Isomorphism of Hilbert modules over stably finite $C^*$-algebras"
13:30 - 17:20Room #050 (Mathematics building)
柏原正樹 (京都大学数理解析研究所) 13:30 - 14:30
"Quantization of complex manifolds"
http://www.ms.u-tokyo.ac.jp/~toshi/index.files/oshima60th200901.html
小林俊行 (東京大学大学院数理科学研究科) 15:00 - 16:00
"Global geometry on locally symmetric spaces — beyond the Riemannian case "
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.
In this talk, I plan to give an exposition on the recent developments on the question about the global natures of locally non-Riemannian homogeneous spaces, with emphasis on the existence problem of compact forms, rigidity and deformation.
大島利雄 (東京大学大学院数理科学研究科) 16:20 - 17:20
"Classification of Fuchsian systems and their connection problem"
We explain a classification of Fuchsian systems on the Riemann sphere together with Katz's middle convolution, Yokoyama's extension and their relation to a Kac-Moody root system discovered by Crawley-Boevey.
Then we present a beautifully unified connection formula for the solution of the Fuchsian ordinary differential equation without moduli and apply the formula to the harmonic analysis on a symmetric space.
2009/01/14
16:00 - 17:30Room #002 (Mathematics building)
片山 統裕 (東北大学 大学院情報科学研究科 応用情報科学専攻)
"中枢ニューロン樹状突起における酵素活性化ウェーブとその数理モデル"
ニューロンの興奮性の調節やシナプス可塑性において重要な役割を担っているC型タンパク質リン酸化酵素(PKC)は,その酵素活性と関連して細胞内局在が変化する性質を有する(トランスロケーション).GFP-γPKC融合タンパクを発現させたマウス小脳プルキンエ細胞において,平行線維シナプスの高頻度刺激に伴い,刺激部位近傍から樹状突起に沿ってトランスロケーションが伝播する現象が報告されている.最近,坪川は,同じ刺激条件で樹状突起内をほぼ同速度で伝播する細胞内Ca2+波が生じることを見出し,これがγPKCトランスロケーション波をリードしている可能性を指摘した.本研究では,生理学的・解剖学的知見に基づいたプルキンエ細胞の数理モデルを構築し,Ca2+波の再現を試みた.その結果に基づき,トランスロケーション伝播のメカニズムと機能的意義について考察する.
2009/01/13
10:30 - 11:30Room #002 (Mathematics building)
Gieri Simonett (Vanderbilt University, USA)
"Analytic semigroups, maximal regularity and nonlinear parabolic problems"
http://www.math.sci.hokudai.ac.jp/sympo/090113/index.html
16:30 - 17:30Room #002 (Mathematics building)
山下 温 (東京大学大学院数理科学研究科)
"Compactification of the homeomorphism group of a graph"
Topological properties of homeomorphism groups, especially of finite-dimensional manifolds,
have been of interest in the area of infinite-dimensional manifold topology.
For a locally finite graph $\Gamma$ with countably many components,
the homeomorphism group $\mathcal{H}(\Gamma)$
and its identity component $\mathcal{H}_+(\Gamma)$ are topological groups
with respect to the compact-open topology. I will define natural compactifications
$\overline{\mathcal{H}}(\Gamma)$ and
$\overline{\mathcal{H}}_+(\Gamma)$ of these groups and describe the
topological type of the pair $(\overline{\mathcal{H}}_+(\Gamma), \mathcal{H}_+(\Gamma))$
using the data of $\Gamma$. I will also discuss the topological structure of
$\overline{\mathcal{H}}(\Gamma)$ where $\Gamma$ is the circle.
2009/01/12
16:30 - 18:00Room #126 (Mathematics building)
西岡斉治 (東京大学大学院数理科学研究科博士課程)
"代数的差分方程式の可解性と既約性"
差分代数の理論を使って,代数的差分方程式の代数函数解や超幾
何函数解の非存在や,存在する場合の特殊解の分類をする。
16:30 - 18:00Room #128 (Mathematics building)
Jacob S. Christiansen
(コペンハーゲン大学)
"Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)"
2009/01/09
17:00 - 18:00Room #123 (Mathematics building)
Eric Opdam (University of Amsterdam)
"The spectral category of Hecke algebras and applications 第2講 Affine Hecke algebras and harmonic analysis.
"
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
16:00 - 17:00Room #370 (Mathematics building)
Leevan Ling (Hong Kong Baptist University)
"Effective Condition Numbers and Laplace Equations
"
The condition number of a matrix is commonly used for investigating the
stability of solutions to linear algebraic systems. Recent meshless
techniques for solving PDEs have been known to give rise to
ill-conditioned matrices, yet are still able to produce results that are
close to machine accuracy. In this work, we consider the method of
fundamental solutions (MFS), which is known to solve, with extremely high
accuracy, certain
partial differential equations, namely those for which a fundamental
solution is known. To investigate the applicability of the MFS, either when
the boundary is not analytic or when the boundary data is not harmonic, we
examine the relationship between its accuracy and the effective condition
number.
16:00 - 17:00Room #370 (Mathematics building)
Leevan Ling (Hong Kong Baptist University)
"Effective Condition Numbers and Laplace Equations"
The condition number of a matrix is commonly used for investigating the stability of solutions to linear algebraic systems. Recent meshless techniques for solving PDEs have been known to give rise to ill-conditioned matrices, yet are still able to produce results that are close to machine accuracy. In this work, we consider the method of fundamental solutions (MFS), which is known to solve, with extremely high accuracy, certain partial differential equations, namely those for which a fundamental solution is known. To investigate the applicability of the MFS, either when the boundary is not analytic or when the boundary data is not harmonic, we examine the relationship between its accuracy and the effective condition number.
2009/01/08
16:30 - 18:00Room #128 (Mathematics building)
Stefaan Vaes (K. U. Leuven)
"Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors"
16:30 - 18:00Room #128 (Mathematics building)
Stefaan Vaes (K. U. Leuven)
"Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors"
16:30 - 17:30Room #056 (Mathematics building)
伊東一文 (North Carolina State University)
"Calibration problems for Black-Scholes American Options under the GMMY process"
The calibration problem is formulated as a control problem for the parabolic variational inequality. The well-posedness of the formulation is discussed and the necessary optimality is derived. A numerical approximation method is also presented.
17:00 - 18:00Room #123 (Mathematics building)
Eric Opdam (University of Amsterdam)
"The spectral category of Hecke algebras and applications
第1講: Reductive p-adic groups and Hecke algebras "
Hecke algebras play an important role in the harmonic analysis of a p-adic reductive group. On the other hand, their representation theory and harmonic analysis can be described almost completely explicitly. This makes affine Hecke algebras an ideal tool to study the harmonic analysis of p-adic groups. We will illustrate this in this series of lectures by explaining how various components of the Bernstein center contribute to the level-0 L-packets of tempered representations, purely from the point of view of harmonic analysis.
We define a "spectral category" of (affine) Hecke algebras. The morphisms in this category are not algebra morphisms but are affine morphisms between the associated tori of unramified characters, which are compatible with respect to the so-called Harish-Chandra μ-functions. We show that such a morphism generates a Plancherel measure preserving correspondence between the tempered spectra of the two Hecke algebras involved. We will discuss typical examples of spectral morphisms.
We apply the spectral correspondences of affine Hecke algebras to level-0 representations of a quasi-split simple p-adic group. We will concentrate on the example of the special orthogonal groups $SO_{2n+1}(K)$. We show that all affine Hecke algebras which arise in this context admit a *unique* spectral morphism to the Iwahori-Matsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam
2009/01/06
16:00 - 17:30Room #123 (Mathematics building)
森洋一朗 (ミネソタ大学)
"GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第3回)"
第3回: 心臓の電気生理
・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播
14:00 - 15:30Room #123 (Mathematics building)
森洋一朗 (ミネソタ大学)
"GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第2回)"
第2回: 神経細胞の電気生理
・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導
2009/01/05
16:00 - 17:30Room #123 (Mathematics building)
森洋一朗 (ミネソタ大学)
"GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第1回)"
第1回: 電気生理学の基礎概念入門 (5日 16:00-17:30)
・ 膜電位とイオンチャネル
・ 細胞の体積調節
・ チャネルの開閉
・ Hodgkin-Huxley モデルと興奮性
第2回: 神経細胞の電気生理 (6日 14:00-15:30)
・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導
第3回: 心臓の電気生理 (6日 16:00-17:30)
・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播
数理生理学は生理現象を数理モデルを用いて解明しようとする営みであって,実験生物学の定量化,計算機の高速化にともなって急速に発展してきている分野です.この講義では数理生理学の中でも古典的な分野である電気生理学の数理について解説します.
生物学の予備知識は仮定しません.ごく初等的な微分方程式の知識で十分理解できる内容ですが,一部で応用数学の標準的手法(接合漸近展開、均質化極限など)を用います.第1回目の内容が講義全体の基礎となりますが,第2回目と第3回目の講義を独立に聴講することも可能です.またテーマにあわせて最近の話題についても触れる予定です。
講演者のプロフィール:
森洋一朗氏は,東京大学医学部を卒業後,渡米してニューヨーク大学(クーラント研究所)で数学の学位を得ました.すでに数々の賞を受賞しており,数理生物学における若手のホープとして国際的に高く評価されています.
2008/12/26
13:30 - 16:00Room #123 (Mathematics building)
軍司圭一 (Postech) 13:30 - 14:30
"On Siegel Eisenstein series of degree two and weight 2"
Cups singularities の組み合わせ論的な解析を援用して、あるレベルのモジュラー群に対する表題の空間の次元を決定する。
未定 (未定) 15:00 - 16:00
"未定"
2008/12/19
16:20 - 17:50Room #128 (Mathematics building)
高野 康 (みずほ第一フィナンシャルテクノロジー)
"金融リスク管理と数理Ⅱ(応用編)"
2008/12/18
16:30 - 18:00Room #128 (Mathematics building)
Benoit Collins (東大数理/Ottawa 大学)
"Some geometric and probabilistic properties of the free quantum group $A_o(n)$"
2008/12/17
13:40 - 14:50Room #002 (Mathematics building)
Ilia Negri (University of Bergamo, Italy)
"Goodness of fit tests for ergodic diffusions by discrete sampling schemes"
We consider a nonparametric goodness of fit test problem for the drift coefficient of one-dimensional ergodic diffusions, where the diffusion coefficient is a nuisance function which is estimated in some sense. Using a theory for the continuous observation case, we construct two kinds of tests based on different types of discrete observations, namely, the data observed discretely in time or in space. We prove that the limit distribution of our tests is the supremum of the standard Brownian motion, and thus our tests are asymptotically distribution free. We also show that our tests are consistent under any fixed alternatives.
joint with Yoichi Nishiyama (Inst. Statist. Math.)
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/09.html
15:00 - 16:10Room #002 (Mathematics building)
Stefano Maria Iacus (Universita degli Studi di Milano, Italy)
"Divergences Test Statistics for Discretely Observed Diffusion Processes"
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, theta)dt + sigma(Xt, theta) dWt, from discrete observations at times ti = i*Dn, i=0, 1, ..., n, under the asymptotic scheme Dn - 0, n*Dn - +oo and n*Dn^2 - 0. The class of phi-divergences is wide and includes several special members like Kullback-Leibler, Renyi, power and alpha-divergences. We derive the asymptotic distribution of the test statistics based on phi- divergences. The limiting law takes different forms depending on the regularity of phi. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.
joint work with A. De Gregorio
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/10.html
16:20 - 17:30Room #002 (Mathematics building)
Nicolas Privault (City University of Hong Kong)
"Stein estimation of Poisson process intensities"
In this talk we will construct superefficient estimators of Stein type for the intensity parameter lambda > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/11.html
2008/12/12
16:20 - 17:50Room #128 (Mathematics building)
吉野 伸 (東京電力)
"ガスタービン翼の伝熱について"
2008/12/11
16:30 - 18:00Room #128 (Mathematics building)
佐藤康彦 (北大理)
"Certain aperiodic automorphisms of unital simple projectionless $C^*$-algebras"
2008/12/10
14:45 - 18:00Room #122 (Mathematics building)
吉田 尚彦 (明治大学大学院理工学研究科) 14:45 - 16:15
"Acyclic polarizations and localization of Riemann-Roch numbers"
前量子化可能な閉シンプレクティック多様体が(特異)Lagrange ファイバー空間の構造を持つ場合,Riemann-Roch 数が Bohr-Sommerfeld ファイバーの個数と一致することがトーリック多様体,ユニタリー群の Gelfand-Cetlin 系や Riemann 面上の平坦 SU(2) 束のモジュライなどの例で,双方を別々に計算し比較することにより,確かめられている.本講演では,spin^c Dirac 作用素の指数に対する Witten 流の局所化を用いることによって,Riemann-Roch 数が非特異 Bohr-Sommerfeld ファイバー及び特異ファイバーに局所化することを示す.(古田幹雄氏(東大数理),藤田玄氏(学習院大学)との共同研究.論文:arXiv:0804.3258)
Megumi Harada (McMaster University) 16:30 - 18:00
"The topology of symplectic and hyperkahler quotients"
Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a Hamiltonian G-action for a Lie group G, i.e. an action with an associated moment map -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as Hamiltonian quotients. In the first part of the talk, I will give a bird's-eye, motivating overview of this subject, and in particular will introduce one of the main technical tools of the field, which is the Morse theory associated to the moment map. In the second part, I will give a more detailed account of recent joint work with Graeme Wilkin, which deals with Nakajima quiver varieties, a special case of hyperkahler Hamiltonian quotients. In particular, we develop a Morse theory for the hyperkahler moment map analogous to the case of the moduli space of Higgs bundles. In particular, we show that the Harder-Narasimhan stratification of spaces of representations of quivers coincide with the Morse-theoretic stratification associated to the norm-square of the real moment map. Our approach also provides insight into the topology of specific examples of small-rank quiver varieties, including hyperpolygon spaces and some ADHM quivers.
2008/12/09
16:30 - 18:00Room #056 (Mathematics building)
Bertrand Deroin (CNRS, Orsay, Universit\'e Paris-Sud 11)
"Tits alternative in $Diff^1(S^1)$"
The following form of Tits alternative for subgroups of
homeomorphisms of the circle has been proved by Margulis: or the group
preserve a probability measure on the circle, or it contains a free
subgroup on two generators. We will prove that if the group acts by diffeomorphisms of
class $C^1$ and does not preserve a probability measure on the circle, then
in fact it contains a subgroup topologically conjugated to a Schottky group.
This is a joint work with V. Kleptsyn and A. Navas.
2008/12/08
10:30 - 12:00Room #128 (Mathematics building)
上田 哲生 (京大理)
"Critically finite holomorphic maps on projective spaces"
2008/12/05
16:20 - 17:50Room #128 (Mathematics building)
池森 俊文 (みずほ第一フィナンシャルテクノロジー)
"金融リスク管理と数理Ⅰ(基礎編)"
2008/12/04
16:30 - 18:00Room #128 (Mathematics building)
戸松玲治 (東大数理)
"カッツ環の作用の分類"
17:00 - 18:00Room #056 (Mathematics building)
Genkai Zhang (Chalmers and Gothenburg University)
"Realization of quanternionic discrete series as spaces of H-holomorphic
functions"
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2008/12/03
17:30 - 19:00Room #122 (Mathematics building)
Freddy Delaben (ETH)
"The structure of dynamic utility functions in a Brownian Filtration
"
The penalty function for monetary dynamic utility functions
has a special form. They can be seen as potentials. In the Brownian Filtration Rao's theorem permits to give a complete description.
16:30 - 17:30Room #056 (Mathematics building)
鈴木正俊 (東京大学大学院数理科学研究科)
"Mean-periodicity and analytic properties of zeta-functions"
Mean-periodicityというのは周期性の概念のひとつの一般化である。最近、I. Fesenko, G. Ricottaとの共同研究により、数論的スキームのゼータ関数を含むある複素関数のクラスと、mean-periodicityとの関連性が新しく見出された。
これはHecke-Weilによる, 解析接続と関数等式を持つDirichlet級数と保型形式との対応の一つの拡張ともみなせる. この背景には, I. Fesenkoの高次元アデール上のゼータ積分の理論があり、数論的スキームのHasseゼータ関数の解析接続を高次元アデール上の調和解析から導こうというプログラムの一環となっている。
この講演ではそのような背景にも若干触れた上、ゼータ関数の解析的性質とmean-periodicityの関連、特に解析接続と関数等式との関連について解説する。
2008/12/02
17:00 - 18:00Room #056 (Mathematics building)
金井雅彦 (名古屋大学)
"消滅と剛性"
The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other.
The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
17:00 - 18:00Room #056 (Mathematics building)
金井 雅彦 (名古屋大学多元数理科学研究科)
"Vanishing and Rigidity"
The aim of my talk is to reveal an unforeseen link between
the classical vanishing theorems of Matsushima and Weil, on the one hand,
andrigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank
noncompact Lie group, on the other. The connection is established via
"transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the
orbit foliation of the Weyl chamber flow that is tangentially closed
(and satisfies a certain mild additional condition) can be extended to a closed 1- form on the
whole space in a canonical manner. In particular, infinitesimal
rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
2008/12/01
10:30 - 12:00Room #128 (Mathematics building)
川上 裕 (九大数理/大阪市立大)
"双曲的Gauss写像の値分布"
17:00 - 18:30Room #002 (Mathematics building)
Kentaro Hori (University of Toronto / IPMU)
"A pair of non-birational but derived equivalent Calabi-Yau
manifolds from non-Abelian gauge theories"
We construct a family of (2,2) supersymmetric gauge theories
in 2-dimensions that flows to a family of (2,2) superconformal fields theories with \hat{c}=3. The family has two limits and three singular points. The two limits correspond to two Calabi-Yau manifolds which are not birationally equivalent. The two are, however, derived equivalent
by general principle of supersymmetric quantum field theory.
2008/11/28
16:20 - 17:50Room #128 (Mathematics building)
中川 淳一 (新日本製鐵先端技術研究所)
"製鐵プロセスの数学Ⅱ"
16:30 - 17:30Room #123 (Mathematics building)
川又雄二郎 (東京大学大学院数理科学研究科)
"曲線の錐体と因子の錐体"
代数多様体上に載っている曲線と因子の交点数を使うと、互いに双対な有限次元実ベクトル空間内の、互いに双対な閉凸錐体 -- 曲線の錐体と因子の錐体が定義される。極小モデル理論では、曲線の錐体の端射線から収縮写像が構成されるが、双有理同値な代数多様体をたくさん同時に考えるためには、因子の錐体のほうが便利である。標準環の有限生成定理は、因子の錐体の集まりの間の壁越えの様子を詳しく調べることによって証明された。一般の代数多様体に対する極小モデルの存在は未解決問題であるが、そのためには因子の錐体についてのより深い理解が必要と思われる。この講演ではそのあたりの事情を解説する。
[開催日にご注意下さい]
14:40 - 16:10Room #002 (Mathematics building)
Andrei Pajitnov (Univ. de Nantes)
"Circle-valued Morse theory
, Lecture 2"
2008/11/26
16:30 - 18:00Room #122 (Mathematics building)
Piotr Pragacz
(Banach Institute)
"Diagonal subschemes and vector bundles"
14:40 - 16:10Room #002 (Mathematics building)
Andrei Pajitnov (Univ. de Nantes)
"Circle-valued Morse theory, Lecture 1"
Morse theory of circle-valued functions, initiated by S. P. Novikov in 1980-1982 is now a rapidly developing domain with applications and connections to many other fields of geometry and topology such as dynamical systems, Lagrangian intersections,
knots and links in three-dimensional sphere.
We will start with the basics of the theory, discuss the construction of the Novikov complex, relations with the dynamical zeta functions, and the knot theory. We will conclude with a list of the open problems of the theory.
16:30 - 17:30Room #056 (Mathematics building)
平田典子 (日本大学理工学部)
"Lang's Observation in Diophantine Problems"
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\varphi$ be a rational function on $E$. Then, for every point $P\in E(K)$ where $\varphi$ does not vanish at $P$, the logarithms of a norm of $\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.
2008/11/25
16:30 - 18:00Room #128 (Mathematics building)
Ovidiu Calin (Eastern Michigan University)
"Heat kernels for subelliptic operators"
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.
16:30 - 18:00Room #118 (Mathematics building)
Xavier Roulleau (東大)
"Cotangent maps of surfaces of general type"
Surfaces are usualy studied and classified via the properties of the pluricanonical maps. For surfaces of general type whose cotangent sheaf is generated by global sections, we propose to study an other map, called the cotangent map, in order to obtain geometric informations on the surface. In this way, we obtain informations on the ampleness of the cotangent sheaf of such a surface. We will illustate this talk with the example of the Fano surface of lines of cubic threefolds.
16:30 - 18:00Room #126 (Mathematics building)
吉野太郎 (東工大)
"$\mathbb R^n$への$\mathbb R^2$の固有な作用と周期性"
Consider $\R^2$ actions on $\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:
"Does the quotient topology admits a manifold structure?"
Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.
If Lipsman's conjecture were true, all of the answer should be affirmative.
But, we shall find a unique action which gives a negative answer for each $n\geq 5$. And, we also find a periodicity on such counterexamples.
As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
16:30 - 18:00Room #056 (Mathematics building)
Andrei Pajitnov (Univ. de Nantes)
"Circle-valued Morse theory for knots and links"
We will discuss several recent developments in
this theory. In the first part of the talk we prove that the Morse-Novikov number of a knot is less than or equal to twice the tunnel number of the knot, and present consequences of this result. In the second part we report on our joint project with Hiroshi Goda on the half-transversal Morse-Novikov theory for 3-manifolds.
2008/11/22
13:30 - 16:00Room #117 (Mathematics building)
桂 法称 ((理化学研究所)
理化学研究所) 13:30 - 14:30
"Quantum Entanglement in Exactly Solvable Models"
近年、量子情報論的な観点からの量子多体問題の研究が盛んに行われている。
特に基底状態におけるentanglementのvon Neumann(entanglement) entropyなどの
指標を用いた特徴づけが盛んに議論されている。これらの研究において可解模型
は、この新しく導入された指標が量子多体系の基本性質を正しく反映しているか
をテストする一種の実験室として重要な役割を果たしてきた。セミナーでは、
先ずentanglement entropyの定義などについての簡単な説明を行い、その後私が
主に行ってきた以下の幾つかのテーマについてご紹介したい。
1. Affleck-Kennedy-Lieb-Tasaki modelのvalence bond solid基底状態におけるenta
nglementと端状態
2. Calogero-Sutherland modelにおける粒子間entanglementと排他的分数統計
3. Bethe ansatz波動関数の行列積表示
尚、本研究は初田泰之(東大理), 平野嵩明(東大工)、丸山勲(大阪大)、初貝安弘(筑
波大)、Ying Xu, Vladimir E. Korepin(SUNY at Stony Brook)各氏との共同研究に基
づくものである。
尾角正人 (阪大基礎工) 15:00 - 16:00
"非例外型KRクリスタルについて"
KRクリスタルとはアフィンリー環gのディンキン図の0以外の頂点と
正整数に付随して定義される量子アフィン代数の特殊な有限次元
表現(KR加群)の結晶基底である。KRクリスタルの存在は非例外型
の場合には昨年確認された。今年になって、それらの結晶グラフの
構造が組合せ論的に具体的にわかる進展があったので、そのこと
についてgが$A_{2n-1}^{(2)}$と$C_n^{(1)}$の場合にお話したい。
また、組合せ論的に与えた結晶グラフが、なぜ表現論的に存在が
わかった結晶基底のグラフと一致するかについての証明の概略に
ついても触れたい。
2008/11/21
16:20 - 17:50Room #128 (Mathematics building)
大本 隆 (野村證券金融工学研究センター)
"デリバティブ・プロダクツの価格付け II"
16:30 - 17:30Room #002 (Mathematics building)
平地健吾 (東京大学大学院数理科学研究科)
"What is Q-curvature? "
共形幾何は次元の偶奇におうじて著しく異なった性質をもちます。その多くは n次元球面の共形自己同型群SO(n+1,1)が奇数次元ならB型,偶数次元ならD型になるといことから説明できます。この講演では偶数次元にのみ現れるQ-曲率とよばれる局所不変量とその周辺に現れる共形不変量および不変作用素の理論を紹介します。Q-曲率はAdS/CFT対応にも自然に現れることもあり,最近の共形幾何の主要テーマになっていますが,その定義は簡単ではありません。Q-曲率の(短い)歴史と表現論の結果をふまえて,なっとくのできる定義を与えることを目指します。
次回開催日は11月28日(金)(講演者:川又雄二郎 氏)です。ご注意下さい。
2008/11/20
16:00 - 17:30Room #002 (Mathematics building)
Jan Haskovec
(Vienna University of Technology(オーストリア))
"Stochastic Particle Approximation for Measure Valued Solutions of the 2D Keller-Segel System"
We construct an approximation to the measure valued, global in time solutions to the Keller-Segel model in 2D, based on systems of stochastic interacting particles. The advantage of our approach is that it reproduces the well-known dichtomy in the qualitative behavior of the system and, moreover, captures the solution even after the possible blow-up events. We present a numerical method based on this approach and show some numerical results. Moreover, we make a first step toward the convergence analysis of our scheme by proving the convergence of the stochastic particle approximation for the Keller-Segel model with a regularized interaction potential. The proof is based on a BBGKY-like approach for the corresponding particle distribution function.
2008/11/19
16:30 - 17:30Room #056 (Mathematics building)
Olivier Fouquet (大阪大学)
"Dihedral Iwasawa theory of ordinary modular forms"
According to Hida theory, the Galois representation attached to a nearly-ordinary Hilbert eigencuspform belongs to a p-adic analytic family of Galois representations parametrized by varying weights. After restricting it to the absolute Galois group of a quadratic totally complex extension, it also belongs to a p-adic family coming from classical dihedral Iwasawa theory. We will explain the proofs of part of the main conjecture in Iwasawa theory in these situations, i.e divisibilities of characteristic ideals when equalities are actually expected.
2008/11/18
16:30 - 18:00Room #126 (Mathematics building)
Jorge Vargas (FAMAF-CIEM, C\'ordoba)
"Liouville measures and multiplicity formulae for admissible restriction of Discrete Series"
Let $H \subset G$ be reductive matrix Lie groups. We fix a square integrable irreducible representation $\pi$ of $G.$
Let $\Omega $ denote the coadjoint orbit of the Harish-Chandra parameter of $\pi.$
Assume $\pi$ restricted to $H$ is admissible. In joint work with Michel Duflo, by means of "discrete" and "continuos" Heaviside functions we relate the multiplicity of each irreducible $H-$factor of $\pi$ restricted to $H$ and push forward to $\mathfrak h^\star$ of the Liouville measure for $\Omega.$ This generalizes work of Duflo-Heckman-Vergne.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
17:00 - 18:00Room #056 (Mathematics building)
宍倉 光広 (京都大学大学院理学研究科)
"複素力学系のくりこみと剛性"
無限に分岐が集積しているような
ある種の力学系においては、相空間やパラメータ空間の
微細構造が取り上げる個々の力学系の族に寄らない
普遍的構造をもったりすることが知られており、
ある意味で剛性の問題とつながっている。この現象の説明には、
ある部分集合への再帰写像の構成から得られる、あるクラスの
力学系全体の空間で定義されるメタ力学系としての
くりこみ作用素の考え方が重要である。これに関して、
講演者と稲生啓行による中立的不動点をもつ複素力学系の
近放物型くりこみの話を中心に解説する。
2008/11/17
10:30 - 12:00Room #128 (Mathematics building)
野沢 啓 (東大数理)
"Deformation of Sasakian metrics"
2008/11/14
16:20 - 17:50Room #128 (Mathematics building)
中川 淳一 (新日本製鐵先端技術研究所)
"製鐵プロセスの数学Ⅰ"
2008/11/13
16:00 - 17:30Room #002 (Mathematics building)
杉山 由恵 (津田塾大学・学芸学部・数学科)
"Aronson-Benilan type estimate and the optimal Hoelder continuity of weak solutions for the 1D degenerate Keller-Segel systems"
We consider the Cauchy problem for the 1D Keller-Segel system of degenerate
type (KS)_m with $m>1$:
u_t= \partial_x^2 u^m - \partial_x (u^{q-2} \partial_x v),
-\partial_x^2 v + v - u=0.
We establish a uniform estimate from below of $\partial_x^2 u^{m-1}$.
The corresponding estimate to the porous medium equation is well-known
as an Aronson-Benilan type.
As an application of our Aronson-Benilan type estimate,
we prove the optimal Hoelder continuity of the weak solution $u$ of (KS)_m.
In addition, we find that the positive region $D(t):=\{x \in \R; u(x,t)>0\}$
of $u$ is monotonically non-decreasing with respect to the time $t$.
16:30 - 18:00Room #128 (Mathematics building)
Mikael Pichot (IPMU)
"Groups of friezes and property RD"
2008/11/11
16:30 - 18:00Room #128 (Mathematics building)
新國 裕昭 (首都大学東京)
"Rotation number approach to spectral analysis of the generalized Kronig-Penney Hamiltonians"
16:30 - 18:00Room #056 (Mathematics building)
Thomas Andrew Putman (MIT)
"The second rational homology group of the moduli space of curves
with level structures"
Let $\Gamma$ be a finite-index subgroup of the mapping class
group of a closed genus $g$ surface that contains the Torelli group. For
instance, $\Gamma$ can be the level $L$ subgroup or the spin mapping class
group. We show that $H_2(\Gamma;\Q) \cong \Q$ for $g \geq 5$. A corollary
of this is that the rational Picard groups of the associated finite covers
of the moduli space of curves are equal to $\Q$. We also prove analogous
results for surface with punctures and boundary components.
2008/11/10
10:30 - 12:00Room #128 (Mathematics building)
川口 周 (阪大理)
"射影空間の射に関する高さ関数の力学系的性質"
2008/11/07
16:20 - 17:50Room #128 (Mathematics building)
大本 隆 (野村證券金融工学研究センター)
"デリバティブ・プロダクツの価格付け I"
16:30 - 18:00Room #118 (Mathematics building)
Misha Verbitsky (ITEP and IPMU)
"Hyperkaehler SYZ conjecture and stability"
Let L be a nef bundle on a hyperkaehler manifold. A Hyperkaehler SYZ conjecture postulates that L is semi-ample. As shown by Matsushita, this implies existence of holomorphic Lagrangian fibrations on hyperkaehler manifolds. It was conjectured by many
people, most recently by Tschinkel, Hassett, Huybrechts and Sawon. We prove that a sufficiently big power of L is effective, assuming that L admits a semi-positive metric. A multiplier ideal version of this argument would give effectivity of L^N for any nef L. The proof uses stability and Boucksom's divisorial
Zariski decomposition.
2008/11/05
14:45 - 18:00Room #122 (Mathematics building)
二木昌宏 (東京大学大学院数理科学研究科) 14:45 - 16:15
"Directed Fukaya category の安定化について"
有向深谷圏(Directed Fukaya category)はホモロジー的ミラー対称性を Fano 多様体に拡張する目的で Kontsevich により提案され,Seidel により定式化された.これはシンプレクティック多様体の深谷圏の類似であり,exact Lefschetz fibration に対して定義される.有向深谷圏には幾つかの計算可能な例が知られているが,その構造については分かっていないことが多い.本講演では有向深谷圏の定義から始め,exact Lefschetz fibration の安定化(stabilization)と言われる操作での挙動に関する研究について報告する.Auroux-Katzarkov-Orlov の研究との関係にも触れる予定である.
服部広大 (東京大学大学院数理科学研究科) 16:30 - 18:00
"四元数ケーラー構造の剛性定理"
四元数ケーラー構造とは,特殊なホロノミー群をもつリーマン計量の一種である.コンパクト多様体上では,四元数ケーラー構造の非自明な変形が存在しないこと(剛性定理)が,ツイスター理論を用いることで証明されている.今回は,ツイスター理論を使わない剛性定理の証明について説明する.
2008/11/04
16:30 - 18:00Room #056 (Mathematics building)
Misha Verbitsky (ITEP, Moscow)
"Lefschetz SL(2)-action and cohomology of Kaehler manifolds"
Let M be compact Kaehler manifold. It is well
known that any Kaehler form generates a Lefschetz SL(2)-triple
acting on cohomology of M. This action can be used to compute
cohomology of M. If M is a hyperkaehler manifold, of real
dimension 4n, then the subalgebra of its cohomology generated by
the second cohomology is isomorphic to a polynomial algebra,
up to the middle degree.
2008/11/01
13:30 - 16:00Room #123 (Mathematics building)
宗野恵樹 (東京大学数理科学) 13:30 - 14:30
"$(\mathfrka{g},K)$-module structure of the principal series of $GL(3,\mathfrak{C})$"
We give explicit description of the action of $\mathfrak{gl}(3,\mathbf{C}$ to the whole space of $K$-finite vectors of a given principal series representation of $GL(3,\mathbf{C})$.
織田孝幸 (東京大学数理科学) 15:00 - 16:00
"Toward effectively computable integral basis of simple $\mathbfrak{gl}_4$-modules of finite dimension. (II) "
This is a continuation of the talk at Osaka in the occation of Kanrei workshop of Prof. T. Ibukiyama.
We discuss a part of the injection $V_{\lambda} \rightarrow \mathfrak{p} \otimes V_{\lambda}$. Here $V_{\lambda}$ is a simple module with highest weight $\lambda$, and $\mathfrak{p}$ is the adjoint representation with highest weight $(1,0,0,-1)$.
2008/10/31
16:20 - 17:50Room #128 (Mathematics building)
岡本 龍明 (NTT研究所)
"暗号の実践編"
2008/10/30
16:20 - 17:30Room #270 (Mathematics building)
若木 宏文 (広島大学大学院理学研究科)
"正規母集団に関する検定統計量の分布の漸近展開の誤差評価"
多変量正規母集団に関する検定統計量の帰無分布の特性関数は、いくつかの多変量ガ ンマ関数の比として表されることが多い。Box (1949) はガンマ関数の漸近展開(ス ターリングの公式)を用いて、このような分布の大標本漸近展開公式を導出したが、 導出過程での剰余項を詳しく評価してゆくことで、分布関数の漸近展開近似の計算可 能な誤差限界を導出することができる。いくつかの検定統計量に対する大標本漸近展 開近似の誤差限界を導出し、高次元・大標本の枠組みで得られているエッジワース展 開近似の誤差限界と比較する。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/08.html
10:00 - 11:00Room #002 (Mathematics building)
Arnaud DUCROT (University of Bordeaux)
"Travelling wave solutions for an infection age structured epidemic model"
In this lecture, we study the existence of travelling wave solutions for a class of epidemic model structured in space and with respect ot the age of infection. We obtain necessary and sufficient conditions for the existence of travelling waves for such a class of problems. As a consequence, we also derive the existence of travelling waves for a class of functional partial differential equations.
2008/10/29
10:30 - 11:30Room #056 (Mathematics building)
木村芳文 (名古屋大学(多元数理科学研究科))
"Stratified turbulence as an element of geophysical fluid dynamics"
Density stratification and rotation are the two major mechanisms that characterize the whole geophysical flows. In this talk, focusing on stable stratification, I will introduce some statistical, mechanical and geometrical aspects of stratified turbulence by showing the recent results of large scale computer simulations.
16:30 - 17:30Room #056 (Mathematics building)
Daniel Caro (Université de Caen)
"Overholonomicity of overconvergence $F$-isocrystals on smooth varieties"
Let $¥mathcal{V}$ be a complete discrete valuation ring
of characteristic $0$, with perfect residue field $k$ of
characteristic $p>0$. In order to construct $p$-adic coefficients
over $k$-varieties, Berthelot introduced the theory of
overconvergent $F$-isocrystals, i.e overconvergent isocrystals with
Frobenius structure. Moreover, to get a $p$-adic cohomology over
$k$-varieties stable under cohomological operations, Berthelot built
the theory of arithmetic $F$-$¥mathcal{D}$-modules. In this talk,
after recalling some elements of these theories, we introduce the
notion of overholonomicity with is a property as stable as the
holonomicity in the classical theory of $¥mathcal{D}$-modules. The
goal of the talk is to prove the overholonomicity of arithmetic
$¥mathcal{D}$-modules associated to overconvergent $F$-isocrystals
over smooth $k$-varieties. In the proof we need Christol's transfert
theorem, a comparison theorem between relative log rigid cohomology
and relative rigid cohomology and last but not least Kedlaya's
semistable reduction theorem. This is a joint work with Nobuo
Tsuzuki.
16:20 - 17:30Room #128 (Mathematics building)
下平 英寿 (東京工業大学 情報理工学研究科)
"マルチスケール・ブートストラップ法による確率値計算とFDR"
ブートストラップ確率はブートストラップ標本において仮説が支持される頻度であり, その実装の容易さから広く用いられている.たとえば,階層型クラスタリングにおいて得られたクラスタ が真実かどうかを判断する指標になる.ところが頻度論の不偏検定の立場で見ると,ブートストラップ確率 には無視できないくらい十分に大きいバイアスがあり,それはある種のパラメータ空間において仮説を あらわす領域の境界の曲率として解釈できることが知られている.本講演ではリサンプリングにおける データサイズを変化させたときの「スケール変換則」からバイアス補正する手法を紹介する. 曲面のテイラー展開のかわりにフーリエ変換をつかった漸近理論であり,錐のように必ずしもなめらかな曲面 でない場合でも適用できる (Shimodaira 2008).また,スケール変換則のアイデアをベイズ的なFalse Discovery Rateの計算に応用した最近の結果についても簡単に触れる.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/07.html
2008/10/28
16:30 - 18:00Room #056 (Mathematics building)
清野 和彦 (東京大学大学院数理科学研究科)
"Nonsmoothable group actions on spin 4-manifolds"
We call a locally linear group action on a topological manifold nonsmoothable
if the action is not smooth with respect to any possible smooth structure.
We show in this lecture that every closed, simply connected, spin topological 4-manifold
not homeomorphic to neither S^2\times S^2 nor S^4 allows a nonsmoothable
group action of any cyclic group with sufficiently large prime order
which depends on the manifold.
16:30 - 18:00Room #126 (Mathematics building)
Joachim Hilgert (Paderborn University)
"Chevalley's restriction theorem for supersymmetric Riemannian symmetric spaces"
We start by explaining the concept of a supersymmetric Riemannian symmetric spaces and present the examples studied by Zirnbauer in the context of universality classes of random matrices. For these classes we then show how to formulate and prove an analog of Chevalley's restriction theorem for invariant super-functions.
This is joint work with A. Alldridge (Paderborn) and M. Zirnbauer (Cologne)
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
17:00 - 18:00Room #123 (Mathematics building)
Serge Alinhac (パリ大学オルセイ校)
"Introduction to geometric analysis of hyperbolic equations"
2008/10/27
10:30 - 12:00Room #128 (Mathematics building)
松野 高典 (大阪府立高専)
"複素射影平面上の有限Galois分岐被覆について"
16:30 - 17:30Room #128 (Mathematics building)
Joachim Hilgert (Paderborn University)
"
Holomorphic extensions of highest weight representations to Olshanskii semigroups
"
In this lecture I will present a proof of Olshanskii's Theorem, which says that
for a simple group of Hermitean type unitarizable highest weight
representations can be holomorphically extended to contractive representations
of a complex semigroup containing the group in its boundary.
2008/10/24
16:30 - 17:30Room #002 (Mathematics building)
Benoit Collins (オタワ大学・東京大学大学院数理科学研究科)
"On the spectral measure of the sum of elements in a finite von Neumann algebra"
Given two self-adjoint n×n matrices A and B with prescribed eigenvalues, the set of all possible spectral distributions for A+B has been conjectured by Horn and proved by Knutson, Tao, Klyachko and Totaro.
We address the same question when A and B have prescribed spectral measures but lie in an arbitrary II_1 factor, and we give elements of answers in terms of inequalities between the spectral measures. We explain the relation with the Connes embedding problem.
2008/10/23
16:30 - 18:00Room #128 (Mathematics building)
Emily Peters (UC Berkeley)
"Planar algebras and the Haagerup subfactor"
2008/10/22
16:30 - 17:30Room #056 (Mathematics building)
Pierre Parent (Universite Bordeaux 1)
"Serre's uniformity in the split Cartan case"
We show that, for large enough prime number p, the modular curve
X_{split}(p) has no other point with values in Q than CM points and the rational cusp. This gives a partial answer to an old question of J.-P. Serre concerning the uniform surjectivity of Galois representations associated to torsion points on elliptic curves without complex multiplication.
(Joint work with Yuri Bilu.)
2008/10/21
17:00 - 18:00Room #126 (Mathematics building)
落合啓之 (名古屋大学)
"Invitation to Atlas combinatorics"
半単純リー群のユニタリ表現の分類を手がける Atlas project(J. Adams, D. Vogan らが主催)では、実簡約(real reductive)線形代数群の admissible 表現をパラメトライズし、それに関するいくつかのプログラムが公開されています。ウェブサイトは www.liegroups.org.
現在、そのメインとなるものは Kazhdan-Lusztig-Vogan 多項式です。リー群として複素単純リー群を実リー群と見なしたケースが、通常の Kazhdan-Lusztig 理論に一致し、それを、ある一方向に拡張したのがここで扱われる KLV 理論と考えられます。
この講演では、リー群に関する背景説明などは軽く済ませ、Atlas で公開されているプログラムにおける方言、特に入出力の読み方を通常の言葉に言い換えることで、
プログラムを使ってもらう入り口での障壁を減らしたいと考えています。
ふむ、なかなか、使えるな、自分もインストールしてみようか、と思ってもらえれば、成功です。
なお、サーベイトークなので私のオリジナルな結果は含まれていません。また、計算機を使ってデモをする予定です。京都では計算機と板書の切り替えでばたばたしたので、照準を絞って慌てないように話したいと思います。
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
16:30 - 18:00Room #002 (Mathematics building)
森山 哲裕 (東京大学大学院数理科学研究科)
"On embeddings of 3-manifolds in 6-manifolds"
In this talk, we give a simple axiomatic definition of an invariant of
smooth embeddings of 3-manifolds in 6-manifolds.
The axiom is expressed in terms of some cobordisms of pairs of manifolds of
dimensions 6 and 3 (equipped with some cohomology class of the complement) and
the signature of 4-manifolds.
We then show that our invariant gives a unified framework for some classical
invariants in low-dimensions (Haefliger invariant, Milnor's triple
linking number, Rokhlin invariant, Casson invariant,
Takase's invariant, Skopenkov's invariants).
2008/10/20
10:30 - 12:00Room #128 (Mathematics building)
岩崎 克則 (九大数理)
"パンルヴェ方程式と複素力学系"
2008/10/17
16:20 - 17:50Room #128 (Mathematics building)
岩根 和郎 (岩根研究所)
"岩根研究所に於ける画像処理技術の紹介Ⅱ; CV技術による空間認識と対象物認識、及び人工知能"
15:00 - 16:00Room #570 (Mathematics building)
Joachim Hilgert (Paderborn University)
" GCOEレクチャー"Holomorphic extensions of unitary representations" その4 "Applications and open problems""
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krotz-Stanton), random matrices (Huckleberry-Puttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
13:00 - 14:30Room #128 (Mathematics building)
Yongnam Lee (Sogang U.)
"Construction of surfaces of general type with pg=0 via
Q-Gorenstein smoothing"
15:00 - 16:00Room #118 (Mathematics building)
Joachim Hilgert (Paderborn University)
"Holomorphic extensions of unitary representations その4 Applications and open problems
"
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krötz-Stanton), random matrices (Huckleberry-Püttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
2008/10/16
16:30 - 18:00Room #128 (Mathematics building)
Scott Morrison (UC Santa Barbara)
"The $D_{2n}$ planar algebras"
15:00 - 16:00Room #570 (Mathematics building)
Joachim Hilgert (Paderborn University)
"GCOEレクチャー"Holomorphic extensions of unitary representations" その3 "Highest weight representations""
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
16:00 - 17:30Room #002 (Mathematics building)
Joseph F. Grotowski (University of Queensland)
"Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow"
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.
15:00 - 16:00Room #123 (Mathematics building)
Joachim Hilgert (Paderborn University)
"Holomorphic extensions of unitary representations その3 Highest weight representations "
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
2008/10/15
10:30 - 11:30Room #056 (Mathematics building)
八木厚志 (大阪大学)
"Asymptotic behavior of solutions for BCF model describing crystal surface growth"
This talk is concerned with the initial-boundary value problem for a nonlinear parabolic equation which was presented Johnson et al. for describing the process of growth of a crystal surface on the
basis of the BCF theory. We will investigate asymptotic behavior of solutions by construct exponential attractors and a Lyapunov function and by examining a structure of the $\omega$ limit set.
16:00 - 17:30Room #002 (Mathematics building)
George Sell (ミネソタ大学)
"連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その2 The role of the 2D limit problem"
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.
In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.
These lectures are based on joint work with Genevieve Raugel,Dragos Iftimie, and Luan Hoang.
15:00 - 16:00Room #570 (Mathematics building)
Joachim Hilgert (Paderborn University)
"GCOEレクチャー"Holomorphic extensions of unitary representations" その2 "Geometric Background" "
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
15:00 - 16:00Room #122 (Mathematics building)
Joachim Hilgert (Paderborn University)
"Holomorphic extensions of unitary representations その2 Geometric background"
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
2008/10/14
16:30 - 18:00Room #056 (Mathematics building)
Jeffrey Herschel Giansiracusa (Oxford University)
"Pontrjagin-Thom maps and the Deligne-Mumford compactification"
An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.
16:00 - 17:30Room #002 (Mathematics building)
George Sell (ミネソタ大学)
"連続講演 "Thin 3D Navier-Stokes equations" (3次元薄層領域上のナビエストークス方程式) その1
Ultimate boundedness of solutions with large data and global attractors"
In both lectures we will examine a new topic of the thin 3D Navier-Stokes equations with Navier boundary conditions.
In the first lecture we will treat the ultimate boundedness of strong solutions and the related theory of global attractors.
In the second lecture, which will include a brief summary of the first lecture, we will examine the role played by the 2D Limit Problem. These issues are a special challenge for analysis because the 2D Limit Problem is NOT imbedded the 3D problem.
These lectures are based on joint work with Genevieve Raugel, Dragos Iftimie, and Luan Hoang.
16:00 - 17:30Room #002 (Mathematics building)
George Sell (ミネソタ大学)
"Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors"
グローバルCOE連続講演会と共催です.詳細はそちらをご覧ください.
15:00 - 16:00Room #570 (Mathematics building)
Joachim Hilgert (Paderborn University)
"GCOEレクチャー"Holomorphic extensions of unitary representations" その1 "Overview and Examples" "
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html
16:30 - 18:00Room #126 (Mathematics building)
Jan Moellers (Paderborn University)
"The Dirichlet-to-Neumann map as a pseudodifferential
operator"
Both Dirichlet and Neumann boundary conditions for the Laplace equation are of fundamental importance in Mathematics and Physics. Given a compact connected Riemannian manifold $M$ with boundary $\partial M$ the Dirichlet-to-Neumann operator $\Lambda_g$ maps Dirichlet boundary data $f$ to the corresponding Neumann boundary data $\Lambda_g f =(\partial_\nu u)|_{\partial M}$ where $u$ denotes the unique solution to the Dirichlet problem $\laplace_g u=0$ in $M$, $u|_{\partial M} = f$.
The main statement is that this operator is a first order elliptic pseudodifferential operator on the boundary $\partial M$.
We will first give a brief overview of how to define the Dirichlet-to-Neumann operator as a map $\Lambda_g:H^{1/2}(\partial M)\longrightarrow H^{-1/2}(\partial M)$ between Sobolev spaces. In order to show that it is actually a pseudodifferential operator we introduce tangential pseudodifferential operators. This allows us to derive a
microlocal factorization of the Laplacian near boundary points. Together with a regularity statement for the heat equation this will finally give the main result.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
15:00 - 16:00Room #118 (Mathematics building)
Joachim Hilgert (Paderborn University)
"Holomorphic extensions of unitary representations" その1 "Overview and Examples" "
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert
2008/10/10
16:20 - 17:50Room #128 (Mathematics building)
岩根 和郎 (岩根研究所)
"岩根研究所における画像処理技術の紹介Ⅰ; 画像の数学的解析によるCV技術開発と3次元GIS"
2008/10/06
10:30 - 12:00Room #128 (Mathematics building)
杉山 健一 (千葉大理)
"Lichtenbaum予想の幾何学的類似"
2008/10/03
16:20 - 17:50Room #128 (Mathematics building)
岡本 龍明 (NTT研究所)
"暗号の基礎編"
2008/09/29
16:30 - 17:30Room #117 (Mathematics building)
Christopher Deninger (Munster大学)
"A determinant for p-adic group algebras"
For a discrete countable group G there is a classical determinant on the units of the L^1-convolution algebra of G. It is defined using functional analysis and can be used for example to calculate the entropy of certain G-actions. We will discuss a p-adic analogue of this theory. Instead of functional analysis the definition of the p-adic determinant uses algebraic K-theory. It has an application to the study of the p-adic distribution of periodic G-orbits in certain G-action.
2008/09/22
14:45 - 15:45Room #122 (Mathematics building)
Jean-Dominique Deuschel (TU Berlin)
"Invariance principle for the random conductance model
with unbounded conductances (a joint work with Martin Barlow)"
16:00 - 17:00Room #122 (Mathematics building)
Sergio Albeverio (Bonn 大学)
"Asymptotic expansions of infinite dimensional integrals with applications (quantum mechanics, mathematical finance, biology)
"
2008/09/17
16:30 - 18:00Room #128 (Mathematics building)
Cyril Houdayer (UCLA)
"Free Araki-Woods Factors and Connes's Bicentralizer Problem"
2008/09/09
16:30 - 18:00Room #128 (Mathematics building)
Yves de Cornulier (CNRS, Rennes)
"The space of subgroups of an abelian group"
2008/09/08
11:00 - 12:00Room #126 (Mathematics building)
Federico Incitti (ローマ第 1 大学)
"Dyck partitions, quasi-minuscule quotients and Kazhdan-Lusztig polynomials"
Kazhdan-Lusztig polynomials were first defined by Kazhdan and Lusztig in [Invent. Math., 53 (1979), 165-184]. Since then, numerous applications have been found, especially to representation theory and to the geometry of Schubert varieties. In 1987 Deodhar introduced parabolic analogues of these polynomials. These are related to their ordinary counterparts in several ways, and also play a direct role in other areas, including geometry of partial flag manifolds and the theory of Macdonald polynomials.
In this talk I study the parabolic Kazhdan-Lusztig polynomials of the quasi-minuscule quotients of the symmetric group. More precisely, I will first show how these quotients are closely related to ``rooted partitions'' and then I will give explicit, closed combinatorial formulas for the polynomials. These are based on a special class of rooted partitions the ``rooted-Dyck'' partitions, and imply that they are always (either zero or) a power of $q$.
I will conclude with some enumerative results on Dyck and rooted-Dyck partitions, showing a connection with random walks on regular trees.
This is partly based on a joint work with Francesco Brenti and Mario Marietti.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/09/03
16:00 - 17:30Room #002 (Mathematics building)
Fred Weissler (University of Paris 13)
"Finite time blowup of oscillating solutions to the nonlinear heat equation"
(This is joint work with T. Cazenave and F. Dickstein.)
We study finite time blowup properties of solutions of the nonlinear heat equation, both on $R^N$, and on a ball in $R^N$ with Dirichlet boundary conditions. We show, among other results, that the set of initial values producing global solutions is not always star-shaped around the 0 solution. This contrasts with the case where only non-negative solutions are considered.
2008/08/27
16:30 - 17:30Room #117 (Mathematics building)
Don Zagier (Max Planck研究所)
"$q$-series and modularity"
2008/08/25
16:30 - 17:30Room #002 (Mathematics building)
Ronald C. King (Emeritus Professor, University of Southampton)
"Affine Weyl groups, grids, coloured tableaux and characters of affine algebras"
It is shown that certain coloured Young diagrams serve to specify not
only all the elements of the affine Weyl groups of the classical
affine Lie algebras but also their action on an arbitrary weight
vector. Through a judicious choice of coset representatives with
respect to the finite Weyl groups of the corresponding maximal rank
simple Lie algebras, both denominator and numerator formulae are
derived and exemplified, along with the explicit calculation of
characters of irreducible representations of the affine Lie algebras.
2008/08/21
15:00 - 15:40Room #126 (Mathematics building)
鎌谷研吾 (東京大学大学院数理科学研究科)
"On some asymptotic properties of the Expectation-Maximization Algorithm and the Metropolis-Hastings Algorithm (EMアルゴリズムとメトロポリス-ヘイスティングスアルゴリズムの漸近的性質)"
2008/08/06
10:30 - 14:00Room #056 (Mathematics building)
Kazufumi Ito (North Carolina State University) 10:30 - 11:30
"Adaptive Tikhonov Regularization for Inverse Problems"
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei (Fudan University) 13:00 - 14:00
"On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems"
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.
17:30 - 19:00Room #122 (Mathematics building)
楠岡 成雄 (東京大)
"オペレーショナルリスクと fat tail を持つ iid 確率変数の和に対する極限定理"
2008/08/01
13:00 - 18:00Room #002 (Mathematics building)
Olivier Brinon (Paris北大学) 13:00 - 14:00
"B_dR-representations and Higgs bundles"
Henrik Russell (Duisburg-Essen大学) 14:15 - 15:15
"Generalized Albanese and duality"
Thomas Geisser (南California大学) 15:45 - 16:45
"Negative K-theory, homotopy invariance and regularity"
The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
Fabien Trihan (Nottingham大学) 17:00 - 18:00
"On Iwasawa theory for abelian varieties over function fields of positive characteristic"
2008/07/29
16:30 - 18:00Room #126 (Mathematics building)
小木曽 岳義 (城西大学)
"Clifford代数の表現から作られる局所関数等式を満たす多項式とそれに付随する空間について(佐藤文広氏との共同研究)"
概均質ベクトル空間の理論の基本定理(局所関数等式)は、大雑把に言うと、正則概均質ベクトル空間の相対不変式の複素ベキのFourier変換が双対概均質ベクトル空間の相対不変式の複素ベキにガンマ因子をかけたものと一致することを主張している。
この講演では、概均質ベクトル空間の相対不変式ではないにもかかわらず、その複素ベキが同種の局所関数等式を満たすような多項式が、Clifford代数の表現より構成できることを報告する。
2008/07/28
17:00 - 18:30Room #002 (Mathematics building)
Lin Weng (Kyushu University)
"Symmetries and the Riemann Hypothesis"
Associated to each pair of a reductive group
and its maximal parabolic, we will introduce an abelian zeta function.
This zeta, defined using Weyl symmetries, is expected
to satisfy a standard functional equation and the Riemann Hypothesis.
Its relation with the so-called high rank zeta,
a very different but closely related non-abelian zeta,
defined using stable lattices and a new geo-arithmetical cohomology,
will be explained.
Examples for $SL, SO, Sp$ and $G_2$ and confirmations of
(Lagarias and) Masatoshi Suzuki on the RH for zetas
associated to rank 1 and 2 groups will be presented
as well.
http://xxx.lanl.gov/abs/0803.1269
2008/07/26
13:30 - 16:00Room #117 (Mathematics building)
星野歩 (上智大理) 13:30 - 14:30
"変形W代数とMacdomald多項式のtableau表示"
A型変形W代数の自由場表示を用いてA型Macdomald多項式のtableau表示を構成する。さらにD型変形W代数の自由場表示を用いて、第一基本ウェイトの正数倍のウェイトを持つD型Macdomald多項式のtableau表示を構成する。尚、本研究は白石潤一氏(東京大学)との共同研究である。
古川俊輔 (理化学研究所) 15:00 - 16:00
"Entanglement Entropy in Conventional and Topological Orders"
量子多体系の基底状態には、しばしば、個々の粒子の状態の直積では表せない構造、すなわち、エンタングルメントが現れる。これを、エンタングルメント・エントロピーという指標を用いて測ることにより、系のユニヴァーサリティを特徴づける重要な情報が得られることが近年、明らかにされてきた。セミナーでは、エンタングルメントについての基礎的な知識から始め、私が取り組んできた(いる)、次の二つのテーマについてご紹介したい。
(1)量子ダイマー模型におけるトポロジカル・エントロピー
トポロジカル秩序を持つ系においては、エンタングルメント・エントロピーに、背景のゲージ理論を特徴づける、負の定数項が含まれることが、Kitaevらによって予想された。我々は、Z2トポロジカル秩序を示すと考えられる量子ダイマー模型において、予想の数値的検証を行い、予想が精度よく成り立つことを示した。
Ref. S. Furukawa & G. Misguich, Phys. Rev. B 75, 214407 (2007).
(2)自発的対称性の破れとマクロスコピック・エンタングルメント
自発的対称性の破れを示す系においては、有限系の基底状態に、秩序を持った状態のマクロな重ね合わせ構造が見られる。この構造がエンタングルメント・エントロピーにも反映され、基底状態縮退度の情報を含む、正の定数項が現れることを示した。
2008/07/24
16:00 - 17:00Room #122 (Mathematics building)
Noriko Yui (Queen's University)
"On the modularity of Calabi-Yau varieties over $\mathbf{Q}$"
2008/07/23
10:30 - 11:30Room #056 (Mathematics building)
Andrei Constantinescu (Ecole Polytechnique)
"Identification of residual stresses: problem settings and results."
Identification of residual stresses is an important task in many engineering fields such as fatigue or fracture mechanics, where their presence can significantly increase or decrease the apparent strength of mechanical components.
The present talk will try to make a review of existing problem settings identification results.
More precisely we shall:
1. discuss the linearization procedure strain and materials behaviour in finite elasticity around a stressed state in order to define in a mathematical precise way the problem settings for the identification of residual stresses.
2. present a series of measurement techniques currently used in industry and research for the measurement of residual stresses like the X-ray technique and strain measurements.
3. present existing results in the identification of residual stresses for the different
10:30 - 14:00Room #056 (Mathematics building)
伊東一文 (North Carolina State University) 10:30 - 11:30
"Adaptive Tikhonov Regularization for Inverse Problems"
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei (Fudan University) 13:00 - 14:00
"On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems"
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.
2008/07/17
16:30 - 18:00Room #056 (Mathematics building)
George Elliott (Univ. Toronto)
"A canonical AF-algebra construction for rank two subgroups of R
(A new description of the Pimsner-Voiculescu embedding)"
2008/07/16
16:30 - 17:30Room #117 (Mathematics building)
Valentina Di Proietto (Padova大学)
"On p-adic differential equation on semi-stable varieties "
2008/07/15
16:30 - 18:00Room #056 (Mathematics building)
松田 浩 (広島大学大学院理学研究科)
"One-step Markov Theorem on exchange classes"
The main theorem in this talk claims the following.
``Let L_A and L_B denote a closed a-braid and a closed b-braid,
respectively, that represent one link type.
After at most (a^2 b^2)/4 exchange moves on L_A,
we can 'see' the pair of closed braids."
In this talk, we explain the main theorem in details, and
we present some applications.
In particular, we propose a strategy to construct an algorithm
that determines whether two links are ambient isotopic.
16:30 - 18:00Room #126 (Mathematics building)
廣惠 一希 (東大数理)
"GL(4,R)の退化主系列表現の一般Whittaker関数"
$GL(n,R)$の退化球主系列表現の一般Whittaker模型の空間は,対称空間$GL(n,R)/O(n)$上の$C^\infty$級関数の中で,ある微分作用素達のkernelとして特徴付けられる.この微分作用素達は,大島利雄氏による退化主系列表現に対するPoisson変換の像の特徴付けに用いられたものであり,その明示的な表示が氏によって得られている.また,こうしたkernel定理は山下博氏のユニタリ最低ウエイト加群の一般Whittaker模型に対する定理の類似にあたる.こういった背景の下,$GL(4,R)$の退化主系列表現に対し、いくつかの具体例を考えたい.そこでは一般Whittaker模型は一変数変形Bessel関数、Hornの二変数合流型超幾何関数によって実現される.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/07/12
13:30 - 16:00Room #123 (Mathematics building)
刈山和俊 (尾道大学経済情報学部
) 13:30 - 14:30
"On certain types and the Hecke algebras for unramified p-adic unitary groups"
鍛治匠一 (東京大学数理科学研究科) 15:00 - 16:00
"The $(\mathfrak{g},K)$-module structures of the principal series resentations for $SL(4,R)$
"
$SL(4,R)$ の主系列表現 $H$ の $(\mathfrak{g},K)$-module としての構造を
明示的に与えることを目標とする。
具体的には、まず $H$ の基底として $K$-module の weight vector になっているものを取り、その基底が $\mathfrak{g}$ の作用でどのように移るかを記述する。
2008/07/10
16:30 - 18:00Room #056 (Mathematics building)
竹崎正道 (UCLA名誉教授)
"The Structure of a Hyponormal Operator (a joint work with Kotaro
Tanahashi)"
16:00 - 17:30Room #002 (Mathematics building)
渡辺 達也 (早稲田大学・理工学術院)
"Two positive solutions for an inhomogeneous scalar field equation"
We consider the following nonlinear elliptic equation:
$$-\Delta u+u=g(u)+f(x), x \in R^N,$$
where $N\ge 3$. When $f(x)\equiv 0$, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though $f(x) \not\equiv 0$, we can expect the existence of a nontrivial solution if $f(x)$ is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when $\| f\|_{L^2}$ is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.
16:20 - 17:30Room #126 (Mathematics building)
吉田 亮 (統計数理研究所)
"Bayesian learning of biological pathways on genomic data assimilation"
States of living cells are controlled by networks of biochemical reactions, referred to as biological pathways, which comprise of, for instance, phosphorylation and binding of protein molecules, gene expressions mediated by transcription factor activities. In systems biology, mathematical modeling and simulation, based on biochemical rate equations, have proved to be a popular approach for unraveling complex machinery of cellular mechanisms. To proceed to simulations, however, it is vital to find the effective values of kinetic rate constants that are difficult to measure directly from in vivo and in vitro experiments. Furthermore, once a set of hypothetical models is given, a proper statistical criterion is needed to test the reliability of the constructed models in terms of predictability and biological robustness. The aim of this research is to present a new statistical technology, called Genomic Data Assimilation, for handling data-driven model construction of biological pathways. The method starts with a knowledge-based pathway modeling with hybrid functional Petri net. It then proceeds to the Bayesian learning of model parameters for which experimental data are available. This process uses time course measurements of biochemical reactants, e.g. gene expression profiles. Another important issue that we consider is statistical evaluation and comparison of the constructed hypothetical models. For this purpose, we developed a new Bayesian information-theoretic measure that assesses the predictability and the biological robustness of models. In this talk, I will detail mathematical aspects of the proposed method, and then, show some statistical issues to be addressed.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/06.html
2008/07/08
16:30 - 18:00Room #056 (Mathematics building)
Otto van Koert (北海道大学大学院理学研究科, JSPS)
"Contact homology of left-handed stabilizations and connected sums"
In this talk, we will give a brief introduction to contact homology, an invariant of contact manifolds defined by counting holomorphic curves in the symplectization of a contact manifold. We shall show that certain left-handed stabilizations of contact open books have vanishing contact homology.
This is done by finding restrictions on the behavior of holomorphic curves in connected sums. An additional application of this behavior of holomorphic curves is a long exact sequence for linearized contact homology.
16:30 - 18:00Room #126 (Mathematics building)
直井 克之 (東大数理)
"construction of extended affine Lie algebras from multiloop Lie algebras"
affine Lie algebra の Kac-Moody Lie algebra とは異なる一般化として、extended affine Lie algebra と呼ばれる Lie algebra の class を考える。
ほとんどの extended affine Lie algebra は、有限次元 simple Lie algebra と、有限個の互いに可換な有限位数自己同型を用いて構成できることがすでに知られている。
この講演では、上の構成によって得られる extended affine Lie algebra がどのような場合に(適当な意味で)同型となるか、という問題に関する結果をお話ししたい。
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/07/07
10:30 - 12:00Room #128 (Mathematics building)
石井 豊 (九大数理)
"Henon 写像の複素力学系"
2008/07/03
16:20 - 17:30Room #126 (Mathematics building)
西山 陽一 (統計数理研究所)
"拡散過程のノンパラメトリック適合度検定"
独立同一分布に従う確率変数列に対する適合度検定問題を考えるとき, Kolmogorov-Smirnov 検定統計量が漸近的に分布不変であることはよく知られて いる.ところが,拡散過程モデルにおいて,例えばエルゴード性を仮定してその 不変分布の経験分布関数から Kolmogorov-Smirnov 型の検定統計量を構成しても, 漸近的分布不変にはならない.本報告では,この問題に対し,score marked empirical process に基づく新しいアプローチを用いて漸近的分布不変な検定統 計量を構成し,かつそれが一致性をもつことを紹介する.モデルとしては小拡散 過程とエルゴード的拡散過程を扱い,また連続観測・離散観測の双方を考察する ので,合計4通りの場合を調べ尽くす.同時期に提案された Dachian and Kutoyants (2008) の結果にも触れる.
本報告は Ilia Negri 氏と共同で執筆した3編の論文(うち1編は増田弘毅氏と も共同)にもとづくものであるが、概要は日本語によるサーベイ論文
http://www.ism.ac.jp/~nisiyama/pism080626.pdf
にまとめてある。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/05.html
2008/07/02
16:30 - 17:30Room #117 (Mathematics building)
近藤 智 (東京大学数物連携宇宙研究機構)
"有限体上のスキームのふたつのモチビックコホモロジー群の計算
(安田正大氏との共同研究)"
2008/07/01
16:30 - 18:00Room #126 (Mathematics building)
奥田 隆幸 (東大数理)
"不変式のzeta多項式の零点と、微分作用素の関係について"
MacWilliams変換と呼ばれる変換で不変な複素2変数斉次多項式に対して、zeta多項式と呼ばれる複素1変数多項式を定義する。
TypeIV extremal と呼ばれる不変式の無限列に対し、deg = 0 (mod 6) の場合には、対応する全ての zeta多項式の零点が同一円周上に乗るという事が証明されているが、deg = 2,4 (mod 6) の場合は未解決であった。
この講演では、不変式に対する微分作用素を用いて、deg = 4 (mod6) の場合にも全てのzeta多項式の零点が同一円周上に乗るということを示したい。
16:30 - 18:00Room #056 (Mathematics building)
佐藤 隆夫 (大阪大学大学院理学研究科, JSPS)
"On the Johnson homomorphisms of the automorphism group of
a free metabelian group"
The main object of our research is the automorphism group of a
free group. To be brief, the Johnson homomorphisms are studied in order to
describe one by one approximations of the automorphism group of a free group
. They play important roles on the study of the homology groups of the autom
orphism group of a free group. In general, to determine their images are ver
y difficult problem. In this talk, we define the Johnson homomorphisms of th
e automorphism group of a free metabelian group, and determine their images.
Using these results, we can give a lower bound on the image of the Johnson
homomorphisms of the automorphism group of a free group.
2008/06/30
10:30 - 12:00Room #128 (Mathematics building)
足助 太郎 (東大数理)
"複素余次元1葉層のFatou-Julia分解について"
17:00 - 18:30Room #002 (Mathematics building)
J.Manuel Garcia-Islas (National Autonomous University of Mexico)
"Quantum topological invariants and black hole entropy"
A type of topological invariants of three manifolds were
introduced by Turaev and Viro. We will define an invariant of graphs
embedded in a three dimensional manifold in a Turaev-Viro spirit.
The relation of these invariants to mathematical physics is
a really nice one. We will show how entropy of a three dimensional
black hole known as BTZ can be described using our formulation.
2008/06/26
16:30 - 18:00Room #056 (Mathematics building)
酒匂宏樹 (東大数理)
"Solid groups and orbit equivalence rigidity"
16:20 - 17:30Room #126 (Mathematics building)
日野 英逸 (早稲田大学)
"アイテムの選好度のモデルとパラメタ推定法 - Plackett-Luceモデルの一般化 -"
アイテムの比較やランキングデータが多数与えられたとき、一つ一つのアイテムが潜在的に持つ 価値を決定する問題は、心理学、経済学、政治学などの分野で古くから研究が行われているが、 近年機械学習の分野でも注目されている。 Plackett-Luceモデルはアイテムへのランキングの確率モデルであり、アイテム一つ一つに 多項分布のパラメタを割り当ててアイテム選択のプロセスを説明する。 本発表では、映画評の生成プロセスに注目し、Plackett-Luceの一般化として グループ化ランキングモデルを提案する。このモデルの尤度関数を直接評価することは 困難であるため、尤度関数の下界を与え、emアルゴリズムを用いて近似的に下界の 最大化を行うことでパラメタ推定を行う。 Toy exampleに対する実験結果と、映画評データに対する適用結果を紹介する。 時間が許せば、個人の嗜好に基づくパラメタの推定と、協調フィルタリングへの 応用についても言及する。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/04.html
2008/06/24
16:30 - 18:00Room #056 (Mathematics building)
Kenneth Shackleton (東京工業大学, JSPS)
"On computing distances in the pants complex"
The pants complex is an accurate combinatorial
model for the Weil-Petersson metric (WP) on Teichmueller space
(Brock). One hopes that many of the geometric properties
of WP are accurately replicated in the pants complex, and
this is the source of many open questions. We compare these
in general, and then focus on the 5-holed sphere and the
2-holed torus, the first non-trivial surfaces. We arrive at
an algorithm for computing distances in the (1-skeleton of the)
pants complex of either surface.
http://www.is.titech.ac.jp/~kjshack5/FYEO.pdf
2008/06/23
10:30 - 12:00Room #128 (Mathematics building)
橋本 健治 (東大数理)
"5次対称群が作用するK3曲面のある1次元族の周期写像と逆写像"
2008/06/20
16:30 - 17:30Room #002 (Mathematics building)
村山斉 (数物連携宇宙研究機構)
"IPMU, Mathematics, Physics, and me"
Institute for the Physics and Mathematics of the Universe (IPMU) was founded to promote synergy between mathematics and physics, and to address deep mysteries about the universe. In this colloquium, I will discuss the mysteries IPMU will address, and why the interaction between mathematicians and physicists are crucial for this purpose. I will also talk about my personal journey about mathematics and physics.
2008/06/19
16:30 - 18:00Room #056 (Mathematics building)
David Kerr (Texas A&M University)
"Turbulence, representations, and trace-preserving actions"
16:00 - 17:30Room #002 (Mathematics building)
谷口 雅治 (東京工業大学大学院情報理工学研究科)
"Allen-Cahn方程式における角錐型進行波の一意性と安定性
(The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations)
"
We study the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front.
16:20 - 17:50Room #052 (Mathematics building)
伊藤 高一 (IRI-DNL)
"インターネットにおける数理科学的手法と実際「DNSとWebアクセス」"
テーマごとに個別の企業活動を紹介し、第一線で活躍する企業研究者を招聘し、現場レポートを聴き、議論を行うことで、インターネット数理科学の原理とその応用の実際を紹介する。
http://www.ms.u-tokyo.ac.jp/lecture/2008/inet/index.html
2008/06/18
16:30 - 18:45Room #117 (Mathematics building)
服部 新 (北海道大学大学院理学研究院) 16:30 - 17:30
"On a ramification bound of semi-stable torsion representations over a local field"
朝倉 政典 (北海道大学大学院理学研究院) 17:45 - 18:45
"Beilinson-Tate予想と楕円曲面のK_1の不分解元"
(佐藤周友氏との共同研究)
代数サイクルのTate予想のK理論における類似であるBeilinson-Tate予想について、
楕円曲面の場合にそれが成り立つ非自明な例を構成する。
これは、p進レギュレーターの非消滅と関係しており、
応用としてK_1の不分解元であって整数環上のモデルからくるようなものを構成する。
17:30 - 19:00Room #122 (Mathematics building)
塩谷 匡介 (日本銀行)
"経済学と金融工学 ―Financial Economics入門―」(講義)
+M. Piazzesi and E. Swanson, "Futures Prices as Risk-Adjusted Forecasts
of Monetary Policy", Journal of Monetary Economics (2008)
"
2008/06/17
16:30 - 18:00Room #056 (Mathematics building)
佐野 友二 (東京大学IPMU)
"Multiplier ideal sheaves and Futaki invariant on toric Fano manifolds."
I would like to discuss the subvarieties cut off by the multiplier
ideal sheaves (MIS) and Futaki invariant on toric Fano manifolds.
Futaki invariant is one of the necessary conditions for the existence
of Kahler-Einstein metrics on Fano manifolds,
on the other hand MIS is one of the sufficient conditions introduced by Nadel.
Especially I would like to focus on the MIS related to the Monge-Ampere equation
for Kahler-Einstein metrics on non-KE toric Fano manifolds.
The motivation of this work comes from the investigation of the
relationship with slope stability
of polarized manifolds introduced by Ross and Thomas.
This talk will be based on a part of the joint work with Akito Futaki
(arXiv:0711.0614).
2008/06/16
10:30 - 12:00Room #128 (Mathematics building)
山ノ井 克俊 (熊本大自然)
"有理型関数の高階導関数の零点について"
2008/06/14
13:30 - 16:00Room #117 (Mathematics building)
孫 娟娟 (東大数理) 13:30 - 14:30
"Confluent KZ equations for $sl_2$ and quantization of monodromy preserving deformation"
We obtain a system of confluent Knizhnik-Zamolodchikov (KZ) equations which generalizes that of KZ equations for $sl_2$,
and give integral solutions of the system. We also study the relation between the system and monodromy preserving deformation theory,
and recover quantizations of Painlev\'e equations P_I-P_V with affine Weyl group symmetry which are introduced by H.Nagoya.
Paul A. Pearce (Univ. of Melbourne) 15:00 - 16:00
"Exact Solution and Physical Combinatorics of Critical Dense
Polymers"
A Yang-Baxter integrable model of critical dense polymers on the
square lattice
is introduced corresponding to the first member ${\cal LM}(1,2)$ of a
family of logarithmic
minimal models. The model has no local degrees of freedom, only non-
local degrees
of freedom in the form of extended polymers. The model is built
diagrammatically using the
planar Temperley-Lieb algebra and solved exactly on finite width
strips using transfer matrix
techniques. The bulk and boundary free energies and finite-size
corrections are
obtained from the Euler-Maclaurin formula. The spectra are classified
by selection rules and
the physical combinatorics of the eigenvalue patterns of zeros in the
complex
spectral-parameter plane. This yields explicit finitized conformal
characters.
In particular, in the scaling limit, we confirm the central charge
$c=-2$ and conformal weights
$\Delta_{1,s}=\frac{(2-s)^2-1}{8}$ for $s=1,2,3,\ldots$ where $s-1$ is
the number
of defects.
2008/06/12
16:30 - 18:00Room #156 (Mathematics building)
見村万佐人 (東大数理)
"On Lubotzky's property $(\tau)$ and expander graphs"
16:20 - 17:30Room #126 (Mathematics building)
福水 健次 (統計数理研究所)
"再生核による指数分布族の構成とその統計的推定への応用"
再生核ヒルベルト空間を用いて、ヒルベルト多様体として指数分布族を 構成する方法について述べる。無限次元指数分布族に関しては、Orlicz 空間を用いたPistone & Sempi (1995) の構成法が知られているが、 有限サンプルによる推定を考える場合、尤度関数が多様体上の連続汎関 数にならない点が問題となる。本講演の構成では、再生核ヒルベルト空 間を用いることにより尤度関数は連続となり、統計的推定の議論が容易 となる。再生核ヒルベルト空間が有限次元の場合は通常の有限次元指数 分布族の推定理論と一致し、無限次元の場合はその自然な拡張を与える。 本講演では、統計的推定への応用として、正則化最尤推定法と、特異点 を持つモデルの漸近理論に関して述べる。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/03.html
2008/06/09
16:30 - 17:30Room #126 (Mathematics building)
中岡 慎治 (東京大学大学院数理科学研究科)
"幼生の行動変化が個体群動態に及ぼす影響の数理モデル"
動物の行動変化は個体群動態に影響を及ぼし得る。群生はもっとも良く知られた
動物行動の一つで、凝集することによって捕食者から狙われるリスクを回避する
ような効果(たとえば希釈効果)などがある。、たとえば幼生は成体に比べて一般に
捕食に会うリスクが高いため、個体の成長は行動を決める上で非常に重要な要因
である。
本研究では捕食者にステージ構造を考慮した捕食者被食者数理モデルを
構築し、動物の行動変化が個体群動態に及ぼす影響を調べた。もし種内で資源を
めぐる競争が激しい場合、上位の捕食者による捕食リスクが増えるにつれて
凝集して群生することは必ずしもメリットとはならず、Allee 効果による突然の
群生消滅が生じる可能性があることを数理モデルの解析・シミュレーションに
よって明らかにした。
16:30 - 18:00Room #470 (Mathematics building)
W. Rundell (Texas A&M Univ.)
"Some Unsolved Inverse Spectral Problems"
Perhaps the first well-studied inverse problem
was the determination of the potential $q(x)$ in
$-u'' + q(x) u = \lambda_n u$ given the eigenvalues
$\{\lambda_n\}$. Despite its venerable age and
the fact that a considerable literature is still being published,
there are several major outstanding problems;
some are quite simple to state.
This seminar will outline some of these.
We will try to show why the problems are hard,
but leave it to the audience to attempt solutions.
10:30 - 12:00Room #128 (Mathematics building)
相原 義弘 (沼津高専)
"Deficiencies of holomorphic curves in algebraic manifolds"
2008/06/05
16:30 - 18:00Room #056 (Mathematics building)
谷本溶 (東大数理)
"Another analogue of the Borel-Weil theory on loop groups"
16:00 - 17:30Room #002 (Mathematics building)
齊藤 宣一 (東京大学大学院数理科学研究科)
"Keller-Segel系に対する離散化手法"
細胞性粘菌の凝集現象を記述するモデルとして広く知られるKeller-Segel(KS)系に対して,講演者の提案した保存的上流差分法および有限要素法を紹介したい.これらスキームは,KS系の解の基本性質である正値性保存と質量保存を厳密に再現し,解が凝集による集中化を起こしても安定な計算が遂行可能である.さらに,離散$L^p$空間における離散的解析半群の理論を応用して,陽的な誤差評価が導出される.なお当日の講演では,誤差解析等の理論よりは,離散スキームの構成方法や条件の説明に焦点をおきたい.
2008/06/04
16:30 - 17:30Room #117 (Mathematics building)
坂内 健一 (慶應義塾大学理工学部 )
"$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure
(joint work with G. Kings)
"
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.
16:00 - 18:15Room #056 (Mathematics building)
William Rundell (Department of Mathematics, Texas A&M University) 16:00 - 17:00
"Inverse Obstacle Recovery when the boundary condition is also unknown"
We consider the inverse problem of recovering the shape, location
and surface properties of an object where the surrounding medium
is both conductive and homogeneous. It is assumed that the physical situation is modeled by either harmonic functions or solutions of the Helmholtz equation and that the boundary condition on the obstacle is one of impedance type. We measure either Cauchy data, on an accessible part of the exterior boundary or the far field pattern resulting from a plane wave. Given sets of Cauchy data pairs we wish to recover both the shape and location of the unknown obstacle together with its impedance.
It turns out this adds considerable complexity to the analysis. We give a local injectivity result and use two different algorithms
to investigate numerical reconstructions. The setting is in two space dimensions, but indications of possible extensions (and difficulties) to three dimensions are provided. We also look at the case of a nonlinear impedance function.
David Colton (Department of Mathematical Sciences, University of Delaware) 17:15 - 18:15
"The Inverse Scattering Problem for an Isotropic Medium "
This talk is concerned with the inverse electromagnetic scattering problem for an isotropic inhomogeneous infinite cylinder. After formulating the direct scattering problem we proceed to the inverse scattering problem which is the main theme of this lecture. After discussing what is known about uniqueness for the inverse problem,we will proceed to the definition and properties of the far field operator. This leads to the study of a rather unusual spectral problem for partial differential equations called the interior transmission problem. We will state what is known about this problem including its role in determining lower bounds for the index of refraction from a knowledge of the far field pattern of the scattered wave, The talk is concluded by briefly considering the case of limited aperture data,in particular the use of the gap reciprocity method to determine the shape and location of buried objects. Numerical examples will be given as well as a number of open problems.
2008/06/03
16:30 - 18:00Room #126 (Mathematics building)
示野 信一 (岡山理科大)
"Matrix valued commuting differential operators with B2 symmetry"
B2 型のWeyl群の作用による対称性を持つ2次正方行列値の2階の可換な微分作用素を構成した。
作用素は Iida (Publ. Res. Inst. Math. Sci. Kyoto Univ. 32 (1996)) により計算された Sp(2,R)/U(2) の等質ベクトル束上の不変微分作用素の動径成分を特別な場合として含み、係数は楕円関数を用いて表される。
講演では、群の場合、可換な作用素の構成、spin Calogero-Sutherland 模型との関係について述べる。
http://akagi.ms.u-tokyo.ac.jp/seminar.html
16:30 - 18:00Room #056 (Mathematics building)
山口 祥司 (東京大学大学院数理科学研究科)
"On the geometry of certain slices of the character variety of a knot group"
joint work with Fumikazu Nagasato (Meijo University)
This talk is concerned with certain subsets in the character variety of a knot group.
These subsets are called '"slices", which are defined as a level set of a regular function associated to a meridian of a knot.
They are related to character varieties for branched covers along the knot.
Some investigations indicate that an equivariant theory for a knot is connected to a theory for branched covers via slices, for example, the equivariant signature of a knot and the equivariant Casson invariant.
In this talk, we will construct a map from slices into the character varieties for branched covers and investigate the properties.
In particular, we focus on slices called "trace-free", which are used to define the Casson-Lin invariant, and the relation to the character variety for two--fold branched cover.
2008/06/02
10:30 - 12:00Room #128 (Mathematics building)
本多 宣博 (東工大理工)
"A new series of compact minitwistor spaces and Moishezon twistor spaces over them"
17:00 - 18:30Room #002 (Mathematics building)
Shinobu Hikami (The University of Tokyo)
"Intersection theory from duality and replica"
Kontsevich's work on Airy matrix integrals has led to explicit results for the
intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on N by N matrices and N-point functions of k by k matrices, plus the replica method, familiar in the theory of disordered systems, allows one to recover Kontsevich's results on the intersection numbers, and to generalize them to other models. This provides an alternative and simple way to compute intersection numbers with one marked point, and leads also to some new results. This is a joint work with E. Brezin (Comm.Math. Phys. in press, arXiv:0708.2210).
2008/05/29
16:30 - 18:00Room #056 (Mathematics building)
Rolf Dyre Svegstrup (東大数理)
"2D models in AQFT from wedge algebras"
2008/05/27
16:30 - 18:00Room #126 (Mathematics building)
笹木集夢 (早稲田大学)
"Visible actions on multiplicity-free spaces"
The holomorphic action of a Lie group G on a complex manifold D is called strongly visible if there exist a real submanifold S such that D':=G・S is open in D and an anti-holomorphic diffeomorphism σ which is an identity map on S and preserves each G-orbit in D'.
In this talk, we treat the case where D is a multiplicity-free space V of a connected complex reductive Lie group G(C), and show that the action of a compact real form of G(C) on V is strongly visible.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/05/26
10:30 - 12:00Room #128 (Mathematics building)
下村 俊 (慶大理工)
"角領域における値分布論とその応用"
2008/05/24
13:30 - 16:00Room #123 (Mathematics building)
Raimandus Vidunas
(神戸大学理学部
) 13:30 - 14:30
"Identities between Appell's and univariate hyeprgeometric functions
"
We look for univariate specializations of Appell'd bivariante hypergeometric functions that can be expressed in terms of univaraite ${}_{i+1} F_{i} ~(i=1,2,3)$ HGF's. The method is identifying cases when the partial differential equations for Appell's functions imply hypegeometric ordinary differential equations for their univariate specializations. In general, ordinary differential equations for univariate specializations of Apell's functions have order at moast 4.
示野 信一 (岡山理科大学理学部) 14:45 - 15:45
"Whittaker functions with one-dimensional $K$-type on a semisimple Lie group of Hermitian type"
橋爪(Hiroshima J. Math. 12(1982))が与えたクラス1 Whittaker関数の表示式のHermitian対称空間上の1次元$K$-typeに付随したWhittaker関数への拡張を与える。またHeckeman-Opdamの超幾何関数の極限として、クラス1または1次元$K$-type を持つWhittaker関数が得られることを調べる。後者は石井-織田-平野(Math. Proc. Cambridge Philos. Soc. 41 (2006))の類似であり、一部は大島利雄氏との共同研究である。
2008/05/23
16:30 - 17:30Room #123 (Mathematics building)
Jean-Michel Bismut (Univ. Paris-Sud, Orsay)
"Functional integration and index theory
"
The heat equation proof of the Atiyah-Singer index theorem involves a local `fantastic cancellation' mechanism, which has long been unexplained conceptually.
In this lecture, I will show how the supersymmetric formalism introduced by physicists has ultimately led to a new understanding of this cancellation mechanism. Ideas of Witten and Atiyah relating the index theorem to the localization formulas of Duistermaat-Heckman in equivariant cohomology have ultimately led to a renewed understanding of the cancellation mechanism as being of geometric nature (albeit in infinite dimensions). The key fact is that when interpreting the heat equation method for the proof of the index theorem, integrals of measures on the loop space of the given manifold, which one obtains via Ito stochastic calculus, should be properly interpreted as integrals of differential forms on the loop space.
I will then explain how this new understanding of the local index theorem has naturally led to a better understanding of spectral invariants, and often to the proof of certain key properties.
2008/05/22
16:00 - 17:30Room #002 (Mathematics building)
森 洋一朗 (University of British Columbia)
"細胞生理学における数理研究のいくつかの話題について"
数理生理学は広汎な分野であり,用いられる手法も近年ますます多様化している.本講演では,数理生理学の中でも古典的な分野である電気生理学の数理モデルに関する最近の研究を紹介する.
電気生理学が対象とするのは細胞および組織レベルでの電気活動であり,これは神経・心・内分泌機能の根幹をなすものである.Hodgkin とHuxley の有名な仕事を契機として,この方面の研究は数理生理学に格好の題材を提供し続けてきた.本講演では,まず電気生理の基礎概念を紹介した後,イオン動態と細胞膜の3次元形状の効果を取り入れたモデルについて解説し,その心臓生理学への応用について語る.さらに時間が許せば,私が今興味を持っている細胞極性の生成,細胞の動きなどの話題についても紹介したい.
16:20 - 17:30Room #126 (Mathematics building)
逸見 昌之 (統計数理研究所)
"信頼区間やP-値の最悪評価による感度解析法について-メタアナリシスにおける出版バイアスの問題に対する1つのアプローチ-"
メタアナリシスとは、目的を同じくする複数の研究から得られる統計的結果を統合し、より強い統計的 エビデンスを得るための統計解析のことで、近年特に、医学・健康科学の分野において盛んに行われて いる。しかしながら、メタアナリシスのために行われる研究結果の選択過程は、必ずしも無作為(ランダ ム)であるとは限らない。例えば、統計的に有意でない結果は有意である結果に比べて公表(出版)されに くいので、公表されている結果だけでメタアナリシスを行うと統合結果も有意になる、ということがしば しば起こる。研究結果を選択する過程で入り込むバイアスの原因はこの他にもいろいろあり得るが、この 問題は一般に「出版バイアス(publication bias)」の問題と呼ばれている。出版バイアスを調整するた めによく使われる一つの方法は、研究結果の選択のされ方を統計的にモデリングすることであるが、そ のためには研究の選択過程に対して、データそのものからは検証できない強い仮定が必要である。その ため、その仮定がデータ以外の背景情報から強く支持されないと、間違った結論を導く可能性がある。 そこで本講演では、できるだけ多くの場合に許容されるような弱い仮定の下で、(メタアナリシスの結 果としての)信頼区間やP-値の最悪評価を行い、それらにもとづいて最終的な統計的有意性の判断を行 う方法を提案する。この信頼区間やP-値の最悪評価は、選択されなかった研究の数という未知数にも 依存しているので一意には決まらないが、この値を現実的に可能性のある範囲で振らせることによって、 どの辺で統計的有意性に関する結論が変化するかを知ることができる。その意味で、提案する方法は感 度解析法となっている。この方法論は、選択関数の作るある関数空間上の最適化問題の結果にもとづい ているが、今回はその数理的部分についてもできる限り詳しくお話しする予定である。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/02.html
2008/05/21
17:30 - 19:00Room #128 (Mathematics building)
尾張 圭太 (一橋大)
"Robust Exponential Hedging and Indifference Valuation "
2008/05/20
16:30 - 18:00Room #128 (Mathematics building)
Vania Sordoni (ボローニャ大学)
"Wave operators for diatomic molecules"
17:00 - 18:30Room #056 (Mathematics building)
Jer\^ome Petit (東京工業大学, JSPS)
"Turaev-Viro TQFT splitting."
The Turaev-Viro invariant is a 3-manifolds invariant. It is obtained in this way :
1) we use a combinatorial description of 3-manifolds, in this case it is : triangulation / Pachner moves
2) we define a scalar thanks to a categorical data (spherical category) and a topological data (triangulation)
3)we verify that the scalar is invariant under Pachner moves, then we obtain a 3-manifolds invariant.
The Turaev-Viro invariant can also be extended to a TQFT. Roughly speaking a TQFT is a data which assigns a finite dimensional vector space to every closed surface and a linear application to every 3-manifold with boundary.
In this talk, we will give a decomposition of the Turaev-Viro TQFT. More precisely, we decompose it into blocks. These blocks are given by a group associated to the spherical category which was used to construct the Turaev-Viro invariant. We will show that these blocks define a HQFT (roughly speaking a TQFT with an "homotopical data"). This HQFT is obtained from an homotopical invariant, which is the homotopical version of the Turaev-Viro invariant. Moreover this invariant can be used to obtain the homological Turaev-Viro invariant defined by Yetter.
16:45 - 18:15Room #126 (Mathematics building)
吉野太郎 (東京工業大学)
"Lipsman予想の反例と代数多様体の特異点について"
リー群$G$が多様体$M$に作用しているとき, その商空間$G\backspace M$のハウスドルフ性は, 不連続群論の研究において重要である. 特に, ベキ零リー群が線型空間にアファインかつ自由に作用するとき, 商位相は常にハウスドルフであるとLipsmanは予想した.
しかし, この予想には反例があり, 商位相は必ずしもハウスドルフでない.
この講演では, この非ハウスドルフ性を`可視化'したい. より正確には, $M$への$G$作用から, 自然に代数多様体$V$が定義され, $V$の特異点が商位相の非ハウスドルフ性に対応することを見る.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/05/19
17:00 - 18:30Room #002 (Mathematics building)
Jean-Michel Bismut (Univ. Paris-Sud, Orsay)
"A survey of Quillen metrics
"
In this lecture, I will survey basic results
on Quillen metrics.
Indeed let $X$ be a complex K\"ahler manifold, and let $E$ be a
holomorphic Hermitian vector bundle on $X$. Let $\lambda$ be the complex line
which is the determinant of the cohomology of $E$. The Quillen metric
is a metric on the line $\lambda$, which one obtains using a spectral
invariant of the Hodge Laplacian, the Ray-Singer analytic torsion.
The Quillen metrics have a number of remarkable properties. Among them
the curvature theorem says that when one considers a family of such
$X$, the curvature of the holomorphic Hermitian connection on
$\lambda$ is given by a formula of Riemann-Roch-Grothendieck type.
I will explain some of the ideas which go into the proof of these
properties, which includes Quillen's superconnections.
10:30 - 12:00Room #128 (Mathematics building)
大沢 健夫 (名大多元数理)
"On the projectively embeddable complex-foliated structures"
16:00 - 17:30Room #126 (Mathematics building)
Jean-Pierre Puel 氏
(ヴェルサイユ大学 (Universite de Versailles St Quentin)
)
"A non standard unique continuation property related to Schiffer conjecture"
Coming from a control problem for a coupled fluid-structure system, we are confronted to the following problem in dimension 2:
\Delta^2 w = -\lambda \Delta w in \Omega w = {\partial w}/{\partial n} = 0 on \Gamma {\partial\Delta w}/{\partial n}=0 on \Gamma_0 \subset \Gamma.
The question is : do we have w=0?
There is a counterexample when \Omega is a disc. The analogous of (local) Schiffer's conjecture is : is the disc the only domain for which we can have a non zero solution?
Notice that the term local means that the additional boundary condition occurs only on a part of the boundary and when this boundary is not analytic, this is a major difference. A sub-conjecture would be : when the boundary is not analytic, do we have w=0?
Here we show that when \Omega has a corner of angle \theta_{0} with \theta_{0} \neq \pi, 3\pi/2 and when $\Gamma_{0}$ is (locally) one edge of this angle then the only solution is w=0.
http://www.ms.u-tokyo.ac.jp/top/general-access.html
2008/05/15
16:30 - 18:00Room #056 (Mathematics building)
Mikael Pichot (東大数理)
"Property RD and CAT(0) geometry"
16:00 - 17:30Room #002 (Mathematics building)
小磯 深幸 (奈良女子大学理学部数学教室)
"非等方的平均曲率一定曲面の安定性と一意性について
( Stability and uniqueness for surfaces with constant anisotropic mean curvature)"
曲面の非等方的表面エネルギーは,法線方向に依存する関数の曲面上での積分として
定義され,結晶やある種の液晶のエネルギーの数学的モデルを与える.曲面が囲む体積
を保つ変分に対する非等方的表面エネルギーの臨界点を非等方的平均曲率一定曲
面(CAMC曲面)という.CAMC曲面が安定であるとは,対応する変分問題の第2変分が非負で
あるときをいう.したがって,エネルギー極小解は安定である.
本講演では,与えられた平行な二平面上に自由境界を持つ曲面全体の中での,囲む体
積一定の条件のもとでの非等方的表面エネルギーと境界での濡れエネルギーの和の臨
界点について論じる.エネルギー汎関数に対するある自然な仮定のもとで,安定解の存
在と一意性を示し,その幾何学的性質を決定する.
2008/05/13
16:30 - 18:00Room #056 (Mathematics building)
Tamas Kalman (東京大学大学院数理科学研究科, JSPS)
"The problem of maximum Thurston--Bennequin number for knots"
Legendrian submanifolds of contact 3-manifolds are
one-dimensional, just like knots. This ``coincidence'' gives rise to an
interesting and expanding intersection of contact and symplectic geometry
on the one hand and classical knot theory on the other. As an
illustration, we will survey recent results on maximizing the
Thurston--Bennequin number (which is a measure of the twisting of the
contact structure along a Legendrian) within a smooth knot type. In
particular, we will show how Kauffman's state circles can be used to solve
the maximization problem for so-called +adequate (among them, alternating
and positive) knots and links.
16:30 - 18:00Room #128 (Mathematics building)
Andr\'e Martinez (ボローニャ大学)
"Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\"ostrand)"
16:30 - 18:00Room #126 (Mathematics building)
加藤晃史 (東京大学)
"On endomorphisms of the Weyl algebra"
Noncommutative geometry has revived the interest in the Weyl algebras, which are basic building blocks of quantum field theories.
The Weyl algebra $A_n(\C)$ is an associative algebra over $\C$ generated by $p_i, q_i$ ($i=1,\cdots,n$) with relations $[p_i, q_j]=\delta_{ij}$. Every endomorphism of $A_n$ is injective since $A_n$ is simple.
Dixmier (1968) initiated a systematic study of the Weyl algebra $A_1$ and posed the following problem: Is every endomorphism of $A_1$ an automorphism?
We give an affirmative answer to this conjecture.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2008/05/12
17:00 - 18:30Room #002 (Mathematics building)
Jean-Michel Bismut (Univ. Paris-Sud, Orsay)
"The hypoelliptic Laplacian"
Let $X$ be a compact Riemannian manifold. The Laplace Beltrami
operator $-\Delta^{X}$, or more generally the Hodge Laplacian
$\square^{X}$, is an elliptic second order self adjoint operator on $X$.
We will explain the construction of a deformation of the elliptic
Laplacian to a family of hypoelliptic operators acting on the total
space of the cotangent bundle $\mathcal{X}$. These operators depend
on a parameter $b>0$, and interpolate between the Hodge Laplacian
(the limit as $b\to 0$) and the geodesic flow (the limit as $b\to +
\infty $).
Actually, the deformed Laplacian is associated with an exotic Hodge
theory on the total space of the cotangent bundle, in which the
standard $L_{2}$ scalar product on forms is replaced by a
symmetric bilinear form of signature $\left( \infty, \infty \right)$.
This deformation can be understood as a version of the Witten
deformation on the loop space associated with the energy functional.
From a probabilistic point of view, the deformed Laplacian
corresponds to a Langevin process.
The above considerations can also be used in complex geometry, in
which the Dolbeault cohomology is considered instead of the Rham cohomology.
Results obtained with Gilles Lebeau on the analysis of the
hypoelliptic Laplacian will also be presented, as well as
applications to analytic torsion.
10:30 - 12:00Room #128 (Mathematics building)
藤川 英華 (千葉大理)
"無限次元タイヒミュラー空間と複素解析的モジュライ空間の構造"
2008/05/08
16:30 - 18:00Room #056 (Mathematics building)
勝良健史 (慶應大学)
"Non-separable UHF algebras"
2008/05/07
16:30 - 17:30Room #117 (Mathematics building)
今井 直毅
(東京大学大学院数理科学研究科)
"On the connected components of moduli spaces of finite flat models"
2008/05/01
16:30 - 18:00Room #056 (Mathematics building)
Rune Johansen (Copenhagen 大学)
"On the structure of graph algebras of presentations of a sofic shift
"
2008/04/30
14:40 - 18:00Room #056 (Mathematics building)
今野宏 (東京大学大学院数理科学研究科) 14:40 - 16:10
"Morse theory for abelian hyperkahler quotients"
Kirwan はモーメント写像のノルムの2乗を Morse 関数として Morse 理論を展開することにより,シンプレクティック商のトポロジーを研究した.本講演では,これらの理論をトーラスによるハイパーケーラー商に拡張する.ハイパーケーラーモーメント写像のノルムの2乗はプロパーな関数でないが,ある場合には Morse 理論が展開できることを示す.さらに,Morse 理論が展開できる場合には,シンプレクティック商の場合より組織的に Betti 数やコホモロジー環が決定できることを示す.
赤穂まなぶ (首都大学東京 都市教養学部理工学系) 16:30 - 18:00
"ラグランジュはめ込みのフレアー理論について"
深谷・Oh・太田・小野は,シンプレクティック多様体 M の中のラグランジュ部分多様体 L に対して,種数 0 の prestable な境界付きリーマン面から M への安定写像で,境界値が L に含まれるようなものを考えることにより,L の鎖複体(の部分複体)上にギャップ・フィルター付き A 無限大代数の構造を定義した.本講演では,上の結果をラグランジュ部分多様体から(横断的な自己交叉をもつ)ラグランジュはめ込みへと拡張する.これにより,(横断的に交わる)有限個のラグランジュ部分多様体の和集合を一つのラグランジュはめ込みと見なすことができるなど,新しい視点が得られることを説明する.
16:30 - 17:30Room #117 (Mathematics building)
原 隆 (東京大学大学院数理科学研究科)
"Iwasawa theory of totally real fields for certain non-commutative $p$-extensions "
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.
2008/04/24
16:00 - 17:30Room #002 (Mathematics building)
宮本 安人 (東京工業大学 大学院理工学研究科)
"円盤領域におけるNeumann問題の分岐問題について"
円盤領域(2次元球領域)におけるNeumann問題 Δu+\lambda f(u)=0 を考える.広いクラスの非線形項 f に対して,第2固有値と第3固有値から非球対称解からなる大域的な枝(シート)が分岐することを示し,第2固有値からの分岐の枝は,分岐直後は一意的であることを示す.
16:20 - 17:30Room #126 (Mathematics building)
白石 友一 (統計数理研究所)
"二値判別機の組合せによる多値判別問題へのゲーム理論的アプローチ"
多値判別という学習理論の問題に対して、ゲーム理論的なアプローチを試みた結果についてお話したいと思います。多値判別問題を解くために実用的に広く用いられている方法に、2値判別機を組み合わせる方法があります。その際に2値判別機の出力結果に誤り訂正符号のモデルを仮定し、MAP推定により出力を決める方法が一般的です。本発表では2値判別機の組合せによる多値判別の問題を、「決定者」と「自然」のゲームとして捉え、既存の手法の解析や新しい手法の提案を行います。まず、多値判別問題における、誤り訂正符号による方法がミニマックスとなるための条件をネットワークフローにより表します。そして、one-vs-oneやone-vs-allなどの方法が自然な条件下でミニマックス戦略となることを検証します。次に、誤り訂正符号による方法に拡張を加え、「自然」の範囲をデータからある程度特定したときのミニマックス戦略を求める方法を提案し、これを2次錐計画法により定式化します。またミニマックス定理やエントロピーなどとの関連についての考察を行います。キーワードとしては
・判別問題(特にクラス数が3以上の多値判別問題)
・誤り訂正符号
・ゲーム理論
・最適化理論(線形計画法、2次錐計画法)
・ネットワークフロー理論
・フォン=ノイマンのミニマックス定理
などが挙げられると思います。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/01.html
17:00 - 18:30Room #056 (Mathematics building)
Motohico Mulase (University of California, Davis)
"Recursion relations in intersection theory on the moduli spaces of Riemann surfaces"
In this talk I will give a survey of recent developments in the intersection theory of tautological classes on the moduli spaces of stable algebraic curves. The emphasis is placed on explaining where the Virasoro constraint conditions are originated. Recently several authors have encountered the same combinatorial recursion relation from completely different contexts, that eventually leads to the Virasoro constraint. This mysterious structure of the theory will be surveyed.
2008/04/22
16:30 - 18:00Room #056 (Mathematics building)
Sergey Yuzvinsky (University of Oregon)
"Special fibers of pencils of hypersurfaces"
We consider pencils of hypersurfaces of degree $d>1$ in the complex
$n$-dimensional projective space subject to the condition that the
generic fiber is irreducible. We study the set of completely reducible
fibers, i.e., the unions of hyperplanes. The first surprinsing result is
that the cardinality of thie set has very strict uniformed upper bound
(not depending on $d$ or $n$). The other one gives a characterization
of this set in terms of either topology of its complement or combinatorics
of hyperplanes. We also include into consideration more general special
fibers are iimportant for characteristic varieties of the hyperplane
complements.
2008/04/21
16:30 - 18:00Room #122 (Mathematics building)
高木寛通 (東大数理)
"Scorza quartics of trigonal spin curves and their varieties of power sums "
Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and non-effective theta characteristics. This is a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartic for any general pairs of curves and non-effective theta characteristics.
10:30 - 12:00Room #128 (Mathematics building)
平地 健吾 (東大数理)
"Ambient realization of conformal jets and deformation complex"
2008/04/17
16:20 - 17:30Room #126 (Mathematics building)
中野 張 (科学技術振興機構)
"動的なリスク分散による保険料計算原理について"
生命保険や銀行貸付け等の長期の商品に対しては、
時間依存の安全割増によるリスク評価を行うことが求められる。
今回の発表では、効用関数の畳み込みにより生成される動的リスク尺度によるアプローチを紹介する。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/00.html
16:30 - 18:00Room #056 (Mathematics building)
小沢登高 (東大数理)
"On a class of II$_1$ factors with at most one Cartan subalgebra II"
16:00 - 17:30Room #002 (Mathematics building)
WEISS Georg (東京大学大学院数理科学研究科)
"Hidden dynamics and pulsating waves in self-propagating high temperature synthesis"
We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term.
In the first part we give a complete characterization of the limit problem in the case of one space dimension. In the second part we construct in any finite dimension a rather large family of pulsating waves for the limit problem. In the third part, we prove that for constant coefficients the limit problem in any finite dimension does not admit non-trivial pulsating waves.
This is a joint work with Regis MONNEAU (CERMICS, France).
2008/04/15
16:30 - 18:00Room #056 (Mathematics building)
村上 順 (早稲田大学理工)
"On the invariants of knots and 3-manifolds related to the restricted quantum group"
I would like to talk about the colored Alexander invariant and the logarithmic
invariant of knots and links. They are constructed from the universal R-matrices
of the semi-resetricted and restricted quantum groups of sl(2) respectively,
and they are related to the hyperbolic volumes of the cone manifolds along
the knot. I also would like to explain an attempt to generalize these invariants to
a three manifold invariant which relates to the volume of the manifold actually.
2008/04/14
10:30 - 12:00Room #128 (Mathematics building)
佐野 友二 (東大IPMU)
"トーリック・ファノ多様体のマルチプライア・イデアル層と二木不変量の関係について"
2008/04/08
10:30 - 12:00Room #002 (Mathematics building)
Akihiro Tsuchiya (IPMU, The University of Tokyo)
"IPMU Komaba Lectures,Homotopy Theory (before 1970)
"
Tuesday, April -- July, 2008
First Lecture Aprl 8
Recently the notion of homotopy theory has been widely used in many areas of
contemporary mathematics including mathematical physics.
The purpose of the lectures is to present an overview of the developments
of homotopy theory mainly from 1940's through 1960's, partly in view of
more recent progress in other areas.
(1) Prehistory of homotopy theory
-- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem
(2) Eilenberg-MacLane space and Postnikov system
(3) Steenrod algebras
(4) Serre's theorem on the homotopy groups of spheres
(5) Rational homotopy theory
(6) Stable homotopy category and Adams spectral sequence
(7) Vector bundles and characteristic classes
(8) Complex cobordism and Quillen's theorem
(9) Miscellaneous topics
Rereferences :
(1) J.P.May, A Concise Course in Algebraic Topology,
The University of Chicago Press
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres
The second edition, AMS Chelsea Series
http://www.math.rochester.edu/u/faculty/doug/mu.html
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra
2008/03/19
10:30 - 11:30Room #056 (Mathematics building)
Juergen Saal (Department of Mathematics and Statistics, University of Konstanz)
"Maximal Regularity for Mixed Order Systems"
In classical boundary value problems the related symbols are homogeneous in space and time. This allows for the application of a standard compactness argument in order to obtain the important maximal regularity. However, quasilinear systems arising e.g. from free boundary problems are in general of mixed order. In other words the related symbols are of intricate structure and in particular highly inhomogeneous. Therefore, the standard compactness argument fails. The purpose of this talk is to introduce the Newton polygon method, which gives a systematic approach to such mixed order systems and to demonstrate its strength by applications to the Stefan problem and a free boundary problem for the Navier-Stokes equations.
2008/03/14
16:30 - 18:00Room #126 (Mathematics building)
David Morrison (UC Santa Barbara)
"Understanding singular algebraic varieties via string theory"
String theory has helped to formulate two major new insights in the study of singular algebraic varieties. The first -- which also arose from symplectic geometry -- is that families of Kaehler metrics are an important tool in uncovering the structure of singular algebraic varieties. The second, more recent insight -- related to independent work in the representation theory of associative algebras -- is that one's understanding of a singular (affine) algebraic variety is enhanced if one can find a non-commutative ring whose center is the coordinate ring of the variety. We will describe both of these insights, and explain how they are related to string theory.
2008/03/13
15:00 - 17:30Room #117 (Mathematics building)
伊藤健一 (東京大学大学院数理科学研究科) 15:00 - 16:00
"Schr/"odinger equations on scattering manifolds and microlocal singularities"
Maciej ZWORSKI (カリフォルニア大学バークレイ校) 16:30 - 17:30
"Local smoothing in the presence of lots of trapping"
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf
2008/02/23
13:00 - 16:30Room #270 (Mathematics building)
岩尾慎介 (東大数理) 13:00 - 14:30
"Solutions of hungry periodic discrete Toda equation and its ultradiscretization"
The hungry discrete Toda equation is a generalization of the discrete Toda
equation. Through the method of ultradiscretization, the generalized
Box-ball system (gBBS) with finitely many kinds of balls is obtained from
hungry discrete Toda eq.. It is to be expected that the general solution of
gBBS should be obtained from the solution of hungry discrete Toda eq.
through ultradiscretization. In this talk, we derive the solutions of hungry
periodic discrete Toda eq. (hpd Toda eq.), by using inverse scattering
method. Although the hpd Toda equation does not linearlized in the usual
sense on the Picard group of the spectral curve, it is possible to determine
its behavior on the Picard group.
竹縄知之 (東京海洋大・海洋工) 15:00 - 16:30
"A tropical analogue of Fay's trisecant identity and its application to the ultra-discrete periodic Toda equation."
The ultra-discrete Toda equation is essentially equivalent to the integrable
Box and Ball system, and considered to be a fundamental object in
ultra-discrete integrable systems. In this talk, we construct the general
solution of ultra-discrete Toda equation with periodic boundary condition,
by using the tropical theta function and the bilinear form. The tropical
theta function is associated with the tropical curve defined through the Lax
matrix of (not ultra-) discrete periodic Toda equation. For the proof, we
introduce a tropical analogue of Fay's trisecant identity. (This talk is
based on the joint work with R. Inoue.)
2008/02/20
16:20 - 17:30Room #122 (Mathematics building)
大屋 幸輔 (大阪大学大学院経済学研究科)
"A Test for Cross-sectional Dependence of Microstructure Noises and their Cross-Covariance Estimator"
高頻度観測される約定データにもとづく Integrated Volatility や Integrated Covariance の推定量は Bid-Ask Bounce に代表される Market Microstructure Noise の存在により、バイアスをもち、その分散も過大なものになっている。さ まざまな推定量の改良が提案されているが、それらの多くは Microstructure Noise の dependence の構造を既知としたものである。この従属性の構造を明ら かにするために、本報告では直接観測できない Microstructure Noise の相互自 己共分散がゼロであるかどうかを検定する統計量と相互自己共分散関数の推定量 を提案する。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/21.html
13:30 - 17:45Room #123 (Mathematics building)
乙部厳己 (信州大理) 13:30 - 14:00
"Divergence formulae on the space of continuous functions and Malliavin calculus"
長田博文 (九大数理) 14:15 - 15:15
"Ginibre random point field and a notion of convergence of Dirichlet forms"
Lorenzo Zambotti (パリ第6大学) 15:30 - 16:30
"Stochastic PDEs and infinite dimensional integration by parts formulae"
志賀徳造 (東工大理工) 16:45 - 17:45
"ランダム環境下の確率モデルに関連する問題
(A problem arising in stochastic models in random environments)"
2008/02/19
16:30 - 17:30Room #118 (Mathematics building)
Eric Stade (Colorado University)
"An overview on archimedean L-factors for G_1xG_2"
When G_1xG_2 is one of pairs GL(n)xGL(n), GL(n)xGL(n+1), GL(n)xSO(2n+1), and GL(n+1)xSO(2n+1), we have evaluation of the archimedian L-factors of automorphic L-functions obtained by Rankin-Selberg convolution.
The last two cases are joint works with Taku Ishii (Chiba Inst. of Tech) which are in progress.
2008/02/13
16:20 - 17:30Room #123 (Mathematics building)
増田 弘毅 (九大数理)
"Realized multipower variationの統計推測への応用について"
確率過程からの高頻度データに基づいて定義されるMultipower variation (MPV)は,飛躍に対して頑健な累積ボラティリティ推定量や,飛躍の検出のための統 計量として,近年計量経済において脚光を浴びている.MPVはモデルの複雑さに依ら ずその計算が容易であるため,飛躍付確率過程に関する様々な統計推測問題への適用 が期待される.本報告では特に,最近Lee and Mykland (The Review of Financial Studies, to appear)によって提案された,MPVを介した飛躍時点(微小区間)の検出 手法を,複合ポアソン型飛躍付拡散過程の漸近推測へ応用することを考える.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/20.html
2008/02/12
17:00 - 18:30Room #056 (Mathematics building)
Katrin Wendland (University of Augrburg)
"How to lift a construction by Hiroshi Inose to conformal field theory"
The moduli space of Einstein metrics is well known to algebraic and differential geometers. Physicists have introduced the notion of conformal field theories (CFTs) associated to K3, and the moduli space of these objects is well understood as well. It can be interpreted as a generalisation of the moduli space of Einstein metrics on K3, which allows us to introduce this space without having to use background knowledge from conformal field theory. However, just as no smooth Einstein metrics on K3 are known explicitly, the explicit construction of CFTs associated to K3 in general remains an open problem. The only known constructions which allow to deal with families of CFTs give CFTs associated to K3 surfaces with orbifold singularities.
We use a classical construction by Hiroshi Inose to explicitly construct a family of CFTs which are associated to a family of smooth algebraic K3 surfaces. Although these CFTs were known before, it is remarkable that they allow a description in terms of a family of smooth surfaces whose complex structure is deformed while all other geometric data remain fixed.
We also discuss possible extensions of this result to higher dimensional Calabi-Yau threefolds.
2008/02/07
16:30 - 18:00Room #002 (Mathematics building)
Luc Illusie (パリ南大学)
"On Gabber's refined uniformization theorem and applications"
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
2008/02/06
13:30 - 14:40Room #056 (Mathematics building)
Jean JACOD (Universite Paris 6)
"Estimation of the integrated volatility in presence of microstructure noise"
The aim is to estimate the integrated volatility of a process observed discretely, in the setting of high frequency data, and when there is a microstructure noise. We use a kind of pre-averaging approach, which is rate-optimal when the noise is i.i.d., and may probably be even variance-optimal for a good choice of the kernel involved. However, the main innovative aspect is that it accommodates other types of noise, and in particular the case where the observations are rounded values of the underlying process plus an additive noise.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/17.html
14:50 - 16:00Room #056 (Mathematics building)
Jean JACOD (Universite Paris 6)
"Estimating the Degree of Activity of jumps in High Frequency Data"
Suppose that a continuous-time process X = (X_t )_{t >= 0} is observed at finitely many times, regularly spaced, on the fixed time interval [0, T ]. We suppose that this process is an It\^o semimartingale, with a non-vanishing diffusion coefficient, and with jumps. The aim is to estimate the so-called ”Blumenthal-Getoor” index of the (partially observed) path on [0, T ], which is the (random) infimum of all reals r such that the sum \sum_{s\le T} |\Delta X_s|^r is finite (\Delta X_s denotes the jump size at time s). When X is a L'evy process, this infimum is non-random, and also independent of T , and has been introduced by Blumenthal and Getoor. Under appropriate assumptions, unfortunately rather restrictive, we provide an estimator, which is consistent when the step size between observations goes to 0, and satisfies in addition a Central Limit Theorem. We also show the (surprising) values that this estimator takes, when applied to real financial data.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/18.html
16:20 - 17:30Room #056 (Mathematics building)
竹原 浩太 (東京大学大学院経済学研究科)
"A Hybrid Asymptotic Expansion Scheme: an Application to Long-term Currency Options"
In this session we develop a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for the valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates.
Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained.
Moreover, the hybrid scheme develops Fourier transform method with an asymptotic expansion to utilize closed-form characteristic functions obtainable in parts of a model.
Our scheme also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of closed-form characteristic functions.
Finally, a series of numerical examples shows the validity of our scheme.
(This is a collaborative research with Professor Akihiko Takahashi(Graduate School of Economics, The University of Tokyo).)
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/19.html
18:00 - 19:30Room #128 (Mathematics building)
Daniel Bloch ( )
"Fast calibration of some Affine and Quadratic models with applications to derivatives on variance swaps
"
2008/01/31
16:30 - 18:00Room #002 (Mathematics building)
見村万佐人 (東大数理)
"A generalization of property (T) of SL(n,R)"
16:30 - 18:00Room #118 (Mathematics building)
Luc Illusie (パリ南大学)
"On Gabber's refined uniformization theorem and applications"
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
2008/01/30
16:30 - 17:30Room #117 (Mathematics building)
Luc Illusie (Universite Paris-Sud 11)
"Odds and ends on finite group actions and traces"
Suppose a finite group G acts on a scheme X separated and of finite type over a field k. This raises several questions about the traces of elements s of G (or more generally products sg, for g in the Galois group of k) on cohomology groups of various types associated with X/k (with compact support or no support, Betti if k = C, l-adic, rigid). Some were considered and solved long ago, others only recently. I will in particular discuss an equivariant generalization of a theorem of Laumon on Euler-Poincar¥'e characteristics.
10:30 - 11:30Room #056 (Mathematics building)
Oleg Yu. Emanouilov (Colorado State University)
"Carleman estimates for parabolic equations, a Stokes system and the Navier-Stokes equations and applications to the control problem"
We prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions. On basis of this estimate we obtain an improved Carleman estimate for the Stokes system and a system of parabolic equations with a parameter which can be viewed as an approximation of the Stokes system. We will discuss the applications to the control problem for these systems.
2008/01/29
10:00 - 12:00Room #128 (Mathematics building)
Dmitry KALEDIN (Steklov研究所, 東大数理)
"Homological methods in non-commutative geometry, part 11 (last lecture)"
http://imperium.lenin.ru/~kaledin/math/tokyo/
16:30 - 18:30Room #056 (Mathematics building)
松田 能文 (東京大学大学院数理科学研究科) 16:30 - 17:30
"The rotation number function on groups of circle diffeomorphisms"
ポアンカレは、円周の向きを保つ同相写像に対して、回転数の有理性と有限軌道の存在が
同値であることを示した。この講演では、この事実が円周の向きを保つ同相写像のなすあ
る種の群に対して一般化できることを説明する。特に、円周の向きを保つ実解析的微分同
相のなす非離散的な群に対して、回転数関数による像の有限性と有限軌道の存在が同値で
あることを示す。
木村 康人 (東京大学大学院数理科学研究科) 17:30 - 18:30
"A Diagrammatic Construction of Third Homology Classes of Knot Quandles"
There exists a family of third (quandle / rack) homology classes,
called the shadow (fundamental / diagram) classes,
of the knot quandle, which are obtained from
the shadow colourings of knot diagrams.
We will show the construction of these homology classes,
and also show their relation to the shadow quandle cocycle
invariants of knots and that to other third homology classes.
2008/01/28
10:30 - 12:00Room #128 (Mathematics building)
都丸 正 (群馬大学)
"閉リーマン面の${¥bf C}^{*}$-作用付き退化族と${¥bf C}^{*}$-作用付き複素2次元特異点"
2008/01/25
17:00 - 18:00Room #123 (Mathematics building)
齊藤宣一 (東京大学数理科学)
"Keller-Segel系に対する保存的上流有限要素法"
非線形放物型偏微分方程式系に対して、有限要素法による数値解法を考え、スキーム構成の勘所と誤差解析の最近の動向についてお話したい。具体的な例としては、細胞性粘菌の凝集現象を記述するモデルとして広く知られるKeller-Segel(KS)系とその保存的上流有限要素法を取り上げる。このスキームは、KS系の解の基本性質である正値性保存と質量保存を厳密に再現し、解が凝集による集中化を起こしても安定に計算が遂行できる。さらに、離散 $L^p$ 空間における離散的解析半群の理論を応用して、陽的な誤差評価が導出される。
2008/01/24
16:00 - 17:30Room #126 (Mathematics building)
Radu IGNAT (パリ南大学(オルセー))
"A compactness result in micromagnetics"
We study a model for the magnetization in thin ferromagnetic films. It comes as a variational problem, depending on two parameters, for maps with values into the unit sphere. There is a physical prediction for the optimal configuration of the magnetization called the Landau state. Our goal is to prove compactness of the Landau state. This is a joint work with Felix Otto.
2008/01/23
16:30 - 17:30Room #117 (Mathematics building)
Weizhe Zheng (Universite Paris-Sud 11)
"Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields"
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
17:30 - 19:00Room #128 (Mathematics building)
二宮 真理子 (東京大)
"確率微分方程式に対するRunge-Kutta法を用いた新たな弱近似手法
"
2008/01/22
16:30 - 18:00Room #128 (Mathematics building)
Serge Richard (Univ. Lyon 1)
"Magnetic Schroedinger operators and twisted crossed product"
During this seminar, we shall study spectral properties of generalized
magnetic Schroedinger operators H(B,V) with anisotropic magnetic field B
and scalar potential V. The essential spectrum of such operators is
expressed as a union of spectra of some asymptotic operators supported by
the quasi-orbits of a suitable dynamical system. A localization property
of the functional calculus of H(B,V) will also be presented. It directly
implies a non-propagation result for the unitary group generated by this
operator. The proofs rely on the use of twisted crossed product
C*-algebras. Twisted dynamical systems and their corresponding algebras
will be introduced and the natural link with magnetic Schroedinger
operators will be clearly established.
16:30 - 18:00Room #126 (Mathematics building)
大島 利雄 (東京大学)
"Connecion problems for Fuchsian differential equations free from accessory parameters"
The classification of Fuchsian equations without accessory parameters was formulated as Deligne-Simpson problem, which was solved by Katz and they are studied by Haraoka and Yokoyama.
If the number of singular points of such equations is three, they have no geometric moduli.
We give a unified connection formula for such differential equations as a conjecture and show that it is true for the equations whose local monodromy at a singular point has distinct eigenvalues.
Other Fuchsian differential equations with accessory parameters and hypergeometric functions with multi-variables are also discussed.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
10:00 - 12:00Room #128 (Mathematics building)
Dmitry KALEDIN (Steklov研究所, 東大数理)
"Homological methods in non-commutative geometry, part 10"
http://imperium.lenin.ru/~kaledin/math/tokyo/
16:30 - 18:00Room #118 (Mathematics building)
Luc Illusie (パリ南大学)
"On Gabber's refined uniformization theorem and applications"
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
2008/01/21
10:30 - 12:00Room #128 (Mathematics building)
篠原知子 (都立産業技術高専)
"周期的不定点に存在する不変曲線族の構成"
16:00 - 17:30Room #126 (Mathematics building)
Torbjorn Lundh (Chalmers & Göteborg University)
"Potential theory of funnels and wounds"
We will talk about a result concerning Green functions, namely the so called 3G-inequality, which I studied together with H. Aikawa. The focus of the talk will be on the description of the way to that result, where we among other tools used numerical methods to get a better intuitive understanding the situation. We will also discuss a possible potential theoretic view-point of an ancient wound healing question.
2008/01/17
16:30 - 18:00Room #056 (Mathematics building)
山下真 (東大数理)
"Cup product on the Periodic Cyclic Cohomology"
17:00 - 18:00Room #123 (Mathematics building)
手塚勝貴 (東大数理)
"Proper actions of SL(2,R) on irreducible complex symmetric spaces"
We determine the irreducible complex symmetric spaces on which SL(2,R) acts properly. We use the T. Kobayashi's criterion for the proper actions. Also we use the symmetry or unsymmetry of the weighted Dynkin diagram of the theory of nilpotent orbits.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
16:30 - 18:00Room #118 (Mathematics building)
Luc Illusie (パリ南大学)
"On Gabber's refined uniformization theorem and applications"
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.
2008/01/16
16:20 - 17:30Room #122 (Mathematics building)
清水 泰隆 (大阪大学大学院 基礎工学研究科)
"Implementation of a jump-detection method and applications to real markets"
株価の確率モデルとして,ジャンプ型拡散過程は収益率分布の裾の厚さを表現しうる モデルとして有用な候補の一つである.その際,離散データによる統計推測は,Mancini('03), Shimizu and Yoshida('06)らによるジャンプ検出フィルターを用いることで可能になる. Shimizu('07)は有限個の離散データからのフィルターの決定法を提案し,実データへの応用を 可能にした.本報告では,これらの手法を計算機に実装する際の問題点とその解決法について 議論した後,日経平均や為替の日次データにMerton('76), Kou('02)など,いくつかのジャンプ型 モデルを仮定して,ジャンプの検出とモデルフィッティングを試みる.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html
16:30 - 17:30Room #117 (Mathematics building)
Antoine Chambert-Loir (Universite de Rennes 1)
"Equidistribution theorems in Arakelov geometry"
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.
14:50 - 16:00Room #122 (Mathematics building)
Marc HOFFMANN (Universite Paris-est Marne la vallee)
"Statistical analysis of fragmentation chains"
We address statistical inference in self-similar conservative fragmentation chains, when only observations on the size of the fragments below a given threshold are available. (Possibly, the measurement of the fragments themselves are subject to further systematic experimental noise.) This framework, introduced by Bertoin and Martinez is motivated by mineral crushing in mining industry. We compute upper and lower rates of estimation for several functionals of the dislocation measure, both in a semi-parametric and a non-parametric framework. The underlying estimated object is the step distribution of the random walk associated to a randomly tagged fragment that evolves along the genealogical tree representation of the fragmentation process. We establish a formal link with the statistical problem of estimating the overshoot of the distribution as the crossing level goes to infinity with the size of the dataset; in particular the difficulty of the estimation problem in the non-parametric case is comparable to ill-posed linear inverse problems of order 1 in signal denoising.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/15.html
2008/01/15
16:30 - 17:30Room #056 (Mathematics building)
飯田 修一 (東京大学大学院数理科学研究科)
"Adiabatic limits of eta-invariants and the Meyer functions"
The Meyer function is the function defined on the hyperelliptic
mapping class group, which gives a signature formula for surface
bundles over surfaces.
In this talk, we introduce certain generalizations of the Meyer
function by using eta-invariants and we discuss the uniqueness of this
function and compute the values for Dehn twists.
16:30 - 18:00Room #126 (Mathematics building)
Fulton Gonzalez (Tufts University)
"Group contractions, invariant differential operators and the matrix Radon transform
"
Let $M_{n,k}$ denote the vector space of real $n\times k$ matrices.
The matrix motion group is the semidirect product $(\text O(n)\times \text O(k))\ltimes M_{n,k}$, and is the Cartan motion group
associated with the real Grassmannian $G_{n,n+k}$.
The matrix Radon transform is an
integral transform associated with a double fibration involving
homogeneous spaces of this group. We provide a set of
algebraically independent generators of the subalgebra of its
universal enveloping algebra invariant under the Adjoint
representation. One of the elements of this set characterizes the range of the matrix Radon transform.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
10:00 - 12:00Room #128 (Mathematics building)
Dmitry KALEDIN (Steklov研究所, 東大数理)
"Homological methods in non-commutative geometry, part 9"
http://imperium.lenin.ru/~kaledin/math/tokyo/
2008/01/09
16:20 - 17:30Room #122 (Mathematics building)
金川 秀也 (武蔵工業大学)
"Parameter estimated standardized U-statistics with degenerate kernel for weakly dependent random variables"
In this paper, extending the results of Gombay and Horv'{a}th (1998), we prove limit theorems for the maximum of standardized degenerate U-statistics defined by some absolutely regular sequences or functionals of them.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/14.html
2008/01/08
16:30 - 18:00Room #128 (Mathematics building)
Nikolay Tzvetkov (Lille大学)
"On the restrictions of Laplace-Beltrami eigenfunctions to curves"
10:00 - 12:00Room #128 (Mathematics building)
Dmitry KALEDIN (Steklov研究所, 東大数理)
"Homological methods in non-commutative geometry, part 8"
2008/01/07
13:30 - 14:30Room #056 (Mathematics building)
伊藤一文 (North Carolina State University)
"An Optimal Feedback Solution to Quantum Control Problems."
Control of quantum systems described by Schrodinger equation is considered. Feedback control laws are developed for the orbit tracking via a controled Hamiltonian. Asymptotic tracking properties of the feedback laws are analyzed. Numerical integrations via time-splitting are also analyzed and used to demonstrate the feasibility of the proposed feedback laws.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2008/01/06
16:30 - 18:00Room #128 (Mathematics building)
青木 貴史 (近畿大理工)
"野海・山田方程式系のWKB解に付随する幾何的構造"
本多尚文氏、梅田陽子氏との共同研究
2007/12/26
16:30 - 18:00Room #056 (Mathematics building)
Pinhas Grossman (Vanderbilt University)
"Pairs of intermediate subfactors"
2007/12/25
16:30 - 18:00Room #128 (Mathematics building)
Gregory Eskin (UCLA)
"Inverse boundary value problems for the Schrodinger equation with time-dependent electromagnetic potentials and the Aharonov-Bohm effect"
We consider the determination of the time-dependent magnetic and electric potentials (modulo gauge transforamtions) by the boundary measurements in domains with obstacles. We use the geometric optics and the tomography of broken rays. The presence of the obstacles leads to the Aharonov-Bohm effect caused by the magnetic and electric fluxes.
2007/12/22
13:00 - 16:30Room #117 (Mathematics building)
池田岳 (岡山理大理) 13:00 - 14:30
"Double Schubert polynomials for the classical Lie groups"
For each infinite series of the classical Lie groups of type $B$,
$C$ or $D$, we introduce a family of polynomials parametrized by the
elements of the corresponding Weyl group of infinite rank. These
polynomials
represent the Schubert classes in the equivariant cohomology of the
corresponding
flag variety. When indexed by maximal Grassmannian elements of the Weyl
group,
these polynomials are equal to the factorial analogues of Schur $Q$- or
$P$-functions defined earlier by Ivanov. This talk is based on joint work
with L. Mihalcea and H. Naruse.
前野 俊昭 (京大工) 15:00 - 16:30
"Nichols-Woronowicz model of the K-ring of flag vaieties G/B"
We give a model of the equivariant $K$-ring $K_T(G/B)$ for
generalized flag varieties $G/B$ in the braided Hopf algebra
called Nichols-Woronowicz algebra. Our model is based on
the Chevalley-type formula for $K_T(G/B)$ due to Lenart
and Postnikov, which is described in terms of alcove paths.
We also discuss a conjecture on the model of the quantum
$K$-ring $QK(G/B)$.
2007/12/21
17:00 - 18:00Room #123 (Mathematics building)
D. Eisenbud (Univ. of California, Berkeley)
"Plato's Cave: what we still don't know about generic projections"
Riemann Surfaces were first studied algebraically by first projecting them into the complex projective plan; later the same idea was applied to surfaces and higher dimensional varieties, projecting them to hypersurfaces. How much damage is done in this process? For example, what can the fibers of a generic linear projection look like? This is pretty easy for smooth curves and surfaces (though there are still open questions), not so easy in the higher-dimensional case. I'll explain some of what's known, including recent work of mine with Roya Beheshti, Joe Harris, and Craig Huneke.
2007/12/20
16:30 - 18:00Room #056 (Mathematics building)
崎山理史 (東大数理)
"Gauge-invariant ideal structure of ultragraph $C^*$-algebras"
10:40 - 12:10Room #128 (Mathematics building)
Mikael Pichot (東大数理)
"Topics in ergodic theory, von Neumann algebras, and rigidity"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007/12/19
16:20 - 17:30Room #122 (Mathematics building)
永井 圭二 (横浜国立大学)
"Sequential Tests for Criticality of Branching Processes."
We consider sequential testing procedures for detection of
criticality of Galton-Watson branching process with or without
immigration. We develop a t-test from fixed accuracy estimation
theory and a sequential probability ratio test (SPRT). We provide
local asymptotic normality (LAN) of the t-test and some asymptotic
optimality of the SPRT. We consider a general framework of
diffusion approximations from discrete-time processes and develop
sequential tests for one-dimensional diffusion processes to
investigate the operating characteristics of sequential tests
of the discrete-time processes. Especially the Bessel process with
constant drift plays a important role for the sequential test
of criticality of branching process with immigration.
(Joint work with K. Hitomi (Kyoto Institute of Technology)
and Y. Nishiyama (Kyoto Univ.))
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/13.html
2007/12/18
16:30 - 18:00Room #056 (Mathematics building)
R.C. Penner (USC and Aarhus University)
"Groupoid lifts of representations of mapping classes"
The "Ptolemy groupoid" is the fundamental path groupoid of the dual to the ideal cell decomposition of the decorated Teichmueller space of a punctured or bordered surface, and the "Torelli groupoid" is thesimilar discretization of the fundamental path groupoid of the quotient
by the Torelli subgroup of mapping classes that acts identically on the first integral homology of the surface. Mapping classes can be represented as appropriate elements of the Ptolemy groupoid and likewise for elements of the Torelli group in the Torelli groupoid.
A natural series of questions is to wonder which representations of mapping class groups, Torelli groups, and their subgroups can be lifted to the groupoid level. In a series of joint works with J. Andersen, A. Bene, N. Kawazumi, and S. Morita, we have given explicit lifts of a number of classical representations: The Johnson representations of the classical and higher Torelli groups
and the symplectic representation of the mapping class group all lift to the Torelli groupoid. Furthermore, the Nielsen representation of the mapping class group as automorphisms of a
free group lifts to the Ptolemy groupoid, and hence so too does any representation
of the mapping class group that factors through its action on the fundamental group of
the surface such as the Magnus representation. We shall survey these various groupoid lifts and discuss current and potential future applications.
16:30 - 18:00Room #126 (Mathematics building)
阿部 紀行 (東京大学)
"On the existence of homomorphisms between principal series of complex
semisimple Lie groups"
The principal series representations of a semisimple Lie group play an important role in the representation theory. We study the principal series representation of a complex semisimple Lie group and determine when there exists a nonzero homomorphism between the representations.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/12/17
10:30 - 12:00Room #128 (Mathematics building)
寺杣友秀 (東京大学)
"種数3の曲線とあるCalabi-Yau threefoldの代数的対応(松本圭司氏との共同研究)"
17:00 - 18:30Room #002 (Mathematics building)
Ken-Ichi Yoshikawa (The University of Tokyo)
"Analytic torsion for Calabi-Yau threefolds"
In 1994, Bershadky-Cecotti-Ooguri-Vafa conjectured that analytic torsion
gives rise to a function on the moduli space of Calabi-Yau threefolds and
that it coincides with the quantity $F_{1}$ in string theory.
Since the holomorphic part of $F_{1}$ is conjecturally the generating function
of the counting problem of elliptic curves in the mirror Calabi-Yau threefold,
this implies the conjectural equivalence of analytic torsion and the counting
problem of elliptic curves for Calabi-Yau threefolds through mirror symmetry.
After Bershadsky-Cecotti-Ooguri-Vafa, we introduced an invariant of
Calabi-Yau threefolds, which we obtained using analytic torsion and
a Bott-Chern secondary class. In this talk, we will talk about the construction
and some explicit formulae of this analytic torsion invariant.
Some part of this talk is based on the joint work with H. Fang and Z. Lu.
2007/12/13
10:40 - 12:10Room #128 (Mathematics building)
Mikael Pichot (東大数理)
"Topics in ergodic theory, von Neumann algebras, and rigidity"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
16:00 - 17:30Room #126 (Mathematics building)
Danielle Hilhorst (CNRS / パリ第11大学)
"Singular limit of a competition-diffusion system"
We revisit a competition-diffusion system for the densities of biological populations, and (i) prove the strong convergence in L^2 of the densities of the biological species (joint work with Iida, Mimura and Ninomiya); (ii) derive the singular limit of some reaction terms as the reaction coefficient tends to infinity (joint work with Martin and Mimura).
2007/12/12
15:20 - 16:30Room #122 (Mathematics building)
Stefano IACUS (Department of Economics, Business and Statistics, University of Milan)
"Inference problems for the telegraph process observed at discrete times"
The telegraph process {X(t), t>0}, has been introduced (see
Goldstein, 1951) as an alternative model to the Brownian motion B(t).
This process describes a motion of a particle on the real line which
alternates its velocity, at Poissonian times, from +v to -v. The
density of the distribution of the position of the particle at time t
solves the hyperbolic differential equation called telegraph equation
and hence the name of the process.
Contrary to B(t) the process X(t) has finite variation and
continuous and differentiable paths. At the same time it is
mathematically challenging to handle. Several variation of this
process have been recently introduced in the context of Finance.
In this talk we will discuss pseudo-likelihood and moment type
estimators of the intensity of the Poisson process, from discrete
time observations of standard telegraph process X(t). We also
discuss the problem of change point estimation for the intensity of
the underlying Poisson process and show the performance of this
estimator on real data.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/12.html
2007/12/11
16:30 - 18:40Room #056 (Mathematics building)
Xavier G\'omez-Mont (CIMAT, Mexico) 16:30 - 17:30
"A Singular Version of The Poincar\'e-Hopf Theorem"
The Poincar\'e-Hopf Theorem asserts that the Euler Characteristic of a compact manifold is the sum of the indices of any vector field on it with isolated singularities.
A hypersurface in real or complex number space may be considered as the limit of the smooth hypersurfaces obtained from nearby regular values. The singularity contains “hidden” topology, which is unfolded by a smooth regeneration. At the singularity one has an algebraic invariant, the Jacobi Algebra, which is obtained by considering analytic functions modulo the partial derivatives. It contains topological information of the singularity.
One may consider vector fields tangent to a hypersurface with isolated singularities, and define topologically an index, which coincides with the sum of the Poincar\'e-Hopf indices of a regeneration of it tangent to a nearby smooth hypersurface.
I will explain how to compute the index of a vector field X tangent to an isolated hypersurface singularity V using Homological Algebra, as the Euler Characteristic of the homology of the complex obtained by contracting differential forms on V with the vector field X. The formula contains several terms, but the higher order terms may be translated from the invariants of the singular point to invariants in the Jacobi Algebra, making this translation a local version of the Poincar\'e-Hopf Theorem.
I will also explain how some of these ideas can be extended to complete intersections.
Miguel A. Xicotencatl (CINVESTAV, Mexico) 17:40 - 18:40
"Chen Ruan cohomology of cotangent orbifolds and Chas-Sullivan string topology"
(Joint with: A. Gonzalez, E. Lupercio, C. Segovia, and B. Uribe)
At the end of 90's, two theories of topology were invented roughly at the same time and attracted considerable interest in the mathematical community. One is the Chas-Sullivan's loop product on the homology of loop space and the second one is Chen-Ruan's stringy cohomology of orbifold. It was an observation of Chen that inertia orbifold (which carries Chen-Ruan cohomology) is the space of constant loops of an orbifold. Therefore, two theories should interact. In this work we show that for an interesting family of orbifolds, the virtual orbifold cohomology, turns out to be a subalgebra of the homology of the loop orbifold, and is isomorphic, as algebras, to the Chen-Ruan orbifold cohomology of its cotangent orbifold.
10:00 - 12:00Room #128 (Mathematics building)
Dmitry KALEDIN (Steklov研究所, 東大数理)
"Homological methods in non-commutative geometry, part 7"
16:30 - 18:00Room #126 (Mathematics building)
井上順子 (鳥取大学)
"Characterization of some smooth vectors for irreducible representations of exponential solvable Lie groups"
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/12/10
10:30 - 12:00Room #128 (Mathematics building)
杉山健一 (千葉大学)
"岩澤予想の幾何学的類似の量子化(予想される結果)"
17:00 - 18:30Room #002 (Mathematics building)
Dmitry Kaledin (Steklov Institute and The University of Tokyo)
"Deligne conjecture and the Drinfeld double."
Deligne conjecture describes the structure which exists on
the Hochschild cohomology $HH(A)$ of an associative algebra
$A$. Several proofs exists, but they all combinatorial to a certain
extent. I will present another proof which is more categorical in
nature (in particular, the input data are not the algebra $A$, but
rather, the tensor category of $A$-bimodules). Combinatorics is
still there, but now it looks more natural -- in particular, the
action of the Gerstenhaber operad, which is know to consist of
homology of pure braid groups, is induced by the action of the braid
groups themselves on the so-called "Drinfeld double" of the category
$A$-bimod.
If time permits, I will also discuss what additional structures
appear in the Calabi-Yau case, and what one needs to impose to
insure Hodge-to-de Rham degeneration.
2007/12/06
10:40 - 12:10Room #128 (Mathematics building)
Mikael Pichot (東大数理)
"Topics in ergodic theory, von Neumann algebras, and rigidity"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
16:00 - 17:30Room #126 (Mathematics building)
柳田 英二 (東北大学大学院理学研究科)
"藤田型方程式における時間大域解の挙動について"
この講演では,藤田型の半線形放物型偏微分方程式に関する M. Fila, J. King, P. Polacik, M. Winkler らとの共同研究による成果についてその概要を紹介する.全空間上の藤田型方程式については,これまで様々な挙動を示す時間大域解の存在が示されている.そこで大域解の時間的挙動と初期値の空間的挙動の関係を詳細に調べることにより,大域解をいくつかに分類し,その挙動がそれぞれ異なるメカニズムに支配されていることを明らかにする.時間が許せば,最近の進展や関連する話題についても触れる予定である.
2007/12/05
16:30 - 17:30Room #117 (Mathematics building)
中村健太郎 (東京大学大学院数理科学研究科)
"Classification of two dimensional trianguline representations of p-adic fields"
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\varphi, \Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\varphi,\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
16:20 - 17:30Room #122 (Mathematics building)
今野 良彦 (日本女子大学理学部)
"A Decision-Theoretic Approach to Estimation from Wishart matrices on Symmetric Cones"
James and Stein(1961) have considered the problem of estimating the mean matrix of Wishart distributions under so-called Stein's loss function and obtained a minimax estimator with a constant risk. Later Stein(1977) has given an unbiased risk estimate for a class of orthogonally invariant estimators, from which he obtained orthogonally invariant minimax estimators which are uniformly better than the best triangular-invariant estimator in James and Stein(1961). The works mentioned above lead to the following natural question: Is it possible for any estimators to improve upon the maximum likelihood estimator for the mean matrix of the complex or quaternion Wishart distributions? This talk shows that we can obtain improved estimators for the mean matrix under these models in a unified manner. The method involves an abstract theory of finite-dimensional Euclidean simple Jordan algebra
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/11.html
2007/12/04
15:00 - 17:15Room #122 (Mathematics building)
Pavel Krejci (Weierstrass Institute for Applied Analysis and Stochastics) 15:00 - 16:00
"Quasilinear hyperbolic equations with hysteresis"
We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov (Wichita State University) 16:15 - 17:15
"Carleman estimates for second order operators with two large parameters"
We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
16:30 - 18:00Room #056 (Mathematics building)
今野 宏 (東京大学大学院数理科学研究科)
"Morse theory for abelian hyperkahler quotients
"
In 1980's Kirwan computed Betti numbers of symplectic quotients by using Morse theory. In this talk, we develop this method to hyperkahler quotients by abelian Lie groups. In this method, many computations are much more simplified in the case of hyperkahler quotients than the case of symplectic quotients. As a result we compute not only the Betti numbers, but also the cohomology rings of abelian hyperkahler quotients.
2007/12/03
10:30 - 12:00Room #128 (Mathematics building)
甲斐千舟 (九州大学)
"等質有界領域の対称性条件、性質の良い有界領域実現について"
2007/11/29
10:40 - 12:10Room #128 (Mathematics building)
Mikael Pichot (東大数理)
"Topics in ergodic theory, von Neumann algebras, and rigidity"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007/11/27
16:30 - 18:00Room #122 (Mathematics building)
Alexander Kuznetsov (Steklov Inst)
"Categorical resolutions of singularities"
I will give a definition of a categorical resolution of singularities and explain how such resolutions can be constructed.
16:30 - 18:00Room #128 (Mathematics building)
小松 彦三郎 (東大数理(名誉教授))
"Heaviside's theory of signal transmission on submarine cables"
16:30 - 18:00Room #056 (Mathematics building)
石井 敦 (京都大学数理解析研究所)
"A quandle cocycle invariant for handlebody-links
"
[joint work with Masahide Iwakiri (Osaka City University)]
A handlebody-link is a disjoint union of circles and a
finite trivalent graph embedded in a closed 3-manifold.
We consider it up to isotopies and IH-moves.
Then it represents an ambient isotopy class of
handlebodies embedded in the closed 3-manifold.
In this talk, I explain how a quandle cocycle invariant
is defined for handlebody-links.
2007/11/26
17:00 - 18:30Room #002 (Mathematics building)
Mich\"ael Pevzner (Universit\'e de Reims and the University of Tokyo)
"Kontsevich quantization of Poisson manifolds and Duflo isomorphism."
Abstract: Since the fundamental results by Chevalley, Harish-Chandra and Dixmier one knows that the set of invariant polynomials on the dual of a Lie algebra of a particular type (solvable, simple or nilpotent) is isomorphic, as an algebra, to the center of the enveloping algebra. This fact was generalized to an arbitrary finite-dimensional real Lie algebra by M. Duflo in late 1970's. His proof was based on the Kirillov's orbits method that parametrizes infinitesimal characters of unitary irreducible representations of the corresponding Lie group in terms of co-adjoint orbits.
The Kontsevich' Formality theorem implies not only the existence of the Duflo map but shows that it is canonical. We shall describe this construction and indicate how does this construction extend to the whole Poisson cohomology of an arbitrary finite-dimensional real Lie algebra.
10:30 - 12:00Room #128 (Mathematics building)
金子宏 (東京理科大学)
"Analysis related to probability theory based on p-adic hierarchical structure"
2007/11/22
16:00 - 17:30Room #126 (Mathematics building)
佐藤 洋平 (早稲田大学・基幹理工学部・数学科)
"Critical frequencyをもつ非線形シュレディンガー方程式のマルチピーク解"
非線形シュレディンガー方程式
$$ -\epsilon2 \Delta u +V(x)u= u^p, u>0 \ \hbox{in} \R^N,
u\in H1(\R^N)$$
において、$\epsilon \to 0$ としたときに V(x) の k個の極小点にピークが集中していくマルチピーク解 $u_\epsilon$ について考える。
ここで、p はsuperlinear, subcriticalの条件を満たし, ポテンシャル関数 V(x) は非負の有界な関数で $\liminf_{|x|\to \infty}V(x)>0$ を満たすとする。
もし V(x) の各極小点に集中するピークがあるとしたら、そのピークの形状や大きさはその極小値が正であるか、0であるかによって大きく異なることが知られている。
この講演では V(x) の各極小値が正であるか 0 であるかにかかわらず、各 k個の極小点にピークが集中するマルチピーク解 $u_\epsilon$ を構成する。
16:30 - 18:00Room #056 (Mathematics building)
張欽 (東大数理)
"Spatial property of the canonical map associated to von Neumann algebras"
10:40 - 12:10Room #128 (Mathematics building)
Mikael Pichot (東大数理)
"Topics in ergodic theory, von Neumann algebras, and rigidity"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/pichot.htm
2007/11/21
16:30 - 17:30Room #117 (Mathematics building)
Christopher Rasmussen (京都大学数理解析研究所)
"Abelian varieties with constrained torsion"
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\Q$.
16:20 - 17:30Room #122 (Mathematics building)
宮尾 祐介 (東京大学理学部情報科学科)
"自然言語処理における構造的・統計的モデル"
本発表では,自然言語処理において代表的な問題である機械翻訳と構文解析に ついて,言語の構造的性質と統計的性質をどのようなモデルで表現するかにつ いて概説する.これらの問題に対しては,古くは構造的規則性に着目し,翻訳 規則や文法などの規則体系を明らかにすることが主な研究目標であった.しか し,統計モデルの自然言語処理への応用が90年代に提案され,大きな成功をお さめたことから,現在では主流となっている.最近では,統計モデルを構造化 することによって言語の複雑な構造をとらえるアプローチがさかんに研究され ており,本発表では,これらの構造的・統計的モデルが言語の構造をどのよう にモデル化しているかを述べる.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/10.html
2007/11/20
16:30 - 18:00Room #056 (Mathematics building)
長郷 文和 (東京工業大学大学院理工学研究科)
"A certain slice of the character variety of a knot group
and the knot contact homology
"
For a knot $K$ in 3-sphere, we can consider representations of
the knot group $G_K$ into $SL(2,\mathbb{C})$.
Their characters construct an algebraic set.
This is so-called the $SL(2,\mathbb{C})$-character variety of
$G_K$ and denoted by $X(G_K)$.
In this talk, we introduce a slice (a subset) $S_0(K)$ of $X(G_K)$.
In fact, this slice is closely related to the A-polynomial
and the abelian knot contact homology.
For example, the A-polynomial $A_K(m,l)$ of a knot $K$ is
a two-variable polynomial knot invariant defined by using
the character variety $X(G_K)$.
Then we can show that for any {\it small knot} $K$, the number of
irreducible components of $S_0(K)$ gives an upper bound of
the maximal degree of the A-polynomial $A_K(m,l)$ in terms of
the variable $l$.
Moreover, for any 2-bridge knot $K$, we can show that
the coordinate ring of $S_0(K)$ is exactly the degree 0
abelian knot contact homology $HC_0^{ab}(K)$.
We will mainly explain these facts.
16:30 - 18:00Room #126 (Mathematics building)
西山 享 (京都大学)
"Asymptotic cone for semisimple elements and the associated variety of degenerate principal series "
Let $ a $ be a hyperbolic element in a semisimple Lie algebra over the real number field. Let $ K $ be the complexification of a maximal compact subgroup of the corresponding real adjoint group. We study the asymptotic cone of the semisimple orbit through $ a $ under the adjoint action by $ K $. The resulting asymptotic cone is the associated variety of a degenerate principal series representation induced from the parabolic associated to $ a $.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/11/19
10:30 - 12:00Room #128 (Mathematics building)
藤野修 (名古屋大学)
"乗数イデアル層の類似物"
2007/11/17
13:30 - 16:00Room #123 (Mathematics building)
小島教知 (東京工業大学理学研究科) 13:30 - 14:30
"Pullback formula for vector valued Siegel modular forms and its applications
"
$H_n$ を $n$ 次 Siegel 上半空間, $E^n_k$ を次数 $n$, 重さ $k$ のSiegel Eisenstein 級数とする. いま $p$, $q$ を自然数としたとき,$H_p\times H_q$ は $H_{p+q}$ の中に埋め込むことができる. Garrett は $E^{p+q}_k$ を $H_p\times H_q$ 上に制限したときに Klingen Eisenstein 級数や Siegel 保型形式の standard $L$ 函数の値などで表示する公式を与へた. この公式は pullback formula とよばれてゐる.
この pullback formula はBoecherer によつて複素パラメータつきの Eisenstein 級数の場合に拡張され, Klingen Eisenstein 級数や standard $L$ 函数についての結果が得られてゐる.
本講演ではこれらの結果がベクトル値 Siegel 保型形式の場合にどれくらゐ拡張できるかについて述べる.
大西良博 (岩手大学) 15:00 - 16:00
"Congruences connecting Tate-Shafarevich groups with Hurwitz numbers"
奇素数 $p$ について, 虚2次体 $\mathbf{Q} (\sqrt{-p})$ の類数を $h(-p)$ と書くことにします. このとき $p≡1, 3 mod 4$ に応じて
$h(-p)≡2^{-1}E_{(p-1)/2} mod p$
$h(-p)≡ -2B_{(p+1)/2} mod p$
となり, 右辺の最小の剰余は左辺そのものを与へます. 但し $B_n$ は Bernoulli 数, $E_n$ は Euler 数. この合同式の一般化として, ある種の楕円曲線の Tate-Shafarevich 群の位数の平方根と Hurwitz 数との間の同様な合同式を与へます.
13:00 - 16:30Room #126 (Mathematics building)
Gleb Novichkov (Keio Univ.) 13:00 - 14:30
"Dynamical r-matrices coupled with dual Poisson Lie group"
The notion dynamical r-matrix coupled with Poisson manifold
is a natural generalization of the notion of the classical
dynamical r-matrix. We will consider special case when
Poisson manifold is a dual Poisson Lie group. We discuss
necessary conditions for the existence dynamical r-matrices
coupled with dual Poisson Lie groups and provide
some examples. We will also discuss some open questions
and possible relations to other subjects.
Vladimir V. Bazhanov (Australian National Univ.) 15:00 - 16:30
"Yang-Baxter Equation and Quantum Geometry"
We demonstrate that certain integrable models
of statistical mechanics and quantum field theory
can be interpreted as quantization's of objects
of classical discrete geometry.
The fluctuating variables in these models take continuous
values. The classical geometry corresponds to stationary
configurations in the quasi-classical (or zero-temperature)
limit of the quantum system.
Our main example is the Faddeev-Volkov model which describes
the quantization of the circle patterns and associated with
the Thurston's discrete analogue of the Riemann mapping theorem
(discrete conformal transformations of the 2D plane).
Other examples will be also considered.
Finally we will discuss the geometric origins of integrability
which stem from from the classical results of Lam\'e,
Darboux and Bianchi in differential geometry.
2007/11/15
16:30 - 18:00Room #056 (Mathematics building)
水田有一 (東大数理)
"Generators of II$_1$ factors (Dykema-Sinclair-Smith-White)の紹介"
2007/11/14
16:20 - 17:30Room #122 (Mathematics building)
塚原 英敦 (成城大学経済学部)
"Estimation of Distortion Risk Measures"
By Kusuoka's representation theorem, the class of distortion risk measures with convex distortions coincides with the set of coherent risk measures that are law invariant and comonotonically additive. The class includes the renowned expected shortfall which has many nice features and is of frequent use in practice. To implement the risk management/regulatory procedure using risk measures, it is necessary to estimate the values of such risk measures. For a distortion risk measure, its form suggests a natural estimator which is a simple form of $L$-statistics. We have seen in our previous work that it has nice asymptotic properties with i.i.d.\ data. After reviewing these results briefly, we investigate the large sample properties of the estimator based on dependent data, especially GARCH sequences, which are often used for modelling financial time series data. Related issues such as semiparametric estimation with the extreme value theory and backtesting are briefly addressed.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/09.html
2007/11/13
16:00 - 17:30Room #052 (Mathematics building)
Jens Starke (Technical University of Denmark)
"Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb"
The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.
(1) Nonlinear dynamics in receptor neurons:
A mathematical model for Ca oscillations in the cilia of olfactory
sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.
(2) Sorting by self-organization:
A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.
(3) Spatio-temporal pattern formation in the olfactory bulb:
Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.
This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.
2007/11/12
10:30 - 12:00Room #128 (Mathematics building)
野口 潤次郎 (東京大学)
"蕭の有理型接続と関連する話題 (Siu's meromorphic connection and related topics)"
2007/11/09
16:40 - 17:40Room #123 (Mathematics building)
吉川謙一 (東京大学数理科学)
"解析的捩率と保型形式"
70年代にRayとSingerは位相幾何学におけるReidemeister捩率の解析的類似を考察し,解析的捩率と呼ばれるスペクトル不変量を導入した. de Rham複体とDolbeault複体に対応して, 解析的捩率には実解析的捩率と正則解析的捩率の二種類の理論があり,80年代から現在に至るBismutの研究により両理論は長足の発展を遂げた.
一般論が整備された後で講演者が興味を持ったのは,解析的捩率を具体的に計算するという問題であった.既にRayとSingerは正則解析的捩率を導入した論文の中で楕円曲線の正則解析的捩率を計算し,それが楕円曲線の判別式のノルムで与えられることを示していた. この講演では「楕円曲線の解析的捩率はモジュライ空間上の保型形式で与えられる」というRay-Singerの主張がどのように高次元化されるのかを対合付きK3曲面とEnriques曲面の場合を中心に概観したい. 時間が許せば, その他の場合(三次元Calabi-Yau多様体やAbel多様体等)についても言及したい.
2007/11/08
16:30 - 18:00Room #118 (Mathematics building)
Alexandru DIMCA (Univ Nice )
"New restrictions on the fundamental groups of complex algebraic varieties"
My talk will be based on joint work with S. Papadima (Bucarest, Romania) and A. Suciu (Boston, USA). First I will recall the basic facts on characteristic varieties $V_k(M)$ associated to rank one local systems on a complex algebraic variety $M$ which are due to Beauville, Simpson and Arapura. Then I will introduce the resonance varities $R_k(M)$, which may be related to the Isotropic Subspace Theorems by Catanese and Bauer. One of the main new results is that for a class of algebraic varieties (the 1-formal ones), the two types of varieties $V_k(M)$ and $R_k(M)$ are strongly related. Applications to right angle Artin groups, Bestvina-Brady groups and to a conjecture by Kollar will be discussed in the end.
16:00 - 17:30Room #126 (Mathematics building)
倉田 和浩 (首都大学東京・理工学研究科・数理情報科学専攻)
"弱い飽和効果をもったGierer-Meinhardt systemにおける軸対称領域上での多重ピーク解の構成と漸近挙動について"
This talk is based on the joint work with Kotaro Morimoto (Tokyo Metropolitan University).
We are concerned with stationary solutions to the following reaction diffusion system which is called the Gierer-Meinhardt system with saturation.
$A_t=\epsilon^2 \Delta A-A+A^2/(H(1+kA^2), A>0,$
$\tau H_t=D\Delta H-H+A2, H>0,$
where $\epsilon >0$, $\tau \geq 0$, $k>0$.
The unknowns $A$ and $H$ represent the concentrations of the activator and the inhibitor. Here $\Omega$ is a bounded smooth domain in $R^N$ and we consider homogeneous Neumann boundary conditions. When $\Omega$ is an $x_N$-axially symmetric domain and $2\leq N\leq 5$, for sufficiently small $\epsilon>0$ and large $D>0$, we construct a multi-peak stationary solution peaked at arbitrarily chosen intersections of $x^N$-axis and $\partial \Omega$, under the condition that $k\epsilon^{-2N}$ converges to some $k_0\in[0,\infty)$ as $\epsilon \to 0$.
In my talk, I will explain related results comparing the differences between the case $k=0$ and $k>0$, the basic strategy of the proof of our results with some details, and open questions.
2007/11/07
16:20 - 17:30Room #122 (Mathematics building)
鎌谷 研吾 (東京大学大学院数理科学研究科)
"ハプロタイプ関連解析:EMアルゴリズムによるアプローチ"
最尤推定量の計算法である, EMアルゴリズムについて考察する. EMアルゴリズムのグローバルな観点の収束を示すことは容易でない事が多い. 一方で局所的な収束は容易に示すことができて, 一次漸近有効な推定量を 構成できる. その構成法とハプロタイプ関連解析への応用を考える. 時間があれば, ベイズ推定量の近似である, MCMCによる統計量の漸近有効性にも触れる.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/08.html
2007/11/06
16:30 - 18:00Room #056 (Mathematics building)
児玉 大樹 (東京大学大学院数理科学研究科)
"Thustion's inequality and open book foliations"
We will study codimension 1 foliations on 3-manifolds.
Thurston's inequality, which implies convexity of the foliation in
some sense, folds for Reebless foliations [Th]. We will discuss
whether the inequality holds or not for open book foliations.
[Th] W. Thurston: Norm on the homology of 3-manifolds, Memoirs of the
AMS, 339 (1986), 99--130.
15:00 - 16:30Room #126 (Mathematics building)
Michaël Pevzner (Université de Reims and University of Tokyo)
"Quantization of symmetric spaces and representation. IV"
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
16:30 - 18:00Room #126 (Mathematics building)
森脇政泰 (広島大学)
"Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group"
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/11/01
16:30 - 18:00Room #052 (Mathematics building)
Michaël Pevzner (Université de Reims and University of Tokyo)
"Quantization of symmetric spaces and representation. III"
Kontsevich's formality theorem and applications in Representation theory.
We shall first give an explicit construction of an associative star-product on an arbitrary smooth finite-dimensional Poisson manifold.
As application, we will consider in details the crucial example of the dual of a finite-dimensional Lie algebra and will sketch a generalization of the Duflo isomorphism describing the set of infinitesimal characters of irreducible unitary representations of the corresponding Lie group.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/10/31
16:20 - 17:30Room #122 (Mathematics building)
深澤 正彰 (東京大学大学院数理科学研究科)
"最尤推定量の漸近展開とその応用:とくに拡散過程の場合について"
最尤推定量とそのスチューデント化統計量の漸近展開公式について、 スキューネス修正の観点から考察し、AR過程や、あるクラスの拡散過程モデルへの応用について述べる。 一般の対称拡散過程モデルにおける最尤推定量のバイアス推定量、 スキューネス推定量も提案する。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/07.html
16:30 - 17:30Room #117 (Mathematics building)
Pierre Colmez (Ecole Polytechnique)
"On the p-adic local Langlands correspondance for GL2(Qp)"
2007/10/30
16:30 - 18:00Room #126 (Mathematics building)
松本久義 (東京大学大学院数理科学研究科)
"On Weyl groups for parabolic subalgebras"
Let ${\mathfrak g}$ be a complex semisimple Lie algebra.
We call a parabolic subalgebra ${\mathfrak p}$ of ${\mathfrak g}$
normal, if any parabolic subalgebra which has a common Levi part with ${\mathfrak p}$
is conjugate to ${\mathfrak p}$ under an inner automorphism of ${\mathfrak g}$.
For a normal parabolic subalgebra, we have a good notion of the restricted root system
or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for
${\mathfrak g}$ and the little Weyl group.
We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
15:00 - 16:30Room #126 (Mathematics building)
Michaël Pevzner (Université de Reims and University of Tokyo)
"Quantization of symmetric spaces and representation. II"
Back to Mathematics. Two methods of quantization.
We will start with a discussion on
-Weyl symbolic calculus on a symplectic vector space
and its asymptotic behavior.
In the second part, as a consequence of previous considerations, we will define the notion of deformation quantization.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
10:00 - 12:00Room #128 (Mathematics building)
Dmitry KALEDIN (Steklov研究所, 東大数理)
"Homological methods in Non-commutative Geometry "
17:00 - 18:00Room #056 (Mathematics building)
太田 啓史 (名大多元数理)
"$L_{\infty}$ action on Lagrangian filtered $A_{\infty}$ algebras."
I will discuss $L_{\infty}$ actions on Lagrangian filtered
$A_{\infty}$ algebras by cycles of the ambient symplectic
manifold. In the course of the construction,
I like to remark that the stable map compactification is not
sufficient in some case when we consider ones from genus zero
bordered Riemann surface. Also, if I have time, I like to discuss
some relation to (absolute) Gromov-Witten invariant and other
applications.
(This talk is based on my joint work with K.Fukaya, Y-G Oh and K. Ono.)
2007/10/29
17:00 - 18:30Room #002 (Mathematics building)
Hiroshige Kajiura (RIMS, Kyoto University)
"Some examples of triangulated and/or $A_\infty$-categories
related to homological mirror symmetry
"
In this talk, I would like to discuss on some examples of
triangulated and/or $A_\infty$-categories associated to
manifolds with additional structures
(symplectic structure, complex structure, ...)
which can appear in the homological mirror symmetry (HMS) set-up
proposed by Kontsevich'94.
The strongest form of the HMS may be to show the equivalence
of Fukaya category on a symplectic manifold with the category
of coherent sheaves on the mirror dual complex manifold
at the level of $A_\infty$-categories.
On the other hand, for a given $A_\infty$-category,
there is a canonical way (due to Bondal-Kapranov, Kontsevich)
to construct an enlarged $A_\infty$-category
whose restriction to the zero-th cohomology forms a triangulated category.
I plan to talk about the triangulated structure of categories
associated to regular systems of weights
(joint work with Kyoji Saito and Atsushi Takahashi),
and also give a realization of higher $A_\infty$-products in
Fukaya categories from the mirror dual complex manifold
via HMS in some easy examples.
2007/10/25
16:30 - 18:00Room #410 (Mathematics building)
見村万佐人 (東大数理)
"An introduction to expander graphs"
16:30 - 18:00Room #002 (Mathematics building)
Michael Pevzner (Universite de Reims and University of Tokyo)
"Quantization of symmetric spaces and representations. I"
The first and introductory lecture of a series of four will be devoted to the discussion of fundamental principles of the Quantum mechanics and their mathematical formulation. This part is not essential for the rest of the course but it might give a global vision of the subject to be considered.
We shall introduce the Weyl symbolic calculus, that relates classical and quantum observables, and will explain its relationship with the so-called deformation quantization of symplectic manifolds.
Afterwards, we will pay attention to a more algebraic question of formal deformation of an arbitrary smooth Poisson manifold and will define the Kontsevich star-product.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/10/24
16:30 - 17:30Room #117 (Mathematics building)
阿部知行 (東京大学大学院数理科学研究科)
"l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて"
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。
2007/10/23
16:30 - 18:00Room #002 (Mathematics building)
Jun O'Hara (首都大学東京)
"Spaces of subspheres and their applications "
The set of q-dimensional subspheres in S^n is a Grassmann manifold which has natural pseudo-Riemannian structure, and in some cases, symplectic structure as well. Both of them are conformally invariant.
I will explain some examples of their applications to geometric aspects of knots and links.
17:00 - 18:00Room #128 (Mathematics building)
Fr\'{e}d\'{e}ric Klopp (パリ北大学)
"Localization for random quantum graphs (joint with K. Pankrashkin)"
2007/10/22
10:30 - 12:00Room #128 (Mathematics building)
志賀弘典 (千葉大学)
"ガウス算術幾何平均定理の多変数化とその保型形式的解釈(小池健二氏との共同研究)"
2007/10/18
16:30 - 18:00Room #056 (Mathematics building)
Mikael Pichot (学振・東大数理)
"On the classification of Bruhat-Tits buildings"
2007/10/17
16:00 - 17:00Room #470 (Mathematics building)
J. Fritz (TU Budapest)
"The method of compensated compactness for
microscopic systems"
2007/10/16
17:00 - 18:00Room #056 (Mathematics building)
二木 昭人 (東京工業大学大学院理工学研究科)
"Toric Sasaki-Einstein manifolds"
A compact toric Sasaki manifold admits a Sasaki-Einstein metric if and only if it is obtained by the Delzant construction from a toric diagram of a constant height. As an application we see that the canonical line bundle of a toric Fano manifold admits a complete Ricci-flat K\"ahler metric.
10:00 - 12:00Room #128 (Mathematics building)
Dmitry KALEDIN (Steklov研究所, 東大数理)
"Homogical methods in Non-commutative Geometry"
Of all the approaches to non-commutative geometry, probably the most promising is the homological one, developed by Keller, Kontsevich, Toen and others, where non-commutative eometry is understood as "geometry of triangulated categories". Examples of "geometric" triangulated categories come from representation theory, symplectic geometry (Fukaya category) and algebraic geometry (the derived category of coherent sheaves on an algebraic variety and
various generalizations). Non-commutative point of view is expected to be helpful even in traditional questions of algebraic geometry such as the termination of flips.
We plan to give an introduction to the subject, with emphasis on homological methods (such as e.g. Hodge theory which, as it turns out, can be mostly formulated in the non-commutative setting).
No knowledge of non-commutative geometry whatsoever is assumed. However, familiarity with basic homological algebra and algebraic geometry will be helpful.
2007/10/15
17:00 - 18:30Room #002 (Mathematics building)
Shinobu Hosono (The University of Tokyo)
"Topics on string theory, mirror symmetry, and Gromov-Witten invariants"
Recently, some technical developments in solving BCOV
(Bershadsky-Cecotti-Ooguri-Vafa) holomorphic anomaly equation has been
made and it has become possible to predict higher genus Gromov-Witten
invariants for some class of Calabi-Yau 3 folds.
With a brief introduction to BCOV equation, I will present some
predictions for Gromov-Witten invariants of certain Calabi-Yau 3 folds,
which are not birational but derived equivalent. (This is based on
a work with Y. Konishi which appeared in mathAG/0704.2928.)
Before coming to this specific topic, I will review some recent
topics of the homological mirror symmetry focusing on
its connection to the `classical' mirror symmetry, where the
variation theory of Hodge structures (VHS) plays a central role.
The BCOV equation and its open string generalization have their grounds
on the VHS.
10:30 - 12:00Room #128 (Mathematics building)
大沢健夫 (名古屋大学)
"On the curvature of holomorphic foliations"
2007/10/13
13:30 - 16:00Room #123 (Mathematics building)
若槻聡 (金沢大学理学部) 13:30 - 14:30
"2次のジーゲルカスプ形式の空間上のヘッケ作用素の明示的跡公式について
2次のジーゲルカスプ形式の空間上のヘッケ作用素の明示的跡公式について"
2次のジーゲルカスプ形式の空間上のヘッケ作用素の跡に、ある明示的公式を与
える。まだ公式から跡の具体的な数値を得ることはできないが、この公式は数値を得る
ための一つのステップとなっている。一変数の場合や一般論と比較しながら、得られた公式と今後の目標について解説する。
平野幹 (成蹊大学理工学部) 15:00 - 16:00
"A propagation formula for principal series Whittaker functions on $GL(3,C)$"
$GL(n,\mathbf{R})$上のクラス1Whittaker関数を$GL(n-1,\mathbf{R})$上の同関数で表す公式が石井-Stadeにより得られてる(J. Funct. Anal. 244 (2007))。また、$GL(n,\mathbf{R})$および$GL(n,\mathbf{C})$上のクラス1Whittaker関数のelementaryな関係(Stade (1995)) により、この公式は$GL(n,\mathbf{C})$上のクラス1Whittaker関数に対しても成立する。ここでは$GL(3,\mathbf{C})$上のクラス1でない主系列Whittaker関数の明示公式(織田孝幸氏との共同研究)に基づき、これを$GL(2,\mathbf{C})$上のクラス1でない主系列Whittaker関数で表す類似の公式を紹介する。
2007/10/11
16:30 - 18:00Room #056 (Mathematics building)
Gandalf Lechner (Erwin Schroedinger Institute)
"Construction of local nets from a wedge algebra"
2007/10/10
16:30 - 17:30Room #117 (Mathematics building)
James Lewis (University of Alberta)
"Abel-Jacobi Maps Associated to Algebraic Cycles, I.
"
This talk concerns the Bloch cycle class map from the higher Chow groups to Deligne cohomology of a projective algebraic manifold. We provide an explicit formula for this map in terms of polylogarithmic type currents.
16:30 - 17:30Room #117 (Mathematics building)
James Lewis (University of Alberta)
"Abel-Jacobi Maps Associated to Algebraic Cycles I
"
This talk concerns the Bloch cycle class map from the higher Chow groups to Deligne cohomology of a projective algebraic manifold. We provide an explicit formula for this map in terms of polylogarithmic type currents.
14:40 - 18:00Room #056 (Mathematics building)
山川 大亮 (京都大学大学院 理学研究科) 14:40 - 16:10
"A multiplicative analogue of quiver variety"
本講演では,箙(quiver)に付随して現れる新しい複素シンプレクティック多様体を紹介する.これは中島によって導入された箙多様体と非常に良く似た構成をする事で得られるが,違いは運動量写像ではなく群値運動量写像と呼ばれるものを使って商を取るところにある.この多様体は箙多様体と良く似た幾何学的性質を有し,一方,星型箙の場合に点付きRiemann球面上の放物接続のモジュライ空間とRiemann-Hilbert対応によって関係している.また箙多様体との直接的な関係も存在している.これらについて説明したい.
加藤 晃史 (東京大学大学院数理科学研究科) 16:30 - 18:00
"AdS/CFT 対応における変分問題について"
弦双対性の一つである AdS/CFT 対応は,重力場(時空の幾何学)とゲージ理論(共形場理論)との間に対応があるという予想である.講演ではこの予想について概観するとともに,その一例として,佐々木・アインシュタイン多様体の体積に関する変分問題と quiver ゲージ理論の a-maximization の関係を説明したい.
16:20 - 17:30Room #122 (Mathematics building)
清 智也 (東大情報理工)
"勾配モデルの摂動解析と許容領域の評価"
多変量標準正規分布を凸関数の勾配写像によって 引き戻すと, 一つの確率分布が得られる. さらにパラメトリックな勾配写像を考えれば, 統計モデルが得られる. この統計モデルを勾配モデルと呼ぶことにする. 本講演は二つの内容からなる. 第一に, 恒等写像に摂動を加えた勾配写像を考え, 対応する密度関数, キュムラント母関数, ダイバージェンスなどの摂動展開を求める. 第二に, より具体的な勾配モデルに対して, パラメータが定義域に属すための十分条件を示す. このような考察の必要性は, 定義域が無限個の 制約式で与えられることによる.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/06.html
15:00 - 16:00Room #122 (Mathematics building)
Dmitry Kaledin (Steklov Institute)
"p-adic Hodge theory in the non-commutative setting"
We will explain what is the natural replacement of the notion of Hodge structure in the p-adic setting, and how to construct such a structure for non-commutative manifolds (something which at present cannot be done for the usual Hodge structures, but works perfectly well for the p-adic analog).
2007/10/09
16:30 - 18:00Room #056 (Mathematics building)
浅岡 正幸 (京都大学大学院理学研究科)
"Classification of codimension-one locally free actions of the affine group of the real line."
By GA, we denote the group of affine and orientation-preserving transformations
of the real line. In this talk, I will report on classification of locally free action of
GA on closed three manifolds, which I obtained recently. In 1979, E.Ghys proved
that if such an action preserves a volume, then it is smoothly conjugate to a homogeneous action. However, it was unknown whether non-homogeneous action exists. As a consequence of the classification, we will see that the unit tangent bundle of a closed surface of higher genus admits a finite-parameter family of
non-homogeneous actions.
16:30 - 18:00Room #126 (Mathematics building)
Michael Pevzner (Reims University and University of Tokyo)
"Rankin-Cohen brackets and covariant quantization"
The particular geometric structure of causal symmetric spaces permits the definition of a covariant quantization of these homogeneous manifolds.
Composition formulae (#-products) of quantizad operators give rise to a new interpretation of Rankin-Cohen brackets and allow to connect them with the branching laws of tensor products of holomorphic discrete series representations.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/10/04
16:30 - 18:00Room #056 (Mathematics building)
Gandalf Lechner (Erwin Schroedinger Institute)
"Local nets of von Neumann algebras and modular theory"
2007/10/02
16:30 - 18:00Room #126 (Mathematics building)
Pablo Ramacher (Gottingen University)
"
Invariant integral operators on affine G-varieties and their kernels"
We consider certain invariant integral operators on a smooth affine variety M carrying the action of a reductive algebraic group G, and assume that G acts on M with an open orbit. Then M is isomorphic to a homogeneous vector bundle, and can locally be described via the theory of prehomogenous vector spaces. We then study the Schwartz kernels of the considered operators, and give a description of their singularities using the calculus of b-pseudodifferential operators developed by Melrose. In particular, the restrictions of the kernels to the diagonal can be described in terms of local zeta functions.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/09/28
16:30 - 17:30Room #123 (Mathematics building)
Marko Tadic' (University of Zagreb)
"Irreducible unitary representations and automorphic forms
"
Unitary representations of adelic groups in the spaces of automorphic forms are big source of important irreducible unitary representations of classical groups over local fields.
We shall present classifications of some classes of irreducible unitary representations (older, as well as quite new), describe
isolated unitary representations among them, and discuss which of them can be obtained from spaces of automorphic forms.
2007/09/26
16:30 - 18:00Room #126 (Mathematics building)
Grigory Mikhalkin (Toronto大学)
"Floor diagrams and enumeration of tropical curves"
The enumerative problems considered in this talk are finding the number of curves in projective spaces (over complex, real and tropical numbers) of given genus and degree constrained by certain incidence conditions (e.g. passing via points or lines). Floor diagrams are a combinatorial tool that reduces an enumerative problem in dimension n to the corresponding problem n dimension n-1. Floor diagrams give a constructive (and rather efficient) way to find all tropical curves for a given enumerative problem. And once we have a tropical solution of the problem we can use it to solve the corresponding problems over the complex and real numbers.
2007/09/19
16:30 - 17:30Room #117 (Mathematics building)
Gereon Quick (Universitaet Muenster)
"Etale cobordism"
We define and study a new candidate of etale topological cohomology theories for schemes over a field of abritrary characteristic: etale cobordism. As etale K-theory is related to algebraic K-theory, etale cobordism is related to algebraic cobordism of Voevodsky and Levine/Morel. It shares some nice properties of topological theories, e.g. it is equipped with an Atiyah-Hirzebruch spectral sequence from etale cohomology. We discuss in particular a comparison theorem between etale and algebraic cobordism after inverting a Bott element and, finally, we give an outlook to further possible applications of this theory.
2007/09/15
13:30 - 16:00Room #117 (Mathematics building)
長谷川泰子 (東京大学数理科学) 13:30 - 14:30
"Siegl principal series Whittaker functions on $Sp(2,\mathbf{R})$
(部屋は056室)"
2次シンプレクティック群のSiegel極大放物型部分群から誘導された一般型主系列表現に対するWhittaker関数の級数表示と積分表示を与えることを目的とし,Whittaker関数の満たす微分評定式を与え,その解の構成に向けて現在進めている研究の方針を述べる.
(部屋は,冷房効く056室に変更です)
市川尚志 (佐賀大学理工学部) 15:00 - 16:00
"A higher rank version of Abel-Jacobi's theorem (Room 056)"
極大退化曲線に近いリーマン面上のベクトル束とそのモジュライについて話す.次数0の安定ベクトル束が,リーマン面を一意化するショットキー群の線形表現から得られることを述べ,ショットキー群の線形表現の空間とベクトル束のモジュライ空間の関係を,アーベル・ヤコビの定理,フェアリンデ公式を用いて考察する.
(部屋は117号室です)
2007/09/12
15:00 - 18:00Room #117 (Mathematics building)
E. Lau (Univ. of Bielefeld) 15:00 - 15:45
"Classification of p-divisible groups by displays and duality"
T. Zink (Univ. of Bielefeld) 16:00 - 16:45
"Applications of the theory of displays"
E. Looijenga (Univ. of Utrecht) 17:00 - 18:00
"Presentation of mapping class groups from algebraic geometry"
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.
15:00 - 18:00Room #117 (Mathematics building)
E. Lau (Univ. of Bielefeld) 15:00 - 15:45
"Classification of p-divisible groups by displays and duality"
T. Zink (Univ. of Bielefeld) 16:00 - 16:45
"Applications of the theory of displays"
E. Looijenga (Univ. of Utrecht) 17:00 - 18:00
"Presentation of mapping class groups from algebraic geometry"
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.
2007/09/05
10:30 - 11:30Room #056 (Mathematics building)
Reinhard Farwig (Darmstadt University of Technology)
"Reguarity of Weak Solutions to the Navier-Stokes System beyond Serrin's Criterion "
Consider a weak instationary solution $u(x,t)$ of the Navier-Stokes equations in a domain $\Omega \subset \mathbb{R}^3$ in the sense of Leray-Hopf. As is well-known, $u$ is is unique and regular if $u\in L^s(0,T;L^q(\Omega))$ satisfies the {\it strong energy inequality} and $s,q$ satisfy Serrin's condition $\frac{2}{s} + \frac{3}{q}=1$, $s>2,\, q>3$. Now consider $u$ such that $$u\in L^r(0,T;L^q(\Omega))\quad \mbox{ where }\quad \frac{2}{r} + \frac{3}{q}>1$$ and has a sufficiently small norm in $L^r(0,T;L^q(\Omega))$. Then we will prove that $u$ is regular. Similar results of local rather than global type in space will be proved provided that $u$ satisfies the {\it localized energy inequality}. Finally H\"older continuity of the kinetic energy in time will imply regularity.
The proofs use local in time regularity results which are based on the {\it theory of very weak solutions} and on uniqueness arguments for weak solutions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2007/08/29
17:00 - 18:00Room #128 (Mathematics building)
Valery Alexeev (Georgia大学)
"Computations on the moduli spaces of weighted log pairs"
2007/08/27
16:30 - 17:30Room #002 (Mathematics building)
Steven Zucker (Johns Hopkins大学)
"The reductive Borel-Serre motive"
2007/08/02
16:30 - 18:00Room #126 (Mathematics building)
De-Qi Zhang (Singapore大学)
"Dynamics of automorphisms on algebraic varieties"
The building blocks of automorphisms / endomorphisms of compact varieties are determined --- an algebro geometric approach towards dynamics.
2007/07/25
16:20 - 17:30Room #122 (Mathematics building)
小林 景 (統計数理研究所, 学振特別研究員)
"大規模ランダム行列のスペクトル理論とデータ解析への応用(Review)"
The empirical spectral distribution of random matrices have been studied since Wigner's pioneering work on the semicircular law in the 1950's. The result says that the empirical spectral distribution of a symmetric matrix with i.i.d. random elements converges to the semicircular law as the size of the matrix becomes large. Though this result is beautiful in theory, its application has been limited to a few problems in nuclear physics and coding theory. The next breakthrough was the Marcenko-Pastur (M-P) law for the asymptotic spectral distribution of sample covariance matrices. The M-P law has found more applications, in particular high dimensional statistical data analysis, than the semicircular law.
In this talk I will first review these two significant results. Each of them has three completely different proofs. Then I will explain several other theoretical results that have mostly been studied this decade. Finally, I will present some of the applications of these results. This review is partly based on lectures on random matrices given by P. Bickel, N. El-Karoui and A. Guionnet, and also some seminars at UC Berkeley.
(# This talk is almost the same as the talk I gave at ISM on June 1.)
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/05.html
2007/07/20
16:30 - 17:30Room #123 (Mathematics building)
和達三樹 (東京理科大学理学部物理学科)
"ソリトン物理はおもしろい---スピノル型ボーズ・アインシュタイン凝縮体におけるソリトン "
2007/07/19
17:00 - 18:30Room #123 (Mathematics building)
李 佳女華 (東京大学大学院総合文化研究科)
"幕末・明治初期の日本における西洋数学の導入と漢訳西洋数学書籍"
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
16:30 - 18:00Room #128 (Mathematics building)
小沢登高 (東大数理)
"On a class of II$_1$ factors with at most one Cartan subalgebra"
2007/07/18
16:30 - 17:30Room #117 (Mathematics building)
梶原 健 (横浜国立大学)
"Tropical toric varieties"
16:20 - 17:30Room #122 (Mathematics building)
増田 弘毅 (九州大学大学院数理学研究院)
"Easy full-joint estimators of stable processes"
安定レヴィ過程からの高頻度観測に基づいた同時推定に関しては,尤度比確率場の漸近挙動は安易に二次項の観測情報量まで見ただけでは解明されず,最尤推定量の典型的な“良い漸近挙動”が保証されないことが分かっている.本発表では,標本メディアンおよび標本メディアンのプラグイン型統計量の漸近挙動に基づき,モデルに入る全パラメータの同時推定を可能とする計算容易な推定量の構成法を紹介し,正則な漸近共分散行列を有する漸近正規性を導出する.推定量の有限標本での挙動を数値実験で検証する.時間があれば,非対称安定レヴィ過程の場合に関して分かっている事柄についても触れる.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/04.html
2007/07/17
16:30 - 18:00Room #056 (Mathematics building)
松村 朝雄 (東京大学大学院数理科学研究科)
"Orbifold Cohomology of Wreath Product Orbifolds and
Cohomological HyperKahler Resolution Conjecture"
Chen-Ruan orbifold cohomology ring was introduced in 2000 as
the degree zero genus zero orbifold Gromov-Witten invariants with
three marked points. We will review its construction in the case of
global quotient orbifolds, following Fantechi-Gottsche and
Jarvis-Kaufmann-Kimura. We will describe the orbifold cohomology of
wreath product orbifolds and explain its application to Ruan's
cohomological hyperKahler resolution conjecture.
2007/07/12
16:30 - 18:00Room #128 (Mathematics building)
酒匂宏樹 (東大数理)
"Normalizers of MASAs and irreducible subfactors"
2007/07/11
16:30 - 17:30Room #117 (Mathematics building)
Andreas Rosenschon (University of Alberta)
"Algebraic cycles on products of elliptic curves over p-adic fields "
2007/07/10
16:30 - 18:00Room #056 (Mathematics building)
Danny C. Calegari (California Institute of Technology)
"Combable functions, quasimorphisms, and the central limit theorem
(joint with Koji Fujiwara)
"
Quasimorphisms on groups are dual to stable commutator length,
and detect extremal phenomena in topology and dynamics. In typical groups
(even in a free group) stable commutator length is very difficult to
calculate, because the space of quasimorphisms is too large to study
directly without adding more structure.
In this talk, we show that a large class of quasimorphisms - the so-called
"counting quasimorphisms" on word-hyperbolic groups - can be effectively
described using simple machines called finite state automata. From this,
and from the ergodic theory of finite directed graphs, one can deduce a
number of properties about the statistical distribution of the values of a
counting quasimorphism on elements of the group.
2007/07/09
10:30 - 12:00Room #128 (Mathematics building)
今野宏 (東京大学)
"Geometry of hyperkahler quotients"
2007/07/06
15:00 - 16:10Room #122 (Mathematics building)
Arturo KOHATSU-HIGA (大阪大学大学院基礎工学研究科)
"Estimating multidimensional densities through the Malliavin-Thalmaier formula"
TBA
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/03.html
2007/07/05
16:30 - 18:00Room #128 (Mathematics building)
Rolf Dyre Svegstrup (東大数理)
"Factorization in $C^*$-Algebras "
2007/07/04
10:30 - 11:30Room #056 (Mathematics building)
Lars Diening (Universitat Freiburg)
"The Lipschitz truncation method"
We study the existence of weak solutions to the incompressible $p$-Navier Stokes equations. This system can be used to describe the flow of honey, ketchup, blood, suspensions, polymers, and glaciers. We are interested in small values of $p$, where the method of monotone operators fails. We establish weak solutions by means of the Lipschitz truncation technique, where Sobolev Functions are approximated by Lipschitz functions in a special way. We apply the technique also to electrorheological fluids, where the exponent $p$ depends on the electric field.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
14:40 - 18:00Room #056 (Mathematics building)
野田尚廣 (名古屋大学大学院多元数理科学研究科) 14:40 - 16:10
"A Special Lagrangian Fibration in the TAUB-NUT Space"
この講演では, Taub-NUT space における special Lagrangian fibration の具体的構成について述べるつもりである.Taub-NUT space は複素多様体としては二次元複素空間であるが,計量が通常と異なり完備で非平坦なリッチ平坦計量をもつ Hyper-Kahler 多様体として特徴づけられる.この空間の special Lagrangian fibration が,Ionel-Min Oo の手法を用いることで具体的に構成できることを見る.
新田泰文 (大阪大学大学院理学研究科) 16:30 - 18:00
"Symmetries in generalized complex geometry"
一般化された複素構造という新しい幾何構造についてお話しします.これは複素構造とシンプレクティック構造を自然に含む非常に大きな枠組みで Hitchin が導入し,Gualtieri らによって複素幾何学的,シンプレクティック幾何学的な視点から盛んに研究されています.本講演では一般化された複素多様体への群作用について,シンプレクティック幾何的立場から解説いたします.一般化された複素多様体への Hamiltonian action という概念を導入し,その群作用に関する簡約定理や,一般化された運動量写像に関する凸性について説明します.
2007/07/03
16:30 - 18:00Room #056 (Mathematics building)
金 英子 (東京工業大学情報理工学研究科)
"Two invariants of pseudo--Anosov mapping classes: hyperbolic volume vs dilatation
(joint work with Mitsuhiko Takasawa)"
We concern two invariants of pseudo-Anosov mapping classes.
One is the dilatation of pseudo--Anosov maps and the other is the volume
of mapping tori. To study how two invariants are related, fixing a surface
we represent a mapping class by using the standard generator set and compute
these two for all pseudo--Anosov mapping classes with up to some word length.
In the talk, we observe two properties:
(1) The ratio of the topological entropy (i.e. logarithm of the dilatation) to
the volume is bounded from below by some positive constant which only
depends on the surface.
(2) The conjugacy class having the minimal dilatation reaches the minimal volume.
On the observation (1), in case of the mapping class group of a once--punctured
torus, we give a concrete lower bound of the ratio.
2007/07/02
10:30 - 12:00Room #128 (Mathematics building)
飯田修一 (東大数理)
"On the Meyer function for theta divisors"
2007/06/29
15:30 - 17:45Room #122 (Mathematics building)
Salem Ben Said (Nancy大)
"On the theory of Bessel functions associated with root systems"
The theory of spherical functions on Riemannian symmetric spaces G/K and on non-compactly causal symmetric spaces G/H has a long and rich history. In this talk we will show how one can use a limit transition approach to obtain generalized Bessel functions on flat symmetric spaces via the spherical functions. A similar approach can be applied to the theory of Heckman-Opdam hypergeometric functions to investigate generalized Bessel functions related to arbitrary root system. We conclude the talk by giving a conjecture about the nature and order of the singularities of the Bessel functions related to non-compactly causal symmetric spaces.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2007/06/28
16:30 - 18:00Room #128 (Mathematics building)
谷本溶 (東大数理)
"A new construction of causal nets of operator algebras"
2007/06/27
16:20 - 17:30Room #122 (Mathematics building)
小方 浩明 (早稲田大学, 国際教養学部)
"Empirical likelihood method for time series analysis"
For a class of vector-valued non-Gaussian stationary processes with unkown parameters, we develop the empirical likelihood approach which was proposed in the i.i.d. setting. In the time series analysis it is known that Whittle likelihood is one of fundamental tools to get a good estimator of unknown parameters and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we take its score as an estimating function and obtain the asymptotic distribution of our test statistic. Since the fitted spectral model may be different from true spectral structure, the results enable us to construct confidence rigions for various important time series parameters without knowing true spectral structure. We also consider the approach to a minimum contrast estimation and Cressie-Read power-divergence statistic. Numerical studies are introduced and illuminate some interesting features of the empirical approach.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/02.html
16:30 - 17:30Room #117 (Mathematics building)
Stephen Lichtenbaum (Brown University)
"The conjecture of Birch and Swinnerton-Dyer is misleading"
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.
17:30 - 19:00Room #128 (Mathematics building)
山本 匡 (東京大)
"Selection and Performance Analysis of Asia-Pacific Hedge Funds"
2007/06/25
10:30 - 12:00Room #128 (Mathematics building)
小櫃邦夫 (鹿児島大学)
"Weil-Petersson 計量とTakhtajan-Zograf 計量の漸近挙動"
2007/06/22
16:30 - 18:00Room #118 (Mathematics building)
Qi Zhang (Missouri大学)
"Projective varieties with nef anti-canonical divisors"
Projective varieties with nef anti-canonical divisors appear naturally in the minimal model program and the theory of classification of higher-dimensional algebraic varieties. In this talk we describe a comprehensive approach to birational geometry of log canonical pair (X, D) with nef anti-canonical class -(K_X+D). In particular, We present two theorems on the birational structure of the varieties. We will also discuss some recent results and new aspects of the subject.
2007/06/21
16:30 - 18:00Room #128 (Mathematics building)
Richard D. Burstein (UC Berkeley)
"Subfactors Arising from Symmetric Commuting Squares (following Jones/Sunder)"
2007/06/20
14:40 - 18:00Room #056 (Mathematics building)
中田文憲 (東京大学大学院数理科学研究科) 14:40 - 16:10
"LeBrun-Mason 対応とその簡約について"
LeBrun と Mason は近年,正則円板の族に関するツイスター型の対応を発見した.彼らは次元の異なる二つのタイプの対応を示しているが,どちらも Penrose や Hitchin による解析的・局所的な理論の,非解析的・大域的な version とみなすことができる.一方 Penrose らの枠組みにおいては,次元の異なるツイスター型対応を関連づける次元簡約という現象が生じることが,Dunajski などによって最近研究されている.この講演では,LeBrun らの大域的な状況で簡約理論を展開しようとするときに生じる問題点を示し,ある種の特異性を導入することでこれを解決できることを説明したい.論文:math.DG/0701116
後藤竜司 (大阪大学大学院理学研究科) 16:30 - 18:00
"Deformations of generalized Kahler and Calabi-Yau structures"
一般化された複素構造,ケーラー 構造は Hitchin,Gualtieri により,導入された複素構造とシンプレクティック構造と統一する幾何構造である.講演では,最近得られた一般化されたケーラー構造の安定性定理を解説する.これは,Kodaira-Spencer によるケーラー構造の複素構造の(small) 変形のもとでの安定性の拡張であり,証明には Calabi-Yau の変形の非障害性定理でのテクニックを用いる.応用として,射影空間や Fano 曲面上に一般化されたケーラー構造が豊富に存在することを示す.また,ケーラー多様体上の正則ポアソン構造から一般化されたケーラー構造が構成されることを見る.
15:00 - 16:00Room #470 (Mathematics building)
Y.S. Chow (台湾中央研究院数学研究所)
"On evolution games with local interaction and mutation "
2007/06/19
16:30 - 18:00Room #128 (Mathematics building)
堤 誉志雄 (京都大学理学研究科)
"Unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schr\"odinger equation"
16:30 - 18:00Room #126 (Mathematics building)
原岡喜重氏 (熊本大学)
"Rigid local systemとその切断の積分表示,および接続係数"
A local system on $CP^1-\{finite points\}$ is called physically rigid if it is uniquely determined up to isomorphisms by the local monodromies. We explain two algorithms to construct every physically rigid local systems. By applying the algorithms we obtain integral representations of solutions of the corresponding Fuchsian differential equation. Moreover we can express connection coefficients of the equation in terms of the integrals. These results will be applied to several differential equations arising from the representation theory.
2007/06/18
10:30 - 12:00Room #128 (Mathematics building)
清水 悟 (東北大学)
"An intrinsic characterization of the unit polydisc"
2007/06/16
13:30 - 16:00Room #117 (Mathematics building)
土岡俊介 (京都大学数理解析研究所) 13:30 - 14:30
"Lie theoretic structures for the generalized symmetric groups"
近年、Ariki, Brundan, Grojnowski, Kleshchev, Vazirani等によって、
modular表現論とKac-Moody Lie環/量子群といったLie theoreticな対象との関係が研究
されて来た。このうち対称群のmodular表現論については、
(1) 標数p>0において、対称群\mathfrak{S}_nの(有限次元)表現のGrothendieck群の
(nを走らせた)直和には、Kac-Moody Lie環g(A^{1}_{p-1})のレベル1基本既約最高
weight表現の構造を入れることが出来る。
(2) 対称群の既約表現の同型類の直和には、量子群U_q(g(A^{1}_{p-1}))の
レベル1基本既約最高weight表現に付随する(Kashiwaraの意味での)結晶構造を
入れることが出来る。
と、その関係をまとめることが出来る。
講演者は以前、複素鏡映群(あるいは一般化対称群)G(m,1,n)のmodular分岐則の
研究において、(A^{(1)}_{p-1})^{\otimes r}(ここでrはpとmから決まる自然数)
に付随する量子群との関係を示唆する結果を得たので、まずはそれを解説したい。
次に、G(m,1,n)における(1),(2)の対応物の構成する現在進行中の試みについて、
当日までに出来ているところを解説する予定である。
なお、G(m,1,n)の群環のq-変形と考えられているcyclotomic Hecke algebraにおいて、
qが1でない1の羃根の場合は既に(1),(2)の対応物が知られているので、時間が許せば
それとの比較についても解説したい。
渡辺文彦 (北見工業大学) 15:00 - 16:00
"Wirtinger 積分の構造について"
Wirtinger はガウスの超幾何函数 $_2F_1$ を一意化する目的でこれを
テータ函数の冪積の積分で表わす表示を1902年に得た.Wirtinger の発見以降,
この積分に関する組織的な研究は講演者の調べた限りではほとんど無いのであるが,
この積分を講演者は前述に因んで Wirtinger 積分と呼んでいる.
この積分は実質的には超幾何函数なのであるが,あえてこの事実を忘れテータ函数の
公式のみを用いて Wirtinger 積分のみたすさまざまな関係式を導出することが
できれば,それはテータ函数論の観点からのガウスの超幾何函数論の再構成と
見做すことができる.
実際,講演者はこの立場から超幾何函数の接続行列やモノドロミー行列,微分方程式の
再導出を最近おこなった.また,講演者がこの積分に注目しているもうひとつの
理由は,超幾何函数の新しい一般化の可能性が Wirtinger 積分に見えているという
ことである.
本講演では Wirtinger 積分と超幾何函数との関係および一般化の可能性について,
講演者のおこなった方法および得た結果を中心に,妄想を交えつつ解説する.
数学のスタイルは古典解析的である(真古典解析ではないが新古典的か).
小生は世間の情報にうといので,講演中などにWirtinger 積分の関連で
何らかの情報をご教示いただければ幸いです.
2007/06/15
16:30 - 17:30Room #123 (Mathematics building)
井原茂男 (東京大学先端科学技術研究センター, システム生物医学ラボラトリー(LSBM), ダイナミカルバイオインフォーマティクス)
"大規模データ解析時代の生物学における数理解析への期待"
21世紀はバイオの時代と言われて10年が経過しようとしている。ゲノムプロジェクトによってヒトのDNA配列は決定され、一塩基多型、コピー数解析とゲノム上での変化と遺伝子の発現、および疾患との関連性も調べられてきた。最近ではエピゲノムといわれるDNAのメチル化などゲノム配列以外の効果によっても、遺伝子発現が制御されるメカニズムが次第に明らかにされつつある。確かに、実験手法の急速な進歩によって大量のデータが得られ、知識も急増している。さらに、IT、データベース技術によって、オリジナルデータやそこから得られた情報なども容易に入手可能である。しかし生命現象で最も基本的でしかも応用上最も最優先で解明すべき遺伝子の転写機構でさえも、様々なモデルが提唱され定説もまだないのが現状である。我々は、データマイニングの観点からデータ処理を進める一方、文献から遺伝子や蛋白質の相互作用を自然言語処理で抽出し、マイクロアレイの解析に適用しいくつかの結果を得た。しかし、実験から得られるデータはますます大規模化が進み、新たな情報処理が必要になってきている。そこで、我々の解析のアプローチといくつかの問題点、さらには今後の解決の方向性について、演者自身が過去にいくつかの分野で採用してきたアプローチについても触れながら考察してみたい。また、生命科学の発展が期待されている領域である臨床研究でのイノベーションとも関連付け、今後の新しい数理解析への期待について述べてみたい。
2007/06/13
10:30 - 11:30Room #056 (Mathematics building)
Walter Strauss (Brown University)
"Steady Water Waves with Vorticity"
Consider a classical 2D water wave under the influence of gravity with an arbitrary vorticity function. Assume such a wave is traveling at a constant speed over a flat bed. Then there exist many families of such waves of large amplitude. The proof is based on elliptic PDEs, bifurcation and degree theory. I will also exhibit some recent numerical computations. If the vorticity is sufficiently large, the first stagnation point occurs not at the crest (as with irrotational flows) but on the bed directly below the crest. For variable vorticity the first stagnation point can occur in the interior of the fluid.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
14:40 - 15:40Room #123 (Mathematics building)
Alex Cook (Actuarial Mathematics and Statistics,
School of Mathematical and Computer Sciences,
Heriot-Watt University)
"Return of the Giant Hogweed: modelling the invasion of Britain by a dangerous alien plant"
As a result of changing climate and land use, as well as due to human intervention, increasingly species are moving to new abitats. We wish to understand the risk of invasive species entering new areas, and as an example consider the spread of Giant Hogweed (Heracleum mantegazzianum) from SW Asia in Great Britain, a species that has been damaging Britain's biodiversity since it was introduced in the 19th C and which is dangerous to human health. We construct a spatio-temporal stochastic model for its spread (both local and at distance) that takes account of covariates such as the heterogeneous land-cover and climate of the island. We then fit the model directly to observed data. Fitting the model was non-trivial and involved the use of Markov chain Monte Carlo techniques. The approach taken allows spatio-temporal predictions of the future spread of the weed can be made, consistent with the invasion history; it also allows the effect of varying habitats and climate to be understood. The approach we have taken can be generalised to other biological systems exhibiting stochastic variability, and there are clear parallels to epidemic models for the spread of disease within heterogeneous host populations.
http://www.ma.hw.ac.uk/~alexc/
2007/06/12
16:30 - 18:00Room #056 (Mathematics building)
Tian-Jun Li (University of Minnesota)
"The Kodaira dimension of symplectic 4-manifolds "
Various results and questions about symplectic4-manifolds can be
formulated in terms of the notion of the Kodaira dimension. In particular,
we will discuss the classification and the geography problems. It is interesting
to understand how it behaves undersome basic constructions.Time permitting
we will discuss the symplectic birational aspect of this notion and speculate
how to extend it to higher dimensional manifolds.
2007/06/07
16:30 - 18:00Room #128 (Mathematics building)
山下真 (東大数理)
"Affine holonomy foliations"
2007/06/06
16:20 - 17:30Room #122 (Mathematics building)
小池 健一 (筑波大学大学院数理物質科学研究科)
"非正則な位置尺度母数分布族における位置母数の逐次点推定について"
有界な台をもつ非正則な位置尺度母数分布族に対して,その位置母数の逐次点推定を考える.ここでは,平均二乗誤差に費用も加えてリスクを考える.レンジに基づく停止則を提案し,これが漸近有効であることを示す.また,良く知られているRobbinsの逐次推定方式との比較を行い,密度関数の台の端点で密度関数が急激に変化する場合には,提案する逐次推定方式が標本数やリスクの意味で優れていることを示す.この結果は,逐次区間推定に関するKoike (2007)のものと同様であることが分かる
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/01.html
2007/06/05
17:00 - 18:30Room #117 (Mathematics building)
Emmanuel Giroux (ENS Lyon)
"Symplectic mapping classes and fillings"
We will describe a joint work in progress with Paul Biran in
which contact geometry is combined with properties of Lagrangian manifolds
in subcritical Stein domains to obtain nontrivaility results for symplectic
mapping classes.
2007/06/04
10:45 - 12:15Room #128 (Mathematics building)
坂井秀隆 (東京大学)
"有理楕円曲面上の微分方程式"
2007/06/02
17:30 - 19:00Room #128 (Mathematics building)
楠岡 成雄 (東京大)
"分布が Fat tail を持つ i.i.d. 確率変数の和に関して
"
2007/05/30
17:30 - 19:00Room #118 (Mathematics building)
新井 拓児 (慶応大)
"非対称関数上の最適ヘッジ戦略"
2007/05/29
15:00 - 16:30Room #002 (Mathematics building)
Marta Asaeda (UC Riverside)
"Galois groups and an obstruction to principal graphs of subfactors "
16:30 - 18:00Room #126 (Mathematics building)
Karl-Hermann Neeb (Technische Universität Darmstadt)
"A host algebra for the regular representations of the canonical commutation relations"
We report on joint work with H. Grundling (Sydney).
The concept of a host algebra generalises that of a group $C^*$-algebra to groups which are not locally compact in the sense that its non-degenerate representations are in one-to-one correspondence with representations of the group under consideration. A full host algebra covering all continuous unitary representations exist for an abelian topological group if and only if it (essentially) has a locally compact completion. Therefore one has to content oneselves with certain classes of representations covered by a host algebra. We show that there exists a host algebra for the set of continuous representations of the countably dimensional Heisenberg group corresponding to a non-zero central character.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070529neeb
2007/05/26
13:00 - 16:30Room #117 (Mathematics building)
酒井一博 (慶応大経済) 13:00 - 14:30
"弦理論対応における可積分性"
概要:N=4超対称ゲージ理論と反ド・ジッター時空を背景とする弦理論の等価性を主
張するAdS/CFT対応は、ここ十年弦理論の分野でもっとも活発に研究されてい
るテーマのひとつである。この枠組の中で、伝統的な一次元量子可積分系や二
次元古典可積分系と同種の可積分構造が発見され、近年飛躍的な研究の進展が
続いている。この流れは、既存の可積分系の知識の単なる応用にとどまらず、
一次元Hubbard模型の可積分性の背景にある代数構造を明らかにするなど、可
積分系の分野へのフィードバックをももたらしている。本講演では、ゲージ理
論・弦理論双方で可積分性がどのように現れるかを概観しながら、この分野の
研究の最前線を紹介する。
加藤晃史 (東大数理) 15:00 - 16:30
"AdS/CFT 対応における $a$-maximization について"
弦双対性の一つである AdS/CFT 対応において、$a$-maximization
と呼ばれる変分問題が4次元超対称共形場理論のスペクトルの決定に
重要な働きをするがわかってきた。本講演では非専門家向けに
$a$-maximization の基本的な構造を説明するとともに、
関連するいくつかの話題を紹介したい。
2007/05/25
14:30 - 16:00Room #122 (Mathematics building)
坊向伸隆 (大阪市立大学)
"The classification of simple irreducible pseudo-Hermitian symmetric spaces: from a view of elliptic orbits"
In this talk, we call a special elliptic element an Spr-element, we create an equivalence relation on the set of Spr-elements of a real form of a complex simple Lie algebra, and we classify Spr-elements of each real form of all complex simple Lie algebras under our equivalence relation. Besides, we demonstrate that the classification of Spr-elements under our equivalence relation corresponds to that of simple irreducible pseudo-Hermitian symmetric Lie algebras under Berger's equivalence relation. In terms of the correspondence, we achieve the classification of simple irreducible pseudo-Hermitian symmetric Lie algebras without Berger's classification.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525boumuki
16:00 - 17:30Room #122 (Mathematics building)
金行壮二 (上智大学名誉教授)
"Causalities, G-structures and symmetric spaces"
Let M be an $n$-dimensional smooth manifold, $F(M)$ the frame bundle of $M$, and let $G$ be a Lie subgroup of $GL(n,\mathbb R)$. We say that $M$ has a $G$-structure, if there exists a principal subbundle $Q$ of $F(M)$ with structure group $G$. Let $C$ be a causal cone in $\mathbb R^n$, and let $Aut C$ denote the automorphism group of $C$.
Starting from a causal structure $\mathcal{C}$ on $M$ with model cone $C$, we construct an $Aut C$-structure $Q(\mathcal{C})$. Several concepts on causal structures can be interpreted as those on $Aut C$-structures. As an example, the causal automorphism group $Aut(M,\mathcal{C})$ of $M$ coincides with the automorphism group $Aut(M,Q(\mathcal{C}))$ of the $Aut C$-structure.
As an application, we will consider the unique extension of a local causal transformation on a Cayley type symmetric space $M$ to the global causal automorphism of the compactification of $M$.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070525kaneyuki
2007/05/23
16:20 - 17:30Room #122 (Mathematics building)
沖本 竜義 (横浜国立大学経済学部・大学院国際社会科学研究科)
"New Evidence of Asymmetric Dependence Structures in International Equity Markets"
A number of recent studies found two asymmetries in dependence structures in international equity markets; specifically, dependence tends to be high in (1) highly volatile markets and (2) bear markets. In this paper, a further investigation on asymmetric dependence structures in international equity markets is performed under the use of the Markov switching model and copula theory. Combining these two theories enables us to model dependence structures with sufficient flexibility. Using this flexible framework we indeed found that there are two distinct regimes in the US-UK market. We also showed that, for the US-UK market, the bear regime is better described by an asymmetric copula with lower tail dependence with clear rejection of the Markov switching multivariate Normal model. In addition, we showed ignorance of this further asymmetry in bear markets is very costly for risk management. Lastly, we conducted similar analysis for other G7 countries, where we found other c ases where the use of a Markov switching multivariate Normal model would be inappropriate.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/00.html
2007/05/22
16:30 - 18:00Room #126 (Mathematics building)
甲斐千舟 (九州大学)
"A characterization of symmetric cones by an order-reversing property of the pseudoinverse maps"
When a regular open convex cone is given, a natural partial order is introduced into the ambient vector space. If we consider the cone of positive numbers, this partial order is the usual one, and is reversed by taking inverse numbers in the cone. In general, for every symmetric cone, the inverse map of the associated Jordan algebra reverses the order.
In this talk, we investigate this order-reversing property in the class of homogeneous convex cones which is much wider than that of symmetric cones. We show that a homogeneous convex cone is a symmetric cone if and only if the order is reversed by the Vinberg's *-map, which generalizes analytically the inverse maps of Jordan algebras associated with symmetric cones. Actually, our main theorem is formulated in terms of the family of pseudoinverse maps including the Vinberg's *-map as a special one. While our result is a characterization of symmetric cones, also we would like to mention O. Güler's result that for every homogeneous convex cone, some analogous pseudoinverse maps always reverse the order.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/05/21
10:30 - 12:00Room #128 (Mathematics building)
厚地淳 (慶応大学)
"熱核を用いたNevanlinna理論 --- Gauss mapへの試み"
2007/05/17
16:30 - 18:00Room #128 (Mathematics building)
小川朋宏 (東大数理)
"On the statistical equivalence for sets of quantum states"
15:00 - 16:30Room #002 (Mathematics building)
真野元 (東京大学数理科学研究科)
"The unitary inversion operator for the minimal representation of the indefinite orthogonal group O(p,q)"
The indefinite orthogonal group $O(p,q)$ ($p+q$ even, greater than four) has a distinguished infinite dimensional irreducible unitary representation called the 'minimal representation'. Among various models, the $L^2$-model of the minimal representation of $O(p,q)$ was established by Kobayashi-Ørsted (2003). In this talk, we focus on and present an explicit formula for the unitary inversion operator, which plays a key role for the analysis on this L2-model as well as understanding the $G$-action on $L^2(C)$. Our proof uses the Radon transform of distributions supported on the light cone.
This is a joint work with T. Kobayashi.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/05/15
14:30 - 16:00Room #122 (Mathematics building)
Mikhail Kapranov (Yale 大学)
"Riemann-Roch for determinantal gerbes and smooth manifolds"
A version of the Riemann-Roch theorem for curves due to Deligne, describes the determinant of the cohomology of a vector bundle E on a curve.
If one realizes E via the Krichever construction, the determinant of the cohomology becomes a Hom-space in the determinantal gerbe for the vector space over the field of power series. So one has a ``local" Riemann-Roch problem of description of this gerbe itself. The talk will present the results of a joint work with E. Vasserot describing the class of such a gerbe in a family which geometrically can be seen as a circle fibration. This can be further generalized to the case of a fibration with fibers being smooth compact manifolds of any dimension d (joint work with P. Bressler, B. Tsygan and E. Vasserot).
16:30 - 18:00Room #128 (Mathematics building)
宮尾 忠宏 (岡山大自然科学研究科 学振特別研究員 )
"量子電磁場中を運動する原子の安定性について"
16:30 - 18:00Room #056 (Mathematics building)
渡邉 忠之 (京都大学数理解析研究所)
"Kontsevich's characteristic classes for higher dimensional homology sphere bundles"
As an analogue of the perturbative Chern-Simons theory, Maxim Kontsevich
constructed universal characteristic classes of smooth fiber bundles with fiber
diffeomorphic to a singularly framed odd dimensional homology sphere.
In this talk, I will give a sketch proof of our result on non-triviality of the
Kontsevich classes for 7-dimensional homology sphere bundles.
2007/05/14
10:30 - 12:00Room #128 (Mathematics building)
Si, Quang Duc (東大数理)
"Unicity problems with truncated multiplicities of mermorphic mappings in several complex variables"
2007/05/10
16:30 - 18:00Room #128 (Mathematics building)
戸松玲治 (東大数理)
"自己準同型の収束と近似的内部性"
2007/05/09
16:30 - 17:30Room #117 (Mathematics building)
宮崎 直 (東京大学大学院数理科学研究科)
"$(g,K)$-module structures of principal series representations
of $Sp(3,R)$"
2007/05/08
16:30 - 18:00Room #056 (Mathematics building)
森山 哲裕 (東京大学大学院数理科学研究科)
"On the vanishing of the Rohlin invariant"
The vanishing of the Rohlin invariant of an amphichiral integral
homology $3$-sphere $M$ (i.e. $M \cong -M$) is a natural consequence
of some elementary properties of the Casson invariant. In this talk, we
give a new direct (and more elementary) proof of this vanishing
property. The main idea comes from the definition of the degree 1
part of the Kontsevich-Kuperberg-Thurston invariant, and we progress
by constructing some $7$-dimensional manifolds in which $M$ is embedded.
17:00 - 18:00Room #126 (Mathematics building)
荒川知幸 (奈良女子大学)
"Affine W-algebras and their representations"
The W-algebras are an interesting class of vertex algebras, which can be understood as a generalization of Virasoro algebra. It was originally introduced by Zamolodchikov in his study of conformal field theory. Later Feigin-Frenkel discovered that the W-algebras can be defined via the method of quantum BRST reduction. A few years ago this method was generalized by Kac-Roan-Wakimoto in full generality, producing many interesting vertex algebras. Almost at the same time Premet re-discovered the finite-dimensional version of W-algebras (finite W-algebras), in connection with the modular representation theory.
In the talk we quickly recall the Feigin-Frenkel theory which connects the Whittaker models of the center of $U({\mathfrak g})$ and affine (principal) W-algebras, and discuss their representation theory. Next we recall the construction of Kac-Roan-Wakimoto and discuss the representation theory of affine W-algebras associated with general nilpotent orbits. In particular, I explain how the representation theory of finite W-algebras (=the endmorphism ring of the generalized Gelfand-Graev representation) applies to the representation of affine W-algebras.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/05/07
10:30 - 12:00Room #128 (Mathematics building)
辻 元 (上智大学)
"Canonical metrics on relative canonical bundles and Extension of pluri log canonical systems"
16:30 - 18:00Room #122 (Mathematics building)
謝啓鴻(Xie Qihong) (東大・数理)
"Pathologies on ruled surfaces in positive characteristic"
We discuss some pathologies of log varieties in positive characteristic. Mainly, we show that on ruled surfaces there are counterexamples of several logarithmic type theorems. On the other hand, we also give a characterization of the counterexamples of the Kawamata-Viehweg vanishing theorem on a geometrically ruled surface by means of the Tango invariant of the base curve.
2007/05/02
16:30 - 17:30Room #117 (Mathematics building)
長谷川 泰子 (東京大学大学院数理科学研究科)
"Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields
"
2007/05/01
16:30 - 18:00Room #128 (Mathematics building)
下村 明洋 (学習院大理学部)
"非線型シュレディンガー方程式の解の長時間挙動について"
16:30 - 18:00Room #126 (Mathematics building)
飯田正敏 (城西大学)
"Harish-Chandra expansion of the matrix coefficients of $P_J$ Principal series Representation of $Sp(2,R)$"
Asymptotic expansion of the matrix coefficents of class-1 principal series representation was considered by Harish-Chandra. The coefficient of the leading exponent of the expansion is called the c-function which plays an important role in the harmonic analysis on the Lie group.
In this talk, we consider the Harish-Chandra expansion of the matrix coefficients of the standard representation which is the parabolic induction with respect to a non-minimal parabolic subgroup of $Sp(2,R)$.
This is the joint study with Professor T. Oda.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
2007/04/26
17:00 - 18:30Room #123 (Mathematics building)
公田 藏 (立教大学名誉教授)
"明治前期の日本において学ばれたユークリッド幾何学"
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
16:30 - 18:00Room #128 (Mathematics building)
緒方芳子 (東大数理)
"Nonequilibrium steady states in quantum systems"
2007/04/25
16:30 - 17:30Room #117 (Mathematics building)
津嶋 貴弘 (東京大学大学院数理科学研究科)
"Localized Characteristic Class and Swan Class"
2007/04/24
16:30 - 18:00Room #056 (Mathematics building)
五味 清紀 (東京大学大学院数理科学研究科)
"Realization of twisted $K$-theory and
finite-dimensional approximation of Fredholm operators"
A problem in twisted $K$-theory is to realize twisted $K$-groups generally by means of finite-dimensional geometric objects, like vector bundles. I would like to talk about an approach toward the problem by means of Mikio Furuta's generalized vector bundles. By using a twisted version of the generalized vector bundle and a finite-dimensional approximation of Fredholm operators, I construct a group into which there exists a natural injection from the twisted $K$-group twisted by any third integral cohomology class.
16:30 - 18:00Room #126 (Mathematics building)
Taro Yoshino (吉野太郎) (University of Tokyo)
"Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds
"
The existence problem of compact Clifford-Klein forms is important in the study of discrete groups. There are several open problems on it, even in the reductive cases, which is most studied. For a homogeneous space of reductive type, one can define its `infinitesimal' homogeneous space.
This homogeneous space is easier to consider the existence problem of compact Clifford-Klein forms.
In this talk, we especially consider the infinitesimal homogeneous spaces of indefinite Stiefel manifolds. And, we reduce the existence problem of compact Clifford-Klein forms to certain algebraic problem, which was already studied from other motivation.
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino
2007/04/23
10:30 - 12:00Room #128 (Mathematics building)
平地健吾 (東京大学)
"Generalization of Q-curvature in CR geometry"
2007/04/19
16:30 - 18:00Room #128 (Mathematics building)
勝良健史 (東大数理)
"Graph algebras, Exel-Laca algebras and ultragraph algebras"
2007/04/17
16:30 - 18:00Room #128 (Mathematics building)
小薗 英雄 (東北大学・大学院理学研究科)
"Some $L^r$-decomposition of $3D$-vector fields and its application to the stationary Navier-Stokes equations in multi-connected domains."
16:30 - 18:00Room #056 (Mathematics building)
小林 俊行 (東京大学大学院数理科学研究科)
"Existence Problem of Compact Locally Symmetric Spaces"
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.
In this talk, I will give a survey on the recent developments on the question about how the local geometric structure affects the global nature of non-Riemannian manifolds with emphasis on the existence problem of compact models of locally symmetric spaces.
2007/04/16
10:30 - 12:00Room #128 (Mathematics building)
本多 宣博 (東京工業大学)
"Joyce計量のツイスター空間の具体的な構成方法"
16:30 - 17:30Room #056 (Mathematics building)
Francois Hamel (エクス・マルセーユ第3大学 (Universite Aix-Marseille III))
"Rearrangement inequalities and isoperimetric eigenvalue problems for second-order differential operators"
The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. We show that, to each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types.
The results are new even for symmetric operators or in dimension 1. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new rearrangement technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.
2007/04/14
13:00 - 16:30Room #117 (Mathematics building)
長尾健太郎 (京大理) 13:00 - 14:30
"q-Fock空間と非対称Macdonald多項式"
斎藤-竹村-Uglov,Varagnolo-Vasserotによって,q-Fock空間に
A型量子トロイダル代数のレベル(0,1)表現の構造が入ることが知られています.
この表現をある可換部分代数に制限して得られる作用の同時固有ベクトルを,
非対称Macdonald多項式を用いて構成することができます.
さらにこの同時固有ベクトルをq-Fock空間の基底とすることで,
量子トロイダル代数の作用を組合せ論的に記述することができます.
今回のセミナーでは,斎藤-竹村-Uglov,Varagnolo-Vasserotの構成を
振り返ったあとで,同時固有ベクトルの構成法を紹介します.
最後に箙多様体の同変K群との関連について少しだけ言及します.
笠谷昌弘 (京大理) 15:00 - 16:30
"The Quantum Knizhnik-Zamolodchikov Equation
and Non-symmetric Macdonald Polynomials"
We construct special solutions of the quantum Knizhnik-Zamolodchikov equation
on the tensor product of the vector representation of
the quantum algebra of type $A_{N-1}$.
They are constructed from non-symmetric Macdonald polynomials
through the action of the affine Hecke algebra.
As special cases,
(i) the matrix element of the vertex operators
of level one is reproduced, and
(ii) we give solutions of level $\frac{N+1}{N}-N$.
(ii) is a generalization of the solution of
level $-\frac{1}{2}$ by V.Pasquier and me.
This is a jount work with Y.Takeyama.
2007/04/12
16:30 - 17:30Room #056 (Mathematics building)
Boris Khesin (University of Toronto)
"Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability"
We describe a simple relation between curvatures of the group of volume-preserving diffeomorphisms (responsible for Lagrangian instability of ideal fluids via Arnold's approach) and the generation of shocks for potential solutions of the inviscid
Burgers equation (important in mass transport). For this we characterize focal points of the group of volume-preserving diffeomorphism, regarded as a submanifold in all diffeomorphisms and the corresponding conjugate points along geodesics in the Wasserstein space of densities.
Further, we consider the non-holonomic optimal transport problem,
related to the following non-holonomic version of the classical Moser theorem: given a bracket-generating distribution on a manifold two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution.
http://coe.math.sci.hokudai.ac.jp/
16:30 - 18:00Room #128 (Mathematics building)
小西由紀子 (東大数理)
"ミラー対称性"
2007/04/11
10:30 - 11:30Room #056 (Mathematics building)
C. W. Oosterlee (Delft University of Technology)
"The numerical treatment of pricing early exercise options under L'evy processes"
In this presentation we will discuss the pricing of American and Bermudan options under L'evy process dynamics.
Two different approaches will be discussed: First of all, modelling with differential operators gives rise to the numerical solution of a partial-integro differential equation for obtaining European option prices. For American prices a linear complementarity problem with the partial integro-differential operator needs to be solved. We outline the difficulties and possible solutions in this context.
At the same time we would also like to present a different pricing approach based on numerical integration and the fast Fourier Transform. Both approaches are compared in terms of accuracy and efficiency.
http://coe.math.sci.hokudai.ac.jp/
16:30 - 17:30Room #117 (Mathematics building)
斎藤 毅 (東京大学大学院数理科学研究科)
"l進層の暴分岐と特性サイクル"
2007/04/10
15:00 - 16:00Room #370 (Mathematics building)
Thomas DURT (ブリユッセル自由大学・VUB)
"Applications of the Generalised Pauli Group in Quantum Information"
http://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf
2007/04/05
16:00 - 17:30Room #126 (Mathematics building)
Robert P. GILBERT (デラウェア大学・数学教室)
"Acoustic Modeling and Osteoporotic Evaluation of Bone"
In this talk we discuss the modeling of the acoustic response of cancellous bone using the methods of homogenization.
This can lead to Biot type equations or more generalized equations. We develop the effective acoustic equations for cancellous bone. It is assumed that the bone matrix is elastic and the interstitial blood-marrow can be modeled as a Navier-Stokes system.
We also discuss the use of the Biot model and consider its applicability to cancellous bone. One of the questions this talk addresses is whether the clinical experiments customarily performed can be used to determine the parameters of the Biot or other bone models. A parameter recovery algorithm which uses parallel processing is developed and tested.
2007/03/26
15:30 - 17:00Room #128 (Mathematics building)
Professor Caucher Birkar (University of Cambridge)
"Existence of minimal models and flips (3rd talk of three)"
2007/03/22
10:30 - 11:30Room #056 (Mathematics building)
Matteo Novaga (Hokkaido University / Universita di Pisa)
"A semidiscrete scheme for the Perona Malik equation"
We discuss the convergence of the spatial semidiscrete scheme for the one-dimensional Perona-Malik equation. If the initial datum is 1-Lipschitz out of a finite number of jump points, we haracterize the problem satisfied by the limit solution. In the general case, we construct a solution by a careful inspection of the behaviour of the approximating solutions in a space-time neighbourhood of the jump points.
http://coe.math.sci.hokudai.ac.jp/
10:30 - 12:00Room #128 (Mathematics building)
Professor Caucher Birkar (University of Cambridge)
"On boundedness of log Fano varieties (2nd talk of three)
"
2007/03/20
16:30 - 18:00Room #128 (Mathematics building)
Professor Caucher Birkar (University of Cambridge
)
"Singularities and termination of flips (1st talk of three)
"
2007/03/17
13:30 - 14:30Room #117 (Mathematics building)
Paul Wiegmann (Chicago Univ.)
"Calogero model and Quantum Benjamin-Ono Equation"
TBA
2007/03/09
10:30 - 12:00Room #123 (Mathematics building)
Kazufumi Ito (North Carolina State University)
"Nonsmooth Optimization and Applications in PDEs"
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
2007/03/08
15:30 - 17:00Room #123 (Mathematics building)
Kazufumi Ito (North Carolina State University)
"Nonsmooth Optimization and Applications in PDEs"
Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.
Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.
2007/03/07
14:00 - 15:00Room #056 (Mathematics building)
Seung Yeal Ha (Seoul National University)
"Stability theory in L^p for the space-inhomogeneous Boltzmann equation"
In this talk, I will present kinetic nonlinear funtionals which are similar in sprit to Glimm type functionals in one-dimensional hyperbolic conservation laws. These functionals measures the dispersive mechanism of the Boltzmann equation near vacuum and can be used to the study of the large-time behavior and L^p-stability of the Boltzmann equation near vacuum. This is a joint work with M. Yamazaki (Univ. of Tsukuba) and Seok-Bae Yun (Seoul National Univ.)
http://coe.math.sci.hokudai.ac.jp/index.html.en
2007/02/22
10:30 - 12:00Room #123 (Mathematics building)
Stan Osher (UCLA)
"The level set method, multivalued solutions and image science"
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
13:00 - 15:00Room #123 (Mathematics building)
Dietmar Hoemberg (Berlin Technical University)
"Optimal control of semilinear parabolic equations and an application to laser material treatments "
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
2007/02/21
10:30 - 12:00Room #123 (Mathematics building)
Stan Osher (UCLA)
"The level set method, multivalued solutions and image science"
During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.
13:30 - 15:00Room #123 (Mathematics building)
Dietmar Hoemberg (Berlin Technical University)
"Optimal control of semilinear parabolic equations and an application to laser material treatments "
Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.
However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.
The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.
2007/02/20
10:30 - 17:20Room #123 (Mathematics building)
Erwin Bolthausen (University of Zurich) 10:30 - 12:00
"Exit distributions for random walks in random environments "
Erwin Bolthausen (University of Zurich) 14:00 - 15:30
"Quasi one-dimensional random walks in random environments"
田村要造 (慶応大理工) 15:50 - 16:30
"Large deviation principle for currents generated by stochasticline integrals
on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada) "
長田博文 (九大数理) 16:40 - 17:20
"Interacting Brownian motions related to Ginibre random point field "
16:30 - 18:00Room #117 (Mathematics building)
Patrick G¥'erard (パリ南大学)
"On the dynamics of the Gross-Pitaevskii equation"
2007/02/17
13:30 - 16:00Room #117 (Mathematics building)
阿部 友紀 (上智理工数学) 13:30 - 14:30
"Finite-dimensional representations of the small quantum algebras"
量子代数は定義にパラメーターを一つ含み、量子代数の表現論は、
そのパラメーターが1のべき根であるか、そうでないかによって大きく異なる。
さらに、1のべき根の場合は、Lusztig氏によって定義された「制限型量子代数」と、
De Conini-Kac氏らによって定義された「非制限型量子代数」の2種類が存在し、
それぞれ表現論が異なる。
また、制限型量子代数は、「小型量子代数(=small quantum algebra)」と
呼ばれる真部分代数を含み、その表現論は、制限型量子代数と非制限型量子代数の
どちらの表現論においても重要な役割を果たしている。
今回の講演では、主に以下の3点について説明したい:
●小型量子代数が、非制限型量子代数のある商代数と同型になることを、
有限型とループ型の場合に示す。
●A, B, C, D, G型の小型量子代数の有限次元既約表現を、
Schnizer表現の部分表現として構成する。
●A型の小型ループ量子代数のevaluation表現の性質を調べる。
Seok-Jin Kang (Seoul National University) 15:00 - 16:00
"Combinatorics of Young walls and crystal bases"
We introduce combinatorics of Young walls and give a realization of crystal bases in terms of reduced Young walls. We also discuss their connection with representation theory of Hecke algebras.
2007/02/16
16:30 - 17:30Room #123 (Mathematics building)
松本幸夫 (東京大学・大学院数理科学研究科)
"トポロジーと私の思い出"
大学院に入ったのが1967年ですから、ちょうど40年前の
ことになります。それから「多様体のトポロジー」の分野で研究を
してきましたが、この40年間にトポロジーもずいぶん変化した
ように思います。自分の思い出話を交えて、その変化の様子をお話
できればと思います。私的な観点のものですので、それほど大所
高所からの話ではありません。
15:00 - 16:00Room #056 (Mathematics building)
Ratnasingham SHIVAJI (ミシシッピ州立大学)
"Multiple positive solutions for classes of elliptic systems with combined nonlinear effects"
We study the existence of multiple positive solutions to systems of the form
-\Delta u = \lambda f(v)
-\Delta v = \lambda g(u)
in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.
2007/02/01
15:00 - 16:00Room #118 (Mathematics building)
Lassi Paivarinta (Helsinki University of Technology, Finland)
"On Calderon's inverse conductivity problem in the plane."
16:15 - 17:15Room #118 (Mathematics building)
Nuuti Huyvonen (Helsinki University of Technology,
Finland)
"Locating transparent cavities in optical absorption and scattering
tomography"
2007/01/31
10:30 - 11:30Room #123 (Mathematics building)
小谷正博 (学習院大学)
"ガラスに吸着した色素分子の一分子観察――ランダムウォークと拡散――"
夜空の星を望遠鏡で観察できる。星の望遠鏡観察から星の一生、ひいては宇宙の成因まで議論できる。同様に蛍光を使えば色素分子一匹を顕微鏡で見ることができる。一分子観察は個々の分子の挙動が見えるので、分子レベルでの確率的な過程を調べる手段、分子のおかれた環境の不均一を研究する手段になることが認識されてきた。
ガラスの上に希薄に吸着した蛍光性の色素を使って分子の表面拡散をしらべた。平均自乗偏位は時間に比例して増大するようにみえ、これから拡散係数を見積もることができる。
このようにして求めた拡散係数は測定環境の湿度に大きく依存することがわかった。こうして、問題はガラス表面にある数ナノメートルの吸着水のなかでの色素分子の運動の議論になってきた。拡散係数に場所ムラはあるのか、時間依存性はあるのか、実験は進行中である。
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
15:15 - 18:45Room #117 (Mathematics building)
Dennis Eriksson (東大数理/Paris) 15:15 - 16:15
"Towards a proof of a metrized Deligne-Riemann-Roch theorem"
小林 真一 (名古屋大学多元数理) 16:30 - 17:30
"CM楕円曲線の超特異点における2変数p進L関数
(A two variable p-adic L-function for CM elliptic curves at supersingular primes)"
Frans Oort (Utrecht) 17:45 - 18:45
"Irreducibility of strata and leaves in the moduli space of abelian varieties"
16:30 - 18:00Room #126 (Mathematics building)
Li Daqian (復旦大学)
"Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
"
16:20 - 17:30Room #128 (Mathematics building)
西山 慶彦 (京都大学経済研究所)
"A Sequential Unit Root Test"
It is well known that conventional unit root tests such as Dickey=Fuller and its variants do not have good power properties when sample size is not large. Lai and Siegmund (1983, AS) proved that OLS estimator of the AR(1) coefficient is asymptotically normally distributed in a sequential framework even if the time series has a unit root unlike the OLS estimator under a standard sampling scheme. We pursue this direction to propose a unit root test under a sequential sampling. The proposed test uses not only the OLS estimator of the AR(1) coefficient, which is asymptotically normal, but also the stopping time to construct the critical region, anticipating a better power property. We obtain analytic expressions of the joint distribution of the two statistics as well as its marginals under the null. We also consider the distribution of the statistics under local alternatives. The properties of the stopping time, to the best of our knowledge, have not been studied in the unit root literature. We calculate its expectation and variance.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/18.html
2007/01/30
16:30 - 18:00Room #056 (Mathematics building)
John F. Duncan (Harvard University)
"Elliptic genera and some finite groups"
Recent developments in the representation theory of sporadic groups
suggest new formulations of `moonshine' in which Jacobi forms take on the
role played by modular forms in the monstrous case. On the other hand,
Jacobi forms arise naturally in the study of elliptic genera. We review
the use of vertex algebra as a tool for constructing the elliptic genus of
a suitable vector bundle, and illustrate connections between this and
vertex algebraic representations of certain sporadic simple groups.
16:30 - 18:00Room #118 (Mathematics building)
Jerome Le Rousseau (Laboratoire d'Analyse Topologie Probabilit\'es
Universit\'e de Provence / CNRS)
"Controllability of parabolic equations with non-smooth coefficients by means of global Carleman estimates"
We shall review the different concepts of controllability for parabolic equations and a fix-point method to achieve null-controllability of classes of semilinear equations. It is mainly based on observability inequalities and a precise knowledge of the observability constant. These inequalities are obtained by means of global Carleman estimates. We shall review their derivations and how they can be obtained in the case of non-smooth coefficients. We shall also present some open questions.
Part of this work is in collaboration with Assia Benabdallah and Yves Dermenjian (also from Universit\'e de Provence).
14:00 - 15:00Room #123 (Mathematics building)
Michael Lashkevich (Landau Institute)
"Scaling limits for the SOS models and bosonization"
Two different scaling limits in the SOS models are considered. The scaling limits of the bosonic construction for form factors provide form factors of some classes of operators in the scaling SOS/RSOS models and the sine-Gordon model.
2007/01/29
16:30 - 18:00Room #126 (Mathematics building)
Li Daqian (復旦大学)
"Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems
"
10:30 - 12:00Room #128 (Mathematics building)
松島敏夫 (石川工業高専)
"Radial cluster set of a bounded holomorphic map in the unit ball of C^n"
2007/01/27
13:30 - 16:00Room #117 (Mathematics building)
清水 寧 (立命館理工物理) 13:30 - 14:30
"マイクロクラスターの特異なダイナミクス"
数十個から数千個の原子からなる有限多体系であるマイクロクラスターは、表面原子と内部の原子という異なる環境にある構成原子からなる空間的に不均一な系である。これが原因となり、マイクロクラスターは静的な面においても動的な面においても結晶やアモルファスのバルクとは大きく異なる特異な振る舞いを見せることが知られている。その一例として、神戸大学保田らの実験グループにより確認されているナノ金属マイクロクラスター内における構成原子の非常に速い拡散現象(急速合金化)を取り上げ、このダイナミクスに関する我々の数値シミュレーションに基づく結果を紹介する。得られたいくつかの数値結果の解釈を通じ、「動的に維持されている物質」としてのマイクロクラスターの一側面を示す。
山田 大輔 (東大数理) 15:00 - 16:00
"例外型アフィンリー環$D_4^{(3)}$に付随するキリロフ・レシェティヒン加群の結晶基底に関する話題"
可解格子模型の1点関数を計算するために、Kang-柏原-Misra-三輪-中島-中屋敷らにより、``完全結晶"という概念が導入された。これはアフィンリー環$\mathfrak{g}$の量子展開代数$U'_q(\mathfrak{g})$に付随する結晶基底の中で、非常に良い性質をもつものである。完全結晶の存在性は、幾つかの場合に証明されたが、その後の研究の中で新たに発見され続けている。ところが、任意の既約な有限次元$U'_q(\mathfrak{g})$-加群が必ずしも結晶基底をもつとは限らない。そこで次の問題を考えたい。
問題:「結晶基底をもつ既約な有限次元$U'_q(\mathfrak{g})$-加群を全て見つけよ。」
この問題にアプローチするために、キリロフ・レシェティヒン加群$W_s^{(r)}$ (以下略してKR加群)を研究したい。これはアフィンリー環のディンキン図形の頂点$0$を除く頂点の番号$r$と、任意の正整数$s$の組によってパラメトライズされる。KR加群に関して、``フェルミ型公式''に起源をもつ以下の予想がある。尚, 現在までにこの予想の反例は見つかっていない。
予想:「KR加群$W_s^{(r)}$は結晶基底をもつ。
さらに$s$が$t_r:=max(1,2/(\alpha_r \vert \alpha_r))$の倍数ならば、KR加群$W_s^{(r)}$の結晶基底$B^{r,s}$は、レベル$s/t_r$の完全結晶である。ただし, $(\cdot \vert \cdot)$はウェイト格子上の標準線形形式。」
我々は, 例外型アフィンリー環$D_4^{(3)}$のKR加群$W_s^{(1)}$と$W_1^{(2)}$について、上の予想が正しいことを示した。その応用として、超離散可積分系の重要な例である「箱玉系」を構成し、そこに現れるソリトンの散乱則を表現論的に記述した。
前回の講演では、$U'_q(D_4^{(3)})$-加群の結晶基底に関する組合せ論的な部分を話した。今回の講演ではその表現論的な部分を解説する。
2007/01/26
16:30 - 17:30Room #128 (Mathematics building)
Professor Frans Oort
(Department of Mathematics
University of Utrecht
)
"Irreducibility of strata and leaves in the moduli space of
abelian varieties I (a survey of results)
"
16:30 - 18:00Room #126 (Mathematics building)
Li Daqian (復旦大学)
"Controllability and Observability:
from ODEs to Quasilinear Hyperbolic Systems"
2007/01/25
16:00 - 17:30Room #056 (Mathematics building)
Michael TRIBELSKY (東大・数理 / モスクワ工科大学)
"Soft-mode turbulence as a new type of spatiotemporal chaos at onset"
15:15 - 18:00Room #126 (Mathematics building)
澤田恒河 (東大数理) 15:15 - 16:15
"The Pimsner-Voiculescu AF-embedding of the irrational rotation $C^*$-algebra and its subalgebra"
水田有一 (東大数理) 16:30 - 18:00
"A Note on Weak Amenability"
14:00 - 17:00Room #370 (Mathematics building)
Ivana Alexandrova (East Carolina University)
"Semi-Classical Structure of the Scattering Amplitude and the Spectral Function for Schrodinger Operators"
2007/01/23
16:30 - 18:30Room #056 (Mathematics building)
中田 文憲 (東京大学大学院数理科学研究科) 16:30 - 17:30
"The twistor correspondence for self-dual Zollfrei metrics
----their singularities and reduction
"
C. LeBrun and L. J. Mason investigated a twistor-type correspondence
between indefinite conformal structures of signature (2,2) with some properties
and totally real embeddings from RP^3 to CP^3.
In this talk, two themes following LeBrun and Mason are explained.
First we consider an additional structure:
the conformal structure is equipped with a null surface foliation
which has some singularity.
We establish a global twistor correspondence for such structures,
and we show that a low dimensional correspondence
between some quotient spaces is induced from this twistor correspondence.
Next we formulate a certain singularity for the conformal structures.
We generalize the formulation of LeBrun and Mason's theorem
admitting the singularity, and we show explicit examples.
大橋 了 (東京大学大学院数理科学研究科) 17:30 - 18:30
"On the homology group of $Out(F_n)$"
Suppose $F_n$ is the free group of rank $n$,
$Out(F_n) = Aut(F_n)/Inn(F_n)$ the outer automorphism group of $F_n$.
We compute $H_*(Out(F_n);\mathbb{Q})$ for $n\leq 6$ and conclude
that non-trivial classes in this range are generated
by Morita classes $\mu_i \in H_{4i}(Out(F_{2i+2});\mathbb{Q})$.
Also we compute odd primary part of $H^*(Out(F_4);\mathbb{Z})$.
2007/01/22
10:30 - 12:00Room #128 (Mathematics building)
Hanjin Lee (Seoul National University)
"Omori-Yau generalized maximum principle"
2007/01/19
10:30 - 12:00Room #056 (Mathematics building)
Alex Mahalov (Arizona State University)
"3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics"
2007/01/18
13:00 - 14:30Room #056 (Mathematics building)
Alex Mahalov (Arizona State University)
"3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics"
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold. The global existence is proven using techniques of fast singular oscillating limits, Lemmas on restricted convolutions and the Littlewood-Paley dyadic decomposition. In the second part of the talk, we analyze regularity and dynamics of the 3D Euler equations in cylindrical domains with weakly aligned large initial vorticity.
16:30 - 18:00Room #126 (Mathematics building)
酒匂宏樹 (東大数理)
"Twisted Bernoulli shift actions of $Z^2 \rtimes SL(2,Z)$"
16:00 - 17:30Room #056 (Mathematics building)
LIANG Xing (東京大学大学院数理科学研究科 / 日本学術振興会)
"Asymptotic Speeds of Spread and Traveling Waves for Monotone Semiflows with Applications"
The theory of asymptotic speeds of spread and monotone traveling waves is established for a class of monotone discrete and continuous-time semiflows and is applied to a functional differential equation with diffusion, a time-delayed lattice population model and a reaction-diffusion equation in an infinite
cylinder.
2007/01/17
10:30 - 11:30Room #056 (Mathematics building)
Alex Mahalov (Department of Mathematics and Statistics, Department of Mechanical and Aerospace Engineering, Program in Environmental Fluid Dynamics, Arizona State University )
"Fast Singular Oscillating Limits of Hydrodynamic PDEs: application to 3D Euler, Navier-Stokes and MHD equations "
Methods of harmonic analysis and dispersive properties are applied
to 3d hydrodynamic equations to obtain long-time and/or global existence results to the Cauchy problem for special classes of 3d initial data. Smoothness assumptions for initial data are the same as in local existence theorems. Techniques for fast singular oscillating limits are used and large and/or infinite time regularity is obtained by bootstrapping from global regularity of the limit equations.
The latter gain regularity from 3d nonlinear cancellation of oscillations.
Applications include Euler, Navier-Stokes, Boussinesq and MHD equations, in infinite, periodic and bounded cylindrical domains.
http://coe.math.sci.hokudai.ac.jp/
15:30 - 17:00Room #470 (Mathematics building)
市原直幸 氏 (大阪大学基礎工学研究科)
" Hamilton-Jacobi方程式の漸近解とその周辺の話題"
16:20 - 17:30Room #128 (Mathematics building)
玉置 健一郎 (早稲田大学)
"Second order optimality for estimators in time series regression models"
We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator $\hat{\beta}$ proposed by Hannan (1963). This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of $\hat{\beta}$. Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that $\hat{\beta}$ has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of $\hat{\beta}$. Numerical studies are given to confirm the theoretical results.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/17.html
16:30 - 18:00Room #122 (Mathematics building)
Mourad Bellassoued (Faculte des Sciences de Bizerte)
"Recovering a potential in the wave equation via Dirichlet-to-Neumann map."
2007/01/16
16:30 - 18:30Room #056 (Mathematics building)
笹平 裕史 (東京大学大学院数理科学研究科) 16:30 - 17:30
"An $SO(3)$-version of $2$-torsion instanton invariants"
We construct invariants for simply connected, non-spin $4$-manifolds using torsion cohomology classes of moduli spaces of ASD connections on $SO(3)$-bundles. The invariants are $SO(3)$-version of Fintushel-Stern's $2$-torsion instanton invariants. We show that this $SO(3)$-torsion invariant of $2CP^2 \# -CP^2$ is non-trivial, while it is known that any invariants of $2CP^2 \# - CP^2$ coming from the Seiberg-Witten theory are trivial
since $2CP^2 \# -CP^2$ has a positive scalar curvature metric.
山口 祥司 (東京大学大学院数理科学研究科) 17:30 - 18:30
"On the non-acyclic Reidemeister torsion for knots"
The Reidemeister torsion is an invariant of a CW-complex and a representation of its fundamental group. We consider the Reidemeister torsion for a knot exterior in a homology three sphere and a representation given by the composition of an SL(2, C)- (or SU(2)-) representation of the knot group and the adjoint action to the Lie algebra.
We will see that this invariant is expressed by the differential coefficient of the twisted Alexander invariant of the knot and investigate some properties of the invariant by using this relation.
16:30 - 18:00Room #122 (Mathematics building)
Mourad Bellassoued (Faculte des Sciences de Bizerte)
"Recovering a potential from partial Cauchy data for the Schrödinger equation."
2007/01/15
10:30 - 12:00Room #128 (Mathematics building)
竹内 潔 (筑波大学数理物質科学研究科)
"Lagragian constructions for various topological invariants of algebraic varieties (東大数理、松井優氏との共同研究)"
16:30 - 18:00Room #122 (Mathematics building)
Mourad Bellassoued (Faculte des Sciences de Bizerte)
" Recovering a potential from full Cauchy data for the Schrödinger equation."
In this lectures we survey recent progress on the problem of determining a potential by measuring the Dirichlet to Neumann map
for the associated Schr\"odinger equation or wave equation. We make emphasis on the new results obtained with M.Yamamoto which is concerned with the case that the measurements are made on a strict
subset of the boundary for the wave equation.
16:00 - 17:30Room #056 (Mathematics building)
Antonio DeSimone (SISSA (International School for Advanced Studies))
"Analysis of physical systems involving multiple spatial scales: some case studies"
Variational methods have recently proved to be a powerful tool in deriving macroscopic models for phenomena whose physics is decided at the sub-miccron scale.
We will use two case studies to illustrate this point, namely, that of liquid crystal elastomers and that of superhydrophobic surfaces.
Liquid crystal elastomers are solids which combine the optical properties of liquid crystals with the mechanical properties of rubbery solids. They display phase transformations, material instabilities, and microstructures in a way simalr to shape-memory alloys.
The richness of the underlying material symmetries makes the mathematical analysis of this system particularly rewarding. Recent progress, ranging from analytical relaxation results to numerical simulations of the macroscopic mechanical response will be reviewed.
2007/01/12
16:30 - 17:30Room #123 (Mathematics building)
鳥海光弘 (東京大学・大学院新領域創成科学研究科)
"地球変動にまつわるおかしな現象、2題
1、プレート境界で砂と泥に起こる雪だるま現象
2、プレート境界地震は確率共鳴か"
地球科学における興味ある現象2題‐巨大固液混合体はどのように振舞うか。
最近の固体地球科学の大きな関心はプレート境界付近における固体・流体混合物質の挙動と境界型地震破壊やすべり運動、火山活動などとの関係である。プレート境界は地球上でもっとも活動的な部分であり、地球表層部分と地球内部とのエネルギー交換や物質交換が最も多く行われる部分でもある。とくに日本海溝や伊豆マリアナ海溝、南海トラフ、琉球海溝などの沈み込み境界部付近の地震波探査、電磁気探査、ボーリング掘削、などの研究がんたくさんの新しい事実を描き出している。
今回興味ある話として紹介するのは、プレート沈み込み境界では、海溝底で堆積した砂泥層が海洋プレートに乗ってプレート境界に引きずり込まれ、排水する過程で砂と泥に分離し、巨大な砂の塊が泥の層の中に分散する現象である。この現象の数理は砂が水を保持して流動化する過程と、プレート境界に持ち込まれた含水地質体が長期にわたりせん断変形を受ける過程で、砂の部分が次第に雪だるま状に衝突・合体する過程で示され、歪により巨大化する砂の塊は数キロに達することもありえる。こうして出来るプレート境界の構造は、大きさ分布がべき的になる砂の塊が境界に沿って拡がった泥の層内にクラスター上に分布するパターンを形成するだう。こうした構造形成はプレート境界部の力学特性を決めているだろう。
第2の話題はプレート境界における破壊の確率共鳴というテーマである、最近の研究ではプレート境界において発生する中小規模の地震はrepeating earthquakesまたはsimilar earthquakesとも呼ばれ、同一場所で繰り返しおこるせん断クラックである。そのサイズは0.01‐1km程度である。一方、巨大地震はこれに比べて大きく100kmx10km以上の破壊面をもつ。しかしこの巨大さにもかかわらず、やはり同一箇所が繰り返し破壊し、これをアスペリティと呼んでいる。一方、こうしたアスペリティの周囲は非アスペリティとよばれ、ゆっくりと滑っていて、流体を保持した岩石が分布し、低密度となっている。問題は大小の規模の破壊がどのような関係にあるのかという古典的なテーマである。プレート境界面上のいろいろな大きさのアスペリティが互いに重ならないであり続けているのか、もしくは互いに重なっているのかは重大である。観測的には巨大地震の破壊面は他の小さい破壊面と重なっている。つまり、境界面では、中小の多数のアスペリティが確率的に活動していて、巨大破壊の時にはそれらのアスペリティが一斉に動き出すということであろう。今回の話題提供ではこうした現象を確率共鳴として考えてみよう。
2007/01/11
16:00 - 17:30Room #123 (Mathematics building)
Oleg Yu. Emanouilov (Colorado State University)
"Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system."
2007/01/10
16:00 - 17:30Room #118 (Mathematics building)
Oleg Yu. Emanouilov (Colorado State University)
"Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system."
2007/01/09
16:00 - 17:30Room #118 (Mathematics building)
Oleg Yu. Emanouilov (Colorado State University)
" Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system."
We show that 1-D Burgers equation is globally uncontrollable with control acting at two endpoints. Then we establish the global controllability of the 2-D Burgers equation. Finally we show that for 2-D Navier-Stokes system the problem of global exact controllability is solvable for the dense set of the initial data with a control acting on part of the boundary.
2006/12/28
16:30 - 18:00Room #126 (Mathematics building)
Roberto Longo (University of Rome)
"Operator Algebras and Conformal Field Theory II"
2006/12/25
13:30 - 16:00Room #123 (Mathematics building)
研究集会の情報 (なし)
"なし"
秋から、少しお休みしていますので、替わりにまとめて集会をします。
12月25日午後から27日午後3時くらいまでです。詳細はURL:
http://www.ms.u-tokyo.ac.jp/activity/meeting061225.htm
をご覧下さい。織田孝幸
2006/12/21
17:00 - 18:30Room #123 (Mathematics building)
楠葉隆徳 (大阪経済大学人間科学部)
"インド数学における証明"
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
16:00 - 17:30Room #056 (Mathematics building)
Susan Friedlander (University of Illinois-Chicago)
"An Inviscid Dyadic Model For Turbulence"
We discuss properties of a GOY type model for the inviscid fluid equations. We prove that the forced system has a unique equilibrium which a an exponential global attractor. Every solution blows up in H^5/6 in finite time . After this time, all solutions stay in H^s, s<5/6, and "turbulent" dissipation occurs. Onsager's conjecture is confirmed for the model system.
This is joint work with Alexey Cheskidov and Natasa Pavlovic.
14:45 - 18:00Room #126 (Mathematics building)
Benoit Collins (Univ. Claude Bernard Lyon 1) 14:45 - 16:15
"Convergence of unitary matrix integrals and free probability"
Roberto Longo (University of Rome) 16:30 - 18:00
"Operator Algebras and Conformal Field Theory"
2006/12/20
16:30 - 18:45Room #117 (Mathematics building)
Anna Cadoret (RIMS/JSPS) 16:30 - 17:30
"On the profinite regular inverse Galois problem"
Given a field $k$ and a (pro)finite group $G$, consider the
following weak version of the regular inverse Galois problem:
(WRIGP/$G$/$k$) \textit{there exists a smooth geometrically
irreducible curve $X_{G}/k$ and a Galois extension $E/k(X_{G})$
regular over $k$ with group $G$.} (the regular inverse Galois
problem (RIGP/$G$/$k$) corresponding to the case
$X_{G}=\mathbb{P}^{1}_{k}$). A standard descent argument shows that
for a finite group $G$ the (WRIGP/$G$/$k$) can be deduced from the
(RIGP/$G$/$k((T))$). For
profinite groups $G$, the (WRIGP/$G$/$k((T))$) has been proved for
lots of fields (including the cyclotomic closure of characteristic $0$
fields) but the descent argument no longer works.\
\indent Let $p\geq 2$ be a prime, then a profinite group
$G$ is said to be \textit{$p$-obstructed} if it fits in a profinite group extension
$$1\rightarrow K\rightarrow G\rightarrow G_{0}\rightarrow 1$$
with $G_{0}$ a finite group and $K\twoheadrightarrow
\mathbb{Z}_{p}$. Typical examples of such profinite groups $G$ are
universal $p$-Frattini covers of finite $p$-perfect groups or
pronilpotent projective groups.\
\indent I will show that the (WRIGP/$G$/$k$) - even under
its weaker formulation: (WWRIGP/$G$/$k$) \textit{there exists a
smooth geometrically irreducible curve $X_{G}/k$ and a Galois
extension $E/k(X_{G}).\overline{k}$ with group $G$ and field of
moduli $k$.} - fails for the whole class of $p$-obstructed profinite
groups $G$ and any field $k$ which is either a finitely generated
field of characteristic $0$ or a finite field of characteristic
$\not= p$.\
\indent The proof uses a profinite generalization of the cohomological obstruction
for a G-cover to be defined over its field of moduli and an analysis of the constrainsts
imposed on a smooth geometrically irreducible curve $X$ by a degree $p^{n}$
cyclic G-cover $X_{n}\rightarrow X$, constrainsts which are too rigid to allow the
existence of projective systems $(X_{n}\rightarrow
X_{G})_{n\geq 0}$ of degree $p^{n}$ cyclic G-covers
defined over $k$. I will also discuss other implicsations of these constrainsts
for the (RIGP).
Eric Friedlander (Northwestern) 17:45 - 18:45
"An elementary perspective on modular representation theory"
2006/12/19
16:30 - 18:30Room #056 (Mathematics building)
境 圭一 (東京大学大学院数理科学研究科) 16:30 - 17:30
"Poisson structures on the homology of the spaces of knots"
We study the homological properties of the space $K$ of (framed) long knots in $\R^n$, $n>3$, in particular its Poisson algebra structures.
We had known two kinds of Poisson structures, both of which are based on the action of little disks operad. One definition is via the action on the space $K$. Another comes from the action of chains of little disks on the Hochschild complex of an operad, which appears as $E^1$-term of certain spectral sequence converging to $H_* (K)$. The main result is that these two Poisson structures are the same.
We compute the first non-trivial example of the Poisson bracket. We show that this gives a first example of the homology class of $K$ which does not directly correspond to any chord diagrams.
吉田 享平 (東京大学大学院数理科学研究科) 17:30 - 18:30
"On projections of pseudo-ribbon sphere-links"
Suppose $F$ is an embedded closed surface in $R^4$.
We call $F$ a pseudo-ribbon surface link
if its projection is an immersion of $F$ into $R^3$
whose self-intersection set $\Gamma(F)$ consists of disjointly embedded circles.
H. Aiso classified pseudo-ribbon sphere-knots ($F$ is a sphere.)
when $\Gamma(F)$ consists of less than 6 circles.
We classify pseudo-ribbon sphere-links
when $F$ is two spheres and $\Gamma(F)$ consists of less than 7 circles.
2006/12/18
10:30 - 12:00Room #128 (Mathematics building)
川口 周 (京都大学大学院理学研究科)
"Height functions and affine space regular automorphisms"
2006/12/14
16:00 - 17:30Room #056 (Mathematics building)
山田 澄生 (東北大・大学院理学研究科・理学部
数学専攻)
"特異点を持つ極小部分多様体の変分原理"
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは
今までによく知られている現象である。幾何学的測度論は、それらの特異点
を許容する存在定理の枠組みを提供する為に発展してきた。こうして
現れる部分集合の幾何学的特徴付けを、写像の持つエネルギー関数の最小化というJ.Douglas
の方法論を発展させることによって試みる。また特異点周辺の面積密度の
単調性公式についても言及したい。
16:30 - 18:00Room #126 (Mathematics building)
Chongying Dong (UC Santa Cruz)
"On uniqueness of the moonshine vertex operator algebra"
16:00 - 17:30Room #056 (Mathematics building)
山田 澄生
(東北大学・大学院理学研究科)
"特異点を持つ極小部分多様体の変分原理"
与えられた境界を持つ極小部分集合に特異点が必然的に現れることは今までによく知られている現象である.幾何学的測度論は,それらの特異点を許容する存在定理の枠組みを提供する為に発展してきた.こうして現れる部分集合の幾何学的特徴付けを,写像の持つエネルギー関数の最小化というJ.Douglas の方法論を発展させることによって試みる.また特異点周辺の面積密度の単調性公式についても言及したい.
2006/12/13
10:30 - 11:30Room #056 (Mathematics building)
C. M. Elliott (University of Sussex)
"Computational Methods for Geometric PDEs"
Computational approaches to evolutionary geometric partial differential equations such as anisotropic motion by mean curvature and surface diffusion are reviewed. We consider methods based on graph, parametric , level set and phase field descriptions of the surface. We also discuss the approximation of partial differential equations which hold on the evolving surfaces. Numerical results will be presented along with some approximation results.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
17:30 - 19:00Room #118 (Mathematics building)
関根 順 (京都大)
"動的なファンドプロテクションと最適化について"
2006/12/12
16:30 - 18:00Room #056 (Mathematics building)
Maxim Kazarian (Steklov Math. Institute)
"Thom polynomials for maps of curves with isolated singularities
(joint with S. Lando)"
Thom (residual) polynomials in characteristic classes are used in
the analysis of geometry of functional spaces. They serve as a
tool in description of classes Poincar\'e dual to subvarieties of
functions of prescribed types. We give explicit universal
expressions for residual polynomials in spaces of functions on
complex curves having isolated singularities and
multisingularities, in terms of few characteristic classes. These
expressions lead to a partial explicit description of a
stratification of Hurwitz spaces.
2006/12/11
10:30 - 12:00Room #128 (Mathematics building)
相原義弘 (沼津高専)
"Modified deficiencies of holomorphic curves and defect relation"
2006/12/08
10:30 - 12:00Room #056 (Mathematics building)
Charles M. Elliott (University of Sussex)
"Computational Methods for Surface Partial Differential Equations"
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.
We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\Gamma$ in $\mathbb R^{n+1}$. The key idea is based on the approximation of $\Gamma$ by a polyhedral surface $\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\Phi$ whose zero level set is $\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.
Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
15:00 - 16:25Room #126 (Mathematics building)
Stefan Kebekus 氏 (Mathematisches Institut
Universität zu Köln
)
"Rationally connected
foliations"
2006/12/07
13:00 - 14:30Room #056 (Mathematics building)
Charles M. Elliott (University of Sussex)
"Computational Methods for Surface Partial Differential Equations"
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.
We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\Gamma$ in $\mathbb R^{n+1}$. The key idea is based on the approximation of $\Gamma$ by a polyhedral surface $\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\Phi$ whose zero level set is $\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.
Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
http://www.u-tokyo.ac.jp/campusmap/map02_02_j.html
16:30 - 18:00Room #126 (Mathematics building)
山下真 (東大数理)
"An introduction to analytic endomotives (after Connes-Consani-Marcolli)"
2006/12/06
10:30 - 11:30Room #056 (Mathematics building)
横山悦郎 (学習院大学)
"Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model "
Chondrules are small particles of silicate material of the order of a few millimeters in radius, and are the main component of chondritic meteorite.
In this paper, we present a model of the growth starting from a seed crystal at the location of an outer part of pure melt droplet into spherical single crystal corresponding to a chondrule. The formation of rims surrounding a chondrule during solidification is simulated by using the phase field model in three dimensions. Our results display a well developed rim structure when we choose the initial temperature of a melt droplet more than the melting point under the condition of larger supercooling. Furthermore, we show that the size of a droplet plays an important role in the formation of rims during solidification.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
16:30 - 18:45Room #117 (Mathematics building)
Vincent Maillot (Jussieu/京大数理研) 16:30 - 17:30
"New applications of the arithmetic Riemann-Roch theorem"
Don Blasius (UCLA) 17:45 - 18:45
"Zariski Closures of Automorphic Galois Representations"
15:00 - 16:10Room #128 (Mathematics building)
Stefano IACUS (Department of Economics Business and Statistics, University of Milan, Italy)
"Inference problems for the standard and geometric telegraph process"
The telegraph process {X(t), t>0}, has been introduced (see Goldstein, 1951) as an alternative model to the Brownian motion B(t). This process describes a motion of a particle on the real line which alternates its velocity, at Poissonian times, from +v to -v. The density of the distribution of the position of the particle at time t solves the hyperbolic differential equation called telegraph equation and hence the name of the process. Contrary to B(t) the process X(t) has finite variation and continuous and differentiable paths. At the same time it is mathematically challenging to handle.
In this talk we will discuss inference problems for the estimation of the intensity of the Poisson process, either homogeneous and non homogeneous, from continuous and discrete time observations of X(t). We further discuss estimation problems for the geometric telegraph process S(t) = S(0) * exp{m - 0.5 * s^2) * t + s X(t)} where m is a known constant and s>0 and the intensity of the underlying Poisson process are two parameter of interest to be estimated. The geometric telegraph process has been recently introduced in Mathematical Finance to describe the dynamics of assets as an alternative to the usual geometric Brownian motion.
For discrete time observations we consider the "high frequency" approach, which means that data are collected at n+1 equidistant time points Ti=i * Dn, i=0,1,..., n, n*Dn = T, T fixed and such that Dn shrinks to 0 as n increases.
The process X(t) in non Markovian, non stationary and not ergodic thus we use approximation arguments to derive estimators. Given the complexity of the equations involved only estimators on the standard telegraph process can be studied analytically. We will also present a Monte Carlo study on the performance of the estimators for small sample size, i.e. Dn not shrinking to 0.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/16.html
2006/12/04
16:30 - 18:00Room #126 (Mathematics building)
Professor Burt Totaro
(University of Cambridge)
"
When does a curve move on a surface, especially over a finite field?
"
10:30 - 12:00Room #128 (Mathematics building)
伊師英之 (横浜市立大学)
"Invariant CR-Laplacian type operator on the Silov boundary of a Siegel domain of rank one"
2006/12/02
13:30 - 14:30Room #117 (Mathematics building)
村上 修一 (東大物工)
"Spin Hall effect in metals and in insulators"
We theoretically predicted that by applying an electric field
to a nonmagnetic system, a spin current is induced in a transverse
direction [1,2]. This is called a spin Hall effect. After its
theoretical predictions on semiconductors [1,2], it has been
extensively studied theoretically and experimentally, partly due
to a potential application to spintronics devices.
In particular, one of the topics of interest is quantum spin
Hall systems, which are spin analogues of the quantum Hall systems.
These systems are insulators in bulk, and have gapless edge states
which carry a spin current. These edge states are characterized
by a Z_2 topological number [3] of a bulk Hamiltonian.
If the topological number is odd, there appear gapless edge states
which carry spin current. In my talk I will briefly review the
spin Hall effect including its experimental results and present
understanding. Then I will focus on the quantum spin Hall systems,
and explain various properties of the Z_2 topological number and
its relation to edge states.
[1] S. Murakami, N. Nagaosa, and S.-C. Zhang, Science 301, 1348 (2003).
[2] J. Sinova et al., Phys. Rev. Lett. 92, 126603 (2004)
[3] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802, 226801 (2005)
15:00 - 16:00Room #117 (Mathematics building)
Yshai Avishai (Ben-Gurion Univ. , 東大物工)
"Disorder in Quantum Spin Hall Systems"
The quantum spin Hall phase is a novel state of matter with
topological properties. It might be realized in graphene and
probably also in type III semiconductors quantum wells.
Most recent theoretical treatments of this phase discuss its
occurrence in clean systems with perfect crystal symmetry.
In this seminar I will report on a recent work (in collaboration
with N. Nagaosa and M. Onoda) on disordered quantum spin Hall
systems. Following a brief introduction and background I will
discuss the persistence of topological terms also in disordered
systems (following a recent work of Sheng and Haldane) and
then present our results on the localization problem in two
dimensional systems. Due to spin-orbit interaction, there
is a metallic phase as is well known
for the symplectic ensemble. Together with the existence of
a topological term it leads to some surprising results regarding
the scaling theory of localization.
2006/12/01
16:00 - 18:00Room #126 (Mathematics building)
竹崎正道 (UCLA)
"von Neumann 環上の群作用"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm
16:30 - 17:30Room #123 (Mathematics building)
James McKernan (UC Santa Barbara)
"Finite generation of the canonical ring"
One of the most fundamental invariants of any smooth projective variety is the canonical ring, the graded ring of all global pluricanonical holomorphic n-forms. We explain some of the recent ideas behind the proof of finite generation of the canonical ring and its connection with the programme of Iitaka and Mori in the classification of algebraic varieties.
2006/11/30
16:00 - 18:00Room #126 (Mathematics building)
竹崎正道 (UCLA)
"von Neumann 環上の群作用"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm
2006/11/29
10:30 - 11:30Room #056 (Mathematics building)
塚本 史郎 (東京大学生産技術研究所)
"Atomistic view of InAs quantum dot self-assembly from inside the growth chamber"
A 'quantum dot' is a tiny region of a solid, typically just nanometres in each direction, in which electrons can be confined. Semiconductor quantum dots are the focus of intense research geared towards exploiting this property for electronic devices. The most economical method of producing quantum dots is by self-assembly, where billions of dots can be grown simultaneously. The precise mechanism of self-assembly is not understood and is hampering efforts to control the characteristics of the dots. We have used a unique microscope to directly image semiconductor quantum dots as they are growing, which is a unique scanning tunnelling microscope placed within the molecular beam epitaxy growth chamber. The images elucidate the mechanism of InAs quantum dot nucleation on GaAs(001) substrate, demonstrating directly that not all deposited In is initially incorporated into the lattice, hence providing a large supply of material to rapidly form quantum dots via islands containing tens of atoms. kinetic Monte Carlo simulations based on first-principles calculations show that alloy fluctuations in the InGaAs wetting layer prior to are crucial in determining nucleation sites.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
16:00 - 18:00Room #122 (Mathematics building)
竹崎正道 (UCLA)
"von Neumann 環上の群作用"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm
17:30 - 19:00Room #118 (Mathematics building)
楠岡 成雄 (東京大)
"Gaussian K-Scheme について"
2006/11/28
16:00 - 18:00Room #122 (Mathematics building)
竹崎正道 (UCLA)
"von Neumann 環上の群作用"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm
17:00 - 18:00Room #056 (Mathematics building)
芥川 和雄 (東京理科大学理工学部)
"The Yamabe constants of infinite coverings and a positive mass theorem"
The {\it Yamabe constant} $Y(M, C)$ of a given closed conformal manifold
$(M, C)$ is defined by the infimum of
the normalized total-scalar-curavarure functional $E$
among all metrics in $C$.
The study of the second variation of this functional $E$ led O.Kobayashi and Schoen
to independently introduce a natural differential-topological invariant $Y(M)$,
which is obtained by taking the supremum of $Y(M, C)$ over the space of all conformal classes.
This invariant $Y(M)$ is called the {\it Yamabe invariant} of $M$.
For the study of the Yamabe invariant,
the relationship between $Y(M, C)$ and those of its conformal coverings
is important, the case when $Y(M, C)> 0$ particularly.
When $Y(M, C) \leq 0$, by the uniqueness of unit-volume constant scalar curvature metrics in $C$,
the desired relation is clear.
When $Y(M, C) > 0$, such a uniqueness does not hold.
However, Aubin proved that $Y(M, C)$ is strictly less than
the Yamabe constant of any of its non-trivial {\it finite} conformal coverings,
called {\it Aubin's Lemma}.
In this talk, we generalize this lemma to the one for the Yamabe constant of
any $(M_{\infty}, C_{\infty})$ of its {\it infinite} conformal coverings,
under a certain topological condition on the relation between $\pi_1(M)$ and $\pi_1(M_{\infty})$.
For the proof of this, we aslo establish a version of positive mass theorem
for a specific class of asymptotically flat manifolds with singularities.
16:30 - 18:00Room #052 (Mathematics building)
打越 敬祐 (防衛大学校)
"非圧縮性完全流体の特異初期値問題"
題材は流体力学ですが,内容的には超局所解析の考え方を駆使する問題
http://agusta.ms.u-tokyo.ac.jp/alganalysis.html
2006/11/27
10:30 - 12:00Room #128 (Mathematics building)
Aleksandr G. Aleksandrov (Institute for Control Sciences, Moscow)
"Logarithmic connections along Saito free divisors"
We develop an approach to the study of meromorphic connections with logarithmic poles along a Saito free divisor. In particular, basic properties of Christoffel symbols of such connections are established. We also compute the set of all integrable meromorphic connections with logarithmic poles and describe the corresponding spaces of horizontal sections for some examples of Saito free divisors including the discriminants of the minimal versal deformations of $A_2$- and of $A_3$-singularities, and a divisor in ${\bf C}^3$ which appeared in a work of M. Sato in the context of the theory of prehomogeneous spaces.
16:00 - 18:00Room #122 (Mathematics building)
竹崎正道 (UCLA)
"von Neumann 環上の群作用"
http://www.ms.u-tokyo.ac.jp/~yasuyuki/mt.htm
2006/11/24
16:30 - 17:30Room #123 (Mathematics building)
佐々真一 (東京大学・大学院総合文化研究科)
"ゆらぎをめぐる風景"
「ゆらぎ」とは、決まった規則がないままにゆらゆらと漂っているさまをあわらしている。わたしたちは、明確な動きの背後には規則があると自然に信じ、その規則を探ろうとするが、「ゆらゆら」に特別の意味をみようとしないだろう。ところで、それがゆえに、「ゆらゆら」の背後に何らかの構造が埋まっていることがわかったときには、衝撃が一段と大きい。
ゆらぎから新しい構造を抜き出した例を並べると、理論物理学史のひとつの断片ができる。講演前半部分では、このなかから20世紀前半のふたりの研究成果をアレンジしながら紹介したい。そのふたりとは、アインシュタインとオンサーガである。ゆらぎと対峙することで、マクロ側の普遍的法則を抽出し、直接みることができないミクロ側の性質を暴いた。これらの成果を踏まえて、講演後半部分では、ゆらぎの背後に新しい構造を見出そうとするわたしたちの最近の試みを紹介したい。
2006/11/22
16:20 - 17:30Room #128 (Mathematics building)
鎌谷 研吾 (東京大学大学院数理科学研究科)
"A Note on Haplotype Estimation"
Haplotype information is important for many analyses but it is not always possible to obtain. This work is motivated to seek haplotype information from diploid population data. We present a new approach to know the haplotype information using classical methods. We do not intend to say that our method is better than the well-known EM based approache for practical purposes, but our way is attractive in some sense.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/15.html
2006/11/21
16:30 - 17:30Room #122 (Mathematics building)
Henrik SHAHGHOLIAN (王立工科大学、ストックホルム)
"Composite membrane and the structure of the singular set"
In this talk we present our study of the behavior of the singular set
$\{u=|\nabla u| =0\}$ for solutions $u$ to the free boundary problem
$$
\Delta u = f\chi_{\{u\geq 0\} } -g\chi_{\{u<0\}},
$$
where $f$ and $g$ are H\"older continuous functions, $f$ is positive and $f+g$ is negative. Such problems arise in an eigenvalue optimization for composite membranes.
We show that if for a singular point $z$ there are $r_0>0$, and $c_0>0$ such that the density assumption
$|\{u< 0\}\cap B_r(z)|\geq c_0 r2 \forall r< r_0$
holds, then $z$ is isolated.
2006/11/20
10:30 - 12:00Room #128 (Mathematics building)
野口潤次郎 (東大数理)
"Advances and examples in the value distribution theory"
2006/11/18
16:30 - 18:00Room #123 (Mathematics building)
安 大玉 (東京大学大学院人文社会系研究科、東アジア思想文化)
"17 世紀西洋実用幾何学の東伝と徐光啓の数学観
─『測量法義』『測量異同』『句股義』を中心として─"
『測量法義』『測量異同』『句股義』は、いずれも 1607 年イエズス会士宣教師マテオ・リッチ(漢名:利瑪竇)と徐光啓によって刊行された『幾何原本』に続いて刊行された測量法および句股術に関する実用数学書である。『幾何原本』が演繹論理にもとづく“度数の宗”といわれる理論書であるのに対し、これら三部作は、いずれも実用レベルの応用数学の範疇に属するものである。
(1)『測量法義』は、西洋の測量用の観測機器である象限義(geometric quadrant)による測高・測深・測遠の方法を中心に西洋の測量術を紹介した書物である。
(2)『測量異同』は、呉敬の『九章算法比類大全』から六つの類型の問題を抽出し、その解法を通じて西法と中法の異同を論じる小論である。
(3)『句股義』は、中法と西法の比較を経て、中法の欠点として「ただ解法を知るのみで、その義は知らない(第能言其法、不能言其義也)」ことを取り上げ、選別された 15 問について、その“義”を論じたものである。
今回の報告は、かかる三部作の内容分析を通じて、徐光啓の三部作構想の狙いがどこにあるかを明らかにし、また三部作のもつ意義を考えてみたい。
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.
13:30 - 14:30Room #117 (Mathematics building)
岩尾慎介 (東大数理)
"離散周期戸田方程式の解の超離散化による周期箱玉系の初期値問題の解法"
周期境界条件をもつ箱玉系の初期値問題の解は、周期境界条件を持つ離散方程式の解を超離散化することによって得られる。離散方程式の解は、あるリーマン面上のアーベル積分を用いて表現される。このリーマン面の周期行列を直接超離散化することによって、任意の初期状態の箱玉系の基本周期を得ることができる。
15:00 - 16:00Room #117 (Mathematics building)
土谷洋平 (東大数理)
"積分変換の項を持つソリトン方程式とその解の構造について"
ソリトン方程式の中には特異積分変換の項を持つIntermediate long wave, Benjamin-Ono, intermediate nonlinear Schr\"{o}dinger などの方程式がある。これらの方程式は,適当な条件の下で微差分系(関数微分方程式)に書き換えると佐藤理論の枠組みで捉えることができるようになる。このような方法を中心に現在分かっていることと問題点を紹介したい。
2006/11/17
15:00 - 16:10Room #118 (Mathematics building)
清水 泰隆 (大阪大学大学院基礎工学研究科)
"Functional estimation of L'evy measure for jump-type processes"
Recently, stochastic processes with Poissonian jumps are frequently used in finance and insurance. In their applications, it often becomes important to estimate some functionals of integral types with respect to L'evy measures. In this talk, we propose a nonparametric estimator of their functionals based on both continuous and discrete observations. If time permits, we shall also mention the application to the mathematical insurance, in particular, the estimates of ruin probabilities for genelarized risk processes.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
2006/11/16
16:30 - 18:00Room #118 (Mathematics building)
Pierre Berthelot (Rennes大学)
"Crystalline complexes and D-modules"
16:00 - 17:30Room #056 (Mathematics building)
奈良 光紀 (東京工業大学)
"The large time behavior of graphical surfaces in the mean curvature flow"
We are interested in the large time behavior of a surface in the whole space moving by the mean curvature flow. Studying the Cauchy problem on $R^{N}$, we deal with moving surfaces represented by entire graphs. We focus on the case of $N=1$ and the case of $N\geq2$ with radially symmetric surfaces. We show that the solution converges uniformly to the solution of the Cauchy problem of the heat equation, if the initial value is bounded. Our results are based on the decay estimates for the derivatives of the solution. This is a joint work with Prof. Masaharu Taniguchi of Tokyo Institute of Technology.
16:30 - 18:00Room #126 (Mathematics building)
戸松玲治 (東大数理)
"商型右余イデアルの特徴づけとポワソン境界の分類"
2006/11/15
16:30 - 18:00Room #117 (Mathematics building)
Pierre Berthelot (Rennes大学)
"Crystalline complexes and D-modules"
17:30 - 19:00Room #118 (Mathematics building)
塚原 英敦 (成城大)
"歪みリスク尺度の1-パラメータ族とその応用"
2006/11/14
16:30 - 18:00Room #056 (Mathematics building)
高瀬将道 (信州大学理学部)
"High-codimensional knots spun about manifolds"
The spinning describes several methods of constructing higher-dimensional knots from lower-dimensional knots.
The original spinning (Emil Artin, 1925) has been generalized in various ways. Using one of the most generalized forms of spinning, called "deform-spinning about a submanifold" (Dennis Roseman, 1989), we analyze in a geometric way Haefliger's smoothly knotted (4k-1)-spheres in the 6k-sphere.
2006/11/13
10:30 - 12:00Room #128 (Mathematics building)
小野 肇 (東京工業大学)
"Sasaki-Futaki invariant and existence of Einstein metrics on toric Sasaki manifolds"
16:30 - 18:00Room #126 (Mathematics building)
青木昌雄 (京大数理研)
"Hom stacks and Picard stacks"
2006/11/10
16:00 - 17:30Room #056 (Mathematics building)
中島啓 (京都大学大学院理学研究科)
"箙多様体のベッチ数の計算"
箙多様体の S^1 作用に関する固定点は, 次数付き箙多様体と呼ばれる. そのベッチ数の母関数は, 量子ループ代数の q-指標の t-類似と呼ばれ, 表現論的に大切な対象である. このベッチ数を, 仮想ホッジ多項式と, 箙多様体の stratified グラスマン束の構造を用いて計算するアルゴリズムを紹介する. 時間があれば, 大型計算機による計算結果についても紹介する.
17:40 - 19:00Room #118 (Mathematics building)
樋上和弘 (東京大学大学院理学系研究科 物理)
"WRT invariant for Seifert manifolds and modular forms"
We study the SU(2) Witten-Reshetikhin-Turaev invariant for Seifert manifold. We disuss a relationship with the Eichler integral of half-integral modular form and Ramanujan mock theta functions.
2006/11/09
16:30 - 18:00Room #126 (Mathematics building)
水田有一 (東大数理)
"Operator-algebraic superrigidity for SL_n(Z) II(Bekkaの論文の紹介)"
16:20 - 17:50Room #123 (Mathematics building)
S. Bloch (シカゴ大学)
"<連続講演> Graphs and motives"
2006/11/08
10:30 - 11:30Room #056 (Mathematics building)
Fredric Flin (Hokkaido University)
"Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation"
Snow, from its fall until its full melting, undergoes transformations of its microstructure with time. This process, named “metamorphism”, drastically influences its physical, thermal and mechanical properties and is of great interest in snow and ice sciences.
The recent possibility of acquiring 3D images of small snow samples opens new opportunities for investigating snow in details. For this purpose, we developed specific algorithms in order to extract the relevant geometrical and physical parameters from the imaged samples (e.g. normal and curvature fields, specific surface area). We then used these estimators to develop 3D models that simulate the time-lapse transformations of snow directly from an experimentally observed microstructure. These models, which can be checked with experiments in cold room, offer new outlooks for the study of snow metamorphism.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
16:20 - 17:50Room #123 (Mathematics building)
S. Bloch (シカゴ大学)
"<連続講演> Graphs and motives"
14:40 - 18:00Room #056 (Mathematics building)
梶原 健 (横浜国立大学大学院工学研究院応用数学) 14:40 - 16:10
"代数多様体の退化とトロピカル幾何"
トロピカル幾何について説明しながら,多様体の退化等との関係や既知の応用について,簡単に紹介します.また,具体的にトロピカル超曲面で記述される退化として,射影トーリック多様体の退化について説明します.ここで現れる退化トーリック多様体は,Alexeev 氏がアーベル多様体のモジュライ空間のコンパクト化の研究において導入した,安定トーリック多様体です.
西納 武男 (京都大学理学研究科数学教室) 16:30 - 18:00
"Counting problem in tropical geometry"
この講演ではここ数年進展したトロピカル曲線を用いたトーリック多様体上の正則曲線の数え上げについて解説したいと思います.
はじめにトロピカル曲線と正則曲線の関係について,正則曲線のアメーバを介して(Target spaceが複素2次元の場合に)直感的な説明を試みます.トロピカル曲線は実1次元のグラフ状の集合ですが,複素構造のような幾何学的対象の退化を考えると自然に現れます.その考えに基づき,トロピカル曲線がトーリック多様体の退化と自然に関わることと,その事実の数え上げへの応用についてお話ししたいと思います.時間があればディスクの数え上げの場合について,閉曲線の場合との関係などにも触れたいと思います.
16:20 - 17:30Room #128 (Mathematics building)
蛭川 潤一 (早稲田大学)
"LAN Theorem for Non-Gaussian Locally Stationary Processes and Their Discriminant and Cluster Analyses"
This talk is concerned with asymptotic inference for non-Gaussian locally stationary processes. Lucien LeCam established the most important and sophisticated foundation of the general statistical asymptotic theory. He introduced the concept of local asymptotic normality (LAN) for the likelihood ratio of general statistical models. Once LAN is proved, the asymptotic optimality of estimators and tests is described in terms of the LAN property. The techniques of statistical inference for stationary time series have been well established. However, stationary time series model is not plausible to describe the real world. One of the difficult problem when we deal with nonstationary processes is how to set up an adequate model. Otherwise, the observation in the future will bring no information for the present structure. Recently, Dahalhaus has proposed an important class of nonstationary processes, called locally stationary processes. Locally stationary processes have the time varying densities whose spectral structures smoothly change in time. In this talk, we first show the LAN results for locally stationary processes under the assumption of the non-Gaussianity. Then, we apply the LAN theorem to estimation and testing theory, non-Gaussian robustness and adaptive estimation. Our LAN theorem elucidates various non-Gaussian asymptotics. Next, we develop asymptotic theory for discriminant and cluster analyses of non-Gaussian locally stationary processes. We discuss about non-Gaussian robustness of our classification statistic. Furthermore, we execute the clustering of stock returns in Tokyo Stock Exchanges. Consequently, we observe that the clustering results well extract features of relationships among companies.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/13.html
2006/11/07
16:20 - 17:50Room #123 (Mathematics building)
S. Bloch (シカゴ大学)
"<連続講演> Graphs and motives"
2006/11/06
10:30 - 12:00Room #128 (Mathematics building)
Mihai Paun (Université Henri Poincaré Nancy)
"On the extension of twisted pluricanonical forms"
2006/11/02
16:30 - 18:00Room #126 (Mathematics building)
水田有一 (東大数理)
"Operator-algebraic superrigidity for SL_n(Z) I(Bekkaの論文の紹介)"
16:00 - 17:30Room #056 (Mathematics building)
Messoud Efendiev (ミュンヘン工科大学)
"On attractor of Swift-Hohenberg equation in unbounded domain and its Kolmogorov entropy"
The main objective of the talk is to give a description of the large-time behaviour of solutions of the Swift-Hohenberg equation in unbounded domain.This will be done in terms of the global attractor. Here we encounter serious difficulties due to the lack of compactness of the embedding theorems and the interplay between the different topologies will play crucial role.We prove the existence of the global attractor and show that the restriction of the attractor to any bounded sets has an infinite fractal dimension and present sharp estimate for its Kolmogorov entropy.Spatio-temporal chaotic dynamics on the attractor will also be discussed.
2006/11/01
16:30 - 18:45Room #117 (Mathematics building)
G.Bayarmagnai (東大数理) 16:30 - 17:30
"Essential dimension of some finite group schemes"
Jacques Tilouine (パリ北大学) 17:45 - 18:45
"Overconvergent Siegel modular forms"
We recall what is known and what is conjectured on p-adic families of overconvergent Siegel modular forms. We show how this relates to a Fontaine-Mazur type conjecture on the classicality of certain overconvergent Siegel forms of genus 2. We explain few results known in this direction.
15:00 - 16:10Room #128 (Mathematics building)
Ilia NEGRI (Department of Management and Information Technology, University of Bergamo, Italy)
"Some problems related to the estimation of the invariant measure of an ergodic diffusion."
We consider a one dimensional ergodic diffusion process solution of a stochastic differential equation. We suppose that the diffusion coefficient is known whereas the drift coefficient $S$ is unknown. Our interest is the invariant measure of the process denoted as $\mu $. We denote by $f_S$ and $F_S$ the invariant density and the invariant distribution function of $\mu$ respectively. We present the problems of finding efficient estimators when we observe the trajectory of the diffusion in continuos time over $[0,T]$ and we study asymptotic properties of the estimators when $T$ goes to infinity.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/12.html
10:30 - 11:30Room #128 (Mathematics building)
Tan Yongji (School of Mathematical Science, Fudan University )
"A case study in petroleum industry: Mathematical modeling and numerical simulation in spontaneous potential well-logging"
Spontaneous well-logging is an important technique in petroleum exploitation. The potential field is of strong discontinuity on the interface since the spontaneous potential differences. It causes difficulty in mathematical analysis and numerical computing.
New mathematical model and numerical method is designed to overcome the difficulty and good results is obtained.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/10/31
16:30 - 18:00Room #126 (Mathematics building)
大島利雄氏 (東大数理)
"ルート系の部分系の分類"
ルート系 Ξ からルート系 Σ へのCartan整数を保つ写像の分類を考える(像は Σ の部分系と見なせる).
Σ のWeyl群(Σ の内部同型)で移りあうものを同値とみたときの分類をまず行い,
同値の条件をさらに Ξ の自己同型(部分系の分類に対応),Ξ の既約成分の自己同型の直積,
Σ の自己同型などを許すものに広げた場合の分類や像が放物型かどうかの判定も与える.
ルート系の dual pair の概念を定義し,同値類への Ξ の自己同型の作用の考察に用いる.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
16:30 - 18:00Room #056 (Mathematics building)
中村 信裕 (東京大学大学院数理科学研究科)
"Unsmoothable group actions on elliptic surfaces"
Let G be a cyclic group of order 3,5 or 7.
We prove the existence of locally linear G-actions on elliptic surfaces which can not be realized by smooth actions with respect to specific smooth structures.
To prove this, we give constraints on smooth actions by using gauge theory.
In fact, we use a mod p vanishing theorem on Seiberg-Witten invariants, which was originally proved by F.Fang.
We give a geometric alternative proof of this, which enables us to extend the theorem.
2006/10/30
16:30 - 17:30Room #128 (Mathematics building)
Matti Lassas (Helsinki University of Technology, Institute of Mathematics)
"Inverse Problems and Index Formulae for Dirac Operators"
We consider a selfadjoin Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M, g)$ with a nonempty boundary.
The operator $D_P$ is specified by a boundary condition $P(u|_{\partial M})=0$ where $P$ is a projector which may be a non-local, i.e. a pseudodifferential operator.
We assume the existence of a chirality operator which decomposes $L2(M, V)$ into two orthogonal subspaces $X_+ \oplus X_-$.
In the talk we consider the reconstruction of $(M, g)$, $V$, and $D_P$ from the boundary data on $\partial M$.
The data used is either the Cauchy data, i.e. the restrictions to $\partial M \times R_+$ of the solutions to the hyperbolic Dirac equation, or the boundary spectral data, i.e. the set of the eigenvalues and the boundary values of the eigenfunctions of $D_P$. We obtain formulae for the index and prove uniqueness results for the inverse boundary value problems. We apply the obtained results to the classical Dirac-type operator in $M\times \C4$, $M \subset \R3$. The presented results have been done in collaboration with Yaroslav Kurylev (Loughborough, UK).
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/10/26
16:30 - 18:00Room #126 (Mathematics building)
Remi Leandre (Univ. Bourgogne)
"Introduction to Brownian surfaces"
2006/10/25
17:00 - 18:00Room #117 (Mathematics building)
平之内 俊郎 (九州大学)
"Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 )"
局所体の拡大とその付値環の或る商である"truncated" dvrの拡大の圏を比較する. 不分岐拡大と剰余体の拡大が一対一対応するのと同じ様に, 分岐に関する条件を加えれば,局所体と "truncated" dvr の拡大の圏が同値になる (Deligne).
今回は, 古典的な(上付き)分岐群の代わりにAbbes-斎藤による分岐群を用いて分岐に関する条件を与える. そして,この分岐群の Rigid 幾何的解釈を踏襲する事でDeligneの定理の剰余体が非完全な場合への一般化が得られる事を述べる.
16:30 - 18:00Room #122 (Mathematics building)
Heinz W. Engl (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences)
"Regularization of nonlinear inverse problems: mathematics, industrial application fields, new challenges"
Motivated by some of the industrial examples presented in the first talk, we outline the theory of regularization methods for the stable solution of nonlinear inverse problems. Then, we turn to some new problem fields of possible future industrial relevance in systems and molecular biology.
2006/10/24
16:30 - 18:00Room #056 (Mathematics building)
Marco Zunino (JSPS, University of Tokyo)
"A review of crossed G-structures"
We present the definition of "crossed structures" as introduced by Turaev and others a few years ago. One of the original motivations in the introduction of these structures and of the related notion of a "Homotopy Quantum Field Theory" (HQFT) was the extension of Reshetikhin-Turaev invariants to the case of flat principal bundles on 3-manifolds. We resume both this aspect of the theory and other applications in both algebra and topology and we present our results on the algebraic structures involved.
16:30 - 18:00Room #052 (Mathematics building)
吉野 邦生 (上智大理工)
"Asymptotic expansions of solutions to heat equations with genelarized function initial value (岡康之氏との共同研究)"
http://agusta.ms.u-tokyo.ac.jp/alganalysis.html
2006/10/23
14:40 - 18:00Room #056 (Mathematics building)
Naichung Conan Leung (Chinese University of Hong Kong) 14:40 - 16:10
"Toric geometry and Mirror Symmetry "
We first review the geometry of toric varieties. Then we will explain the SYZ mirror symmetry conjecture and how toric geometry plays an important role here.
Xiaowei Wang (Chinese University of Hong Kong) 16:30 - 18:00
"Balance point and stability of vector bundles over a projective manifold"
In this talk, we will start with some basic theory of GIT and symplectic quotient, then introduce various kind of stability of a holomorphic vector bundle over a projective manifold. As an application of the general theory, we will answer a question raised by Donaldson by showing that GIT stable vector bundle produces a sequence of balanced embedding of the underlying projective manifold to the Grassmanian.
10:30 - 12:00Room #128 (Mathematics building)
泊 昌孝 (日本大学文理学部)
"Classification of hypersurface simple K3 singularities -- 95 and others"
16:30 - 18:00Room #122 (Mathematics building)
Heinz W. Engl (Industrial Mathematics Institute, Kepler University, Linz and Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences )
"Mathematical modelling and numerical simulation: from iron and steel making via inverse problems to finance"
We first describe the industrial mathematics structure in linz, extending from basic research via graduate education to industrial collaboration. We then present a few projetcs from our experience, ranging from aspects of iron and steel processing via mathematical simulation and optimization in car industry to robust and fast pricing methods for financial derivates. Since some of the projects involve inverse problem, we give a first introduction into this field, which will be deepened in the second talk.
2006/10/21
13:30 - 14:30Room #117 (Mathematics building)
国場敦夫 (東大総合文化)
"組合せベーテ仮説とタウ関数"
組合せベーテ仮説ではベーテ根とベーテベクトルの代わりにその組合せ論的類似物として rigged configuration と highest pathを対象物とする.
これらは Kerov-Kirillov-Reshetikhin (KKR)全単射により1対1対応する.
今回のお話では rigged configuration に付随した超離散タウ関数を導入し,以下の性質,結果について(時間の許すところまで)紹介します.
アフィン・クリスタルのエネルギー関数に一致する.
超離散双線形方程式をみたす.
KKR全単射の明示公式を与える.
箱玉系の角転送行列に相当し,一般Nソリトン解を与える
周期的 highest pathでは超離散リーマンテータ関数になる.
(坂本玲峰氏,山田泰彦氏との共同研究)
15:00 - 16:00Room #117 (Mathematics building)
小森 靖 (名古屋大学) (名古屋大学多元数理)
"ルート系に付随した多重ゼータ関数とベルヌーイ多項式"
ルート系に付随した多重ゼータ関数とは E. Witten によって導入された半単純リー代数の既約表現に関するゼータ関数を松本氏が多変数化したものである. この視点から見るとリーマンゼータ関数は A_1 型であり, Euler-Zagier 多重ゼータ関数は A_n 型で適当な変数を 0 にしたものであるといえる.
講演では, 特殊値とその間の関係式, 関数関係式, 母関数および付随するベルヌーイ多項式の性質を紹介する予定である.
(松本耕二氏, 津村博文氏との共同研究)
2006/10/20
16:30 - 17:30Room #123 (Mathematics building)
新井 仁之 (東大・数理)
"視覚科学における数学的方法
"
眼球から入った視覚情報は,網膜から始まり LGN,そして脳内で処理が行われる.この講演で扱うのはこのうち網膜から主として大脳皮質の V1 野で加えられる視覚情報処理である.研究のキーワードは「錯視」.錯視は視覚の解明のための一つの重要な鍵と考えられており,100年以上前からさまざまな方法で研究されてきた.しかし未だ不明な点が多い.本講演では,視覚情報処理の離散ウェーブレットを用いた新しい非線形数理モデルを作り,それを用いて行った色や明暗の錯視発生のメカニズムに関する研究結果を述べる.
http://faculty.ms.u-tokyo.ac.jp/~seminar/colloquium.html
16:30 - 17:30Room #118 (Mathematics building)
Petr Kulish (Steklov Math. Inst.)
"Spin systems related to Temperley - Lieb algebra"
2006/10/19
16:30 - 18:00Room #126 (Mathematics building)
酒匂宏樹 (東大数理)
"A unique decomposition result for HT factors with torsion free core (Popa の論文の紹介)"
2006/10/18
16:30 - 18:45Room #117 (Mathematics building)
Fabrice Orgogozo (東大数理・Ecole Polytechnique de Paris) 16:30 - 17:30
"p-dimension of henselian fields: an application of Ofer Gabber's algebraization technique"
Kim Minhyong (Purdue大学・京大数理研) 17:45 - 18:45
"Fundamental groups and Diophantine geometry"
16:20 - 17:30Room #128 (Mathematics building)
松田 安昌 (東北大学大学院経済学研究科)
"Fourier analysis of irregularly spaced data on R^d"
1970年代にはじまった時系列解析の研究は、1変量時系列からはじまり、多変量時系列、空間系列、時空間系列へと対象が拡張されてきている。近年の空間系列、時空間系列の文献を調べてみれば、時系列と同じく等間隔に観測されたデータ(regularly spaced data) を前提としている場合が多い。しかし時系列とは異なり、空間系列ではランダムに散らばった地点で観測されたデータ (irregularly spaced data)を仮定する方が、応用範囲がひろい。そこで本発表では、irregularly spaced dataによる空間相関の推定問題を扱う。具体的にはデータを周波数領域に変換してスペクトルを推定する方法を提案し、推定量が一致性、漸近正規性を持つための条件を示す。本方法による東京地価データ分析例も紹介する。本研究は、矢島美寛教授(東京大学大学院経済学研究科)との共同研究です。
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/11.html
16:00 - 18:15Room #122 (Mathematics building)
E. Esteves (IMPA) 16:00 - 17:00
"
Jets of singular foliations and applications
to curves and their moduli spaces
"
F. Zak (Independent Univ. of Moscow) 17:15 - 18:15
"Dual varieties, ramification, and Betti numbers
of projective varieties
"
2006/10/17
16:30 - 18:00Room #056 (Mathematics building)
Arnaud Deruelle (University of Tokyo)
"Networking Seifert Fibered Surgeries on Knots (joint work with Katura Miyazaki and Kimihiko Motegi)"
We define a Seifert Surgery Network which consists of integral Dehn surgeries on knots yielding Seifert fiber spaces;here we allow Seifert fiber space with a fiber of index zero as degenerate cases. Then we establish some fundamental properties of the network. Using the notion of the network, we will clarify relationships among known Seifert surgeries. In particular, we demonstrate that many Seifert surgeries are closely connected to those on torus knots in Seifert Surgery Network. Our study suggests that the network enables us to make a global picture of Seifert surgeries.
2006/10/16
10:30 - 12:00Room #128 (Mathematics building)
Sebastien Boucksom (東大数理 JSPS研究員)
"Differentiability of the volume of divisors and Khovanskii-Teissier inequalities"
2006/10/12
16:30 - 18:00Room #126 (Mathematics building)
酒匂宏樹 (東大数理)
"保測同値関係の Haagerup property"
2006/10/11
16:20 - 17:30Room #128 (Mathematics building)
石川保志 (愛媛大学)
"Optimal stopping problem associated with jump-diffusion processes"
We study an optimal stopping problem of some performance function with respect to a jump-diffusion process.
2006/10/10
16:30 - 18:00Room #056 (Mathematics building)
Elmar Vogt (Frie Universitat Berlin)
"Estimating Lusternik-Schnirelmann Category for Foliations:A Survey of Available Techniques"
The Lusternik-Schnirelmann category of a space $X$ is the smallest number $r$ such that $X$ can be covered by $r + 1$ open sets which are contractible in $X$.For foliated manifolds there are several notions generalizing this concept, all of them due
to Helen Colman. We are mostly concerned with the concept of tangential Lusternik-Schnirelmann category (tangential LS-category). Here one requires a covering by open sets $U$ with the following property. There is a leafwise homotopy starting with the inclusion of $U$ and ending in a map that throws for each leaf $F$ of the foliation each component of $U \cap F$ onto a single point. A leafwise homotopy is a homotopy moving points only inside leaves. Rather than presenting the still very few results obtained about the LS category of foliations, we survey techniques, mostly quite elementary, to estimate the tangential LS-category from below and above.
2006/10/06
16:30 - 17:30Room #123 (Mathematics building)
石井 太 (国立社会保障・人口問題研究所)
"人口指標の精度について"
近年の急速な少子化の進行に伴い、出生率の動向への関心が高まっている。しかしながら、その指標が注目され、様々に論じられる中に、指標の持つ精度を度外視した議論なども見受けられる。人口統計は人口分析の中心となるデータソースであり、人口指標の精度は重要な問題であるが、わが国においてはこれまで比較的精度の高い人口統計が取得されてきたこともあり、それほど重視せず、確定的なものと捉えがちな傾向があったように思われる。一方では、近年、統計調査環境の悪化などもあり、各々の人口指標についてどこまで詳細な議論が可能なのか、指標の精度について理論的・実務的な観点からより深い認識を持つことが必要となってきている。
本報告では、出生率での具体例を中心に、さまざまな誤差の発生要因に応じた人口指標の評価について提示することとしたい。
2006/10/05
16:30 - 17:30Room #123 (Mathematics building)
成田誠 (Department of Mathematics, National Taiwan University)
"Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field"
We study global properties of Gowdy symmetric (the existence of a symmetry group with two-dimensional spacelike orbits) spacetimes with nonlinear scalar field, which naturally arises in modern cosmology based on superstring theory.
The system of the Einstein and scalar field equations becomes a system consisting of wave map and nonlinear wave equations in one space dimension. We prove a global existence theorem for this system. Also, asymptotic energy decay will be discussed.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2006/09/27
10:30 - 11:30Room #056 (Mathematics building)
Professor Vakhtang Kokilashvili (A. Razmadze Mathematical Institute, Georgian Academy of Science)
"Integral operators in the weighted Lebesgue spaces with a variable exponent"
We present a boundedness criteria of the maximal functions and the singular integral operators defined on Carleson curves in the weighted Lebesgue spaces with a variable exponent. There are also given the weighted estimates for the generalized singular integrals raised in the theory of generalized analytic functions of I.N.Vekua and the weighted Sobolev theorems for potentials on Carleson curves. The weight functions may be of power function type as well as oscillating type. The certain version of a Muckenhoupt-type condition for a variable exponent will be considered.
We also expect to treat two-weight problems for the classical integral operators in the variable Lebesgue spaces and to give some applications of the obtained results to the summability problems of Fourier series in two-weighted setting.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
16:30 - 17:30Room #123 (Mathematics building)
中丸麻由子 (東京工業大学)
"The coevolution of altruism and punishment:role of the selfish punisher"
Punishment is an important mechanism promoting the evolution of altruism among nonrelatives. We investigate the coevolution of altruism and punitive behavior, considering four strategies: a cooperator who punishes defectors (AP), a pure cooperator (AN), a defector who punishes defectors (selfish punisher or SP), and a pure defector (SN). We especially focus on the effects of SP on the coevolution of altruism and punishment, studying both the score-dependent viability model (whereby the game's score affects survivorship only) and the score-dependent fertility model (whereby the score affects fertility only). In the viability model of a completely mixed population, SP helps cooperators to evolve, but SP does not in the fertility model. In both models of a lattice-structured population, SP promotes the spread of AP, but AN discourages it. These results indicate that punishment is a form of spite behavior and that different models give different magnitude of advantage to spite behavior.
2006/09/25
13:00 - 14:10Room #128 (Mathematics building)
西山 陽一 (統計数理研究所)
"Nonparametric testing time-homogeneity for L'evy processes"
First, a review about uniform central limit theorems for martingales is given. The main part of the talk is concerned with a change point problem for L'evy processes. The null hypothesis is that the L'evy process is time-homogeneous, and the alternative is that the L'evy measure changes at a certain time point of the observation period. We propose an empirical process type statistics, and derive its asymptotic behaviour under the null and the alternative hypotheses. The limiting distribution under the null hypothesis is a functional of the standard Brownian motion.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/09.html
2006/09/13
13:00 - 16:45Room #123 (Mathematics building)
Andre' Martinez (Bologna University) 13:00 - 14:00
"On the determination of non-analytic resonances
(joint work with T.Ramond and J. Sjostrand)"
Nicolas Burq (Université de Paris Sud) 14:15 - 15:15
"Global existence for energy critical waves in 3-d domains
(joint work with G. Lebeau and F. Planchon)"
I will present some recent results obtained recently with G. Lebeau and F. Planchon. We prove that the energy critical (quintic) non linear wave equation in 3-d domains with Dirichlet boundary conditions is globally well posed for any initial data (with finite energy). I will give some hints about the proof of this result which is based on some recent results by Smith and Sogge on $L^p$ estimates for spectral projectors and a carefull study of the boundary value problem.
Vania Sordoni (Bologna University) 15:45 - 16:45
"On the Born-Oppenheimer approximation of wave-operators"
2006/09/11
16:30 - 18:00Room #128 (Mathematics building)
Claude-Alain Pillet (Univ. de Toulon et du Var)
"Operator-algebraic techniques in nonequilibrium statistical mechanics"
2006/09/06
16:30 - 17:30Room #128 (Mathematics building)
Bas Edixhoven (Univ. of Leiden)
"Computation of the mod l Galois representations associated to Delta"
2006/09/04
17:00 - 18:30Room #117 (Mathematics building)
Freddy Delbaen (ETH)
"Dynamic Risk Measures and Backward Stochastic Differential Equation
"
15:45 - 16:45Room #117 (Mathematics building)
楠岡成雄氏・梅澤祐二 (東京大)
"リスク尺度入門及び概説"
2006/08/25
16:30 - 17:30Room #128 (Mathematics building)
A. Marmora (パリ北大・東大/学振)
"p-adic local constants"
2006/08/22
15:30 - 16:40Room #128 (Mathematics building)
Jeannette H.C. WOERNER (University of Gottingen)
"A unifying approach to inference in semimartingale and long-memory models"
Over the recent years classical stochastic volatility models based on Brownian motion have been generalized in different ways, either replacing the Brownian motion by a pure jump Levy process, which leads to a pure jump model, or by a fractional Brownian motion, which makes it possible to model both long memory or turbulent behaviour. We consider robust and easily computable estimators for the inte- grated volatility, providing insight in the level of volatility, as needed for risk measurement and pricing of variance and volatility swaps. We discuss consistency and distributional results for the power and multi- power variation estimates based on high frequency data. Furthermore, we consider robustness against additive components and compare the results for the different classes of semimartingale and fractional Brow- nian motion models.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/07.html
16:50 - 18:00Room #128 (Mathematics building)
Delphine DAVID (Departement de Mathematiques, Universite de La Rochelle)
"A computation of Theta in a jump diffusion model by integration by parts"
Using Malliavin weights in a jump-diffusion model we obtain an expression for Theta (the sensitivity of an option price with respect to the time remaining until exercise), with application to non-smooth payoff functions. Optimal weights are computed by minimization of variance and numerical simulations are presented for digital and European options. Some results are also presented for Asian options. Our representation formula for Theta differs in general from the one obtained from the Black-Scholes PDE in terms of Delta and Gamma.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/08.html
2006/08/03
16:30 - 18:00Room #128 (Mathematics building)
George Elliott (University of Toronto)
"The Cuntz semigroup as an invariant for $C^*$-algebras"
2006/07/31
15:00 - 17:30Room #126 (Mathematics building)
Guster Olafsson (Louisiana State University) 15:00 - 16:00
"The Heat equation, the Segal-Bargmann transform and generalizations - II"
http://akagi.ms.u-tokyo.ac.jp/seminar.html
Boris Rubin (Louisiana State University) 16:30 - 17:30
"Radon transforms on Grassmannians and Matrix Spaces"
Diverse geometric problems in $R^N$ get a new flavor if a generic point $x=(x_1,...,x_N)$ is regarded as a matrix with appropriately organized entries (set, e.g., $x=(x_{i,j})_{n \times m}$ for $N=nm$). This well known observation has led to a series of breakthrough achievements in mathematics. In integral geometry it suggests a number of the so-called ``higher-rank" problems when such traditional scalar notions as ``distance", ``angle", and ``scaling" become matrix-valued. I will be speaking about Radon transforms on Grassmann manifolds and matrix spaces and some related problems of harmonic analysis where these phenomena come into play.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2006/07/25
16:30 - 18:00Room #126 (Mathematics building)
Boris Rubin (Louisiana State University)
"Radon Transforms: Basic Concepts"
How can we reconstruct a function on a manifold from integrals of this function over certain submanifolds?
This is one of the central problems in integral geometry and tomography, which leads to the notion of the Radon transform.
The first talk is of introductory character.
We discuss basic ideas of the original Radon's paper (1917), then proceed to the Minkowski-Funk transform and more general totally geodesic Radon transforms on the $n$-dimensional unit sphere.
The main emphasis is an intimate connection of these transforms with the relevant harmonic analysis.
We will see that Radon transforms of this type and their inverses can be regarded as members of analytic families of suitable convolution operators and successfully studied in the framework of these families.
I also plan to discuss an open problem of small divisors on the unit sphere, which arises in studying injectivity of generalized Minkowski-Funk transforms for non-central spherical sections.
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2006/07/24
16:30 - 17:30Room #056 (Mathematics building)
Boris Hasselblatt (Tufts University)
"Invariant foliations in hyperbolic dynamics:
Smoothness and smooth equivalence"
The stable and unstable leaves of a hyperbolic dynamical system are smooth and form a continuous foliation. Smoothness of this foliation sometimes constrains the topological type of the foliation, other times restricts at least the smooth equivalence class of the dynamical system, or for geodesic flows, the type of the underlying manifold. I will present a broad introduction as well as recent work, work in progress, and open problems.
http://faculty.ms.u-tokyo.ac.jp/~topology/
2006/07/20
16:30 - 18:00Room #052 (Mathematics building)
緒方芳子 (東大数理・学振)
"Linear response theory in quantum statistical mechanics"
16:30 - 18:00Room #126 (Mathematics building)
Guster Olafsson (Louisiana State University)
"The Heat equation, the Segal-Bargmann transform and generalizations - I"
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2006/07/19
16:20 - 17:30Room #128 (Mathematics building)
深澤 正彰 (東京大学大学院数理科学研究科)
"Edgeworth Expansion for Likelihood Analysis on Ergodic Diffusions with applications to Bootstrap"
We shall consider the maximal lilelihood estimator for the drift coefficient of a given one-dimensional diffusion. An Edgeworth expansion formula will be presented and verify a second-order correct confidence interval we shall newly propose. We are also going to mention the likelihood ratio statistic, which enjoys second-order correctness. There are Bootstrap methods closely related to the subject and introduced recently by the author. Some generalized results on those methods will be also introduced in this talk.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/06.html
2006/07/13
16:30 - 18:00Room #052 (Mathematics building)
小沢登高 (東大数理)
"Property (T) for universal lattices, after Y. Shalom"
I will talk on Shalom's recent result that
$SL_n(Z[X])$ ($n\geq 3$) has the property (T).
The talk should be elementary.
2006/07/12
16:30 - 17:30Room #117 (Mathematics building)
桜井 真 (東京大学理学系研究科)
"Beilinson-Drinfeld chiral algebra, geometric Langlands program and open Gromov-Witten invariants"
都合により、とりやめになりました。
18:30 - 20:00Room #118 (Mathematics building)
高岡 浩一郎 (一橋大)
"A complete-market generalization of the Black-Scholes model
"
10:30 - 11:30Room #056 (Mathematics building)
Piotr Rybka (Warsaw University)
"Analysis of a crystal growth model"
We are concerned with mathematical model of a single crystal growing from vapor. Mathematically this is an exterior, one-phase Stefan-type problem with Gibbs-Thomson law. We restrict our attention to an idealization of a ice crystal, i.e. our evolving free boundary is a circular cylinder. The system under consideration consists of an equation for the motion of the free boundary (the crystal surface) coupled to the quasi-steady approximation of the diffusion equation for the supersaturation of vapor. We present analysis of the system, we show well-posedness and draw the phase portrait, we use here the fact that we need just to variable to describe evolution of a cylinder.
We are mostly concerned with the shape-persitency problem of the
evolution. The problem is, the Gibbs-Thomson relation is in fact a
driven, weighted, mean, singular curvature flow and it is not obvious that the shape of the initial interface will persists throughout the evolution or even for some time. In order to solve this problem we show existence of the region in the phase plane which is a neighborhood of a unique steady state, such that in this region the shape of the cylinder is preserved. However, this set is not invariant with respect to dynamics of the problem.
It is a very interesting question what happens to surface of our crystal at the boundary of the shape-persitency (or shape stability) region. This problem in its full generality is open. However, we give some insight by studying the Gibbs-Thomson relation with a given driving, which inherits properties of the coupling to the diffusion field. We study the resulting driven weighted mean curvature flow for graphs and some special closed Lipschitz curves. We show well-posedness of the problem, but mainly we exhibit the phenomenon of bending flat parts of the curve, which grow ``too big''.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/07/11
17:00 - 18:30Room #056 (Mathematics building)
野田健夫 (秋田大学工学資源学部)
"全葉層の存在について(浅岡正幸,Emmanuel Dufraineとの共同研究)"
n次元多様体上のn個の余次元1葉層構造の組で、n個の葉層構造の接空間の共通部分が各点で0になるものを全葉層と呼ぶ。3次元の場合においては任意の有向閉多様体上に全葉層が存在することが Hardorpによって示されていた。3次元多様体上の全葉層をなす各々の葉層構造の接平面場は互いにホモトピックでありオイラー類が0になることが容易に分かるが、逆にオイラー類が0の平面場を与えたときそれを実現する全葉層が存在するかという問題が自然に生じる。
本講演ではこの問題に肯定的な解決をあたえる。
また、この結果の応用として双接触構造、すなわち横断的に交わる正と負の接触構造の組の存在問題にも触れたい。
http://faculty.ms.u-tokyo.ac.jp/~topology/
16:30 - 18:00Room #126 (Mathematics building)
縫田 光司 (産業技術総合研究所)
"On the isomorphism problem of Coxeter groups and related topics "
コクセター群について、そのコクセター系としての同型類がコクセターグラフと一対一対応することは周知の事実であるが、一方で抽象群としての同型類は(ワイル群の場合に限っても)そのような対応をしていない。今回は、この同型類の決定問題について、その歴史のあらまし(特に、無限群も含めた一般の場合について、10年ほど前まで殆ど何の結果も得られていなかったことは特筆に価する)と、近年の研究の進展状況を、具体例や関連する結果を交えつつ紹介する。
http://akagi.ms.u-tokyo.ac.jp/seminar.html
2006/07/10
10:30 - 12:00Room #128 (Mathematics building)
Do Duc Thai (Hanoi教育大)
"Characterization of domains in $C^n$ by their noncompact automorphism groups"
In this talk, the characterization of domains in $C^n$ by their noncompact automorphism groups are given. By this characterization, the Bedford-Pinchuk theorem is true for any domain (not necessary bounded) in $C^n$.
2006/07/08
13:30 - 15:45Room #123 (Mathematics building)
伴 克馬 (東京大学大学院数理科学研究科) 13:30 - 14:30
"Rankin-Cohen-Ibukiyama operators for holomorphic automorphic forms on type I symmetric domains"
谷口 隆 (東京大学大学院数理科学研究科) 14:45 - 15:45
"On Dirichlet series counting cubic alegebras"
2006/07/07
16:30 - 17:30Room #123 (Mathematics building)
重定 南奈子 (同志社大学)
"周期的変動環境下における侵入生物の時空間パターンと伝播速度"
侵入生物の空間的な伝播に関する数理的研究は,Fisher (1937)の先駆的研究以来,外来植物や昆虫,伝染病などの侵入を中心に,主として一様な空間における拡散増殖モデルを用いて進められてきた.しかし,実際の自然環境は,森,林,河川,道路などの,生物にとって好適な環境と不適な環境がパッチ状に入り混じっており,決して一様な空間とはいえない.
本研究では、帯状の好適生息地と不適な生息地が交互に配列する2次元縞状 分断環境の中を、侵入生物が分布拡大する過程を拡散係数と増殖率が好適生息 地と不適生息地で異なる拡張Fisher modelを用いて記述し、それを heuristicな方法を用いて解くことにより,侵入種の分布拡大パターン,ならびに,伝播速度の数学公式を導いた.
2006/07/06
17:00 - 18:30Room #123 (Mathematics building)
斎藤 憲 (大阪府立大学 人間社会学部)
"ユークリッドをめぐる最新の研究動向"
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html
16:30 - 18:00Room #052 (Mathematics building)
Rolf Dyre Svegstrup (東大数理)
"Endomorphisms of half-sided modular inclusions"
2006/07/05
10:30 - 11:30Room #056 (Mathematics building)
Y. H. Richard Tsai (University of Texas)
"Level Set Methods and Multi-valued solutions"
We review the level set methods for computing multi-valued
solutions to a class of nonlinear first order partial differential
equations, including Hamilton-Jacobi equations, quasi-linear
hyperbolic equations, and conservative transport equations with
multi-valued transport speeds.
The multivalued solutions are embedded as the zeros of a set of scalar functions that solve the initial value problems of a time dependent partial differential equation in an augmented space.
We discuss the essential ideas behind the techniques, the coupling of these techniques to the projection of the interaction of zero level sets and a collection of applications including the omputation of the semiclassical limit for Schr\"{o}dinger quations and the high frequency geometrical optics limits of linear wave equations.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2006/07/04
16:30 - 18:00Room #056 (Mathematics building)
Alexander A. Ivanov (Imperial College (London))
"Amalgams: a machinery of the modern theory of finite groups"
http://faculty.ms.u-tokyo.ac.jp/~topology/
2006/07/03
14:00 - 15:30Room #128 (Mathematics building)
Jörg Winkelmann (Université Henri Poincaré Nancy)
"Complex Semi-Abelian Varieties II --- Compactifications and etc."
2006/06/28
16:30 - 17:30Room #117 (Mathematics building)
原下秀士 (北海道大学・学振)
"Configuration of the central streams in the moduli of abelian varieties"
17:30 - 19:00Room #118 (Mathematics building)
楠岡 成雄 (東京大)
"転換社債の価格:均衡論的アプローチ"
10:30 - 11:30Room #056 (Mathematics building)
Jian Zhai (Zhejiang University)
"Uniqueness of Constant Anisotropic Mean Curvature Immersion of Sphere $S^2$ In $\Bbb E^3$"
We prove that the constant anisotropic mean curvature immersion of sphere $S^2$ in $\Bbb E^3$ is unique, provided that the energy density function $\gamma$ satisfies some reasonable assumptions.
2006/06/27
16:30 - 18:00Room #056 (Mathematics building)
Cedric Tarquini (Ecole Nomale Superieure of Lyon)
"Lorentzian foliations on 3-manifolds"
a joint work with C. Boubel (Ecole Nomale Superieure of Lyon) and P. Mounoud (University of Bordeaux 1 sciences and technologies)
The aim of this work is to give a classification of transversely Lorentzian one dimensional foliations on compact manifolds of dimension three. There are the foliations which admit a transverse pseudo-Riemanniann metric of index one. It is the Lorentzian analogue of the better known Riemannian foliations and they still have rigid transverse geometry.
The Riemannian case was listed by Y. Carriere and we will see that the Lorentzian one is very different and much more complicated to classify. The difference comes form the fact that the completness of the transverse structure, which is automatic in the Riemannian case, is a very strong hypothesis for a transverse Lorentzian foliation.
We will give a classification of complete Lorentzian foliations and some examples which are not complete. As a natural corollary of this classification we will list the codimension one timelike geodesically complete totally geodesic foliations of Lorentzian compact three manifolds.
2006/06/26
10:30 - 12:00Room #128 (Mathematics building)
織田孝幸 (東大数理)
"Toward construction of Green current for modular cycles in modular varieties"
2006/06/23
17:00 - 18:00Room #123 (Mathematics building)
Robert Gompf (University of Texas at Austin)
"25 years of exotic $\mathbb{R}^4s$"
A quarter century ago, 4-manifold theory was revolutionized by the Fields-Medal winning breakthroughs of Freedman and Donaldson, with Freedman showing that topological 4-manifolds behave like their higher dimensional counterparts, but Donaldson showing that smooth 4-manifolds behave in a completely different way. The interplay between these theories produces results unique to dimension 4: A fixed topological 4-manifold often admits infinitely many distinct smooth structures, for which no classification scheme is yet available. The quintessential example is that in contrast with other dimensions, Euclidean 4-space admits exotic smooth structures. That is, there are "exotic R^4s" homeomorphic to R4 but not diffeomorphic to it. We will survey what has been learned about these strange creatures in the last quarter century, and exhibit an explicit example.
2006/06/22
16:30 - 18:00Room #052 (Mathematics building)
Detlev Buchholz (Univ. Göttingen)
"Integrable models and operator algebras"
Recently, it has been possible to establish rigorously the existence of an abundance of 1+1-dimensional local nets of von Neumann algebras describing an interacting massive particle with factorizing scattering matrix. This novel approach is based on structural results in algebraic quantum field theory concerning the modular structure of such theories. It is thus complementary to the older methods of constructive quantum field theory and settles some longstanding questions in the context of integrable models (form-factor program). In this talk, a survey is given on basic ideas, results and perspectives of this promising new approach.
2006/06/21
16:20 - 17:30Room #128 (Mathematics building)
石川 保志 (愛媛大学理学部)
"Malliavin calculus applied to mathematical finance and a new formulation of the intgration-by-parts"
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/05.html
2006/06/19
10:30 - 12:00Room #128 (Mathematics building)
後藤竜司 (大阪大学)
"Deformations and smoothing of (generalized) holomorphic symplectic structures"
2006/06/15
16:00 - 17:30Room #056 (Mathematics building)
Mark Bowen (東京大学大学院数理科学研究科/日本学術振興会)
"Spreading and draining in thin fluid films"
The surface tension driven flow of a thin fluid film arises in a number of contexts. In this talk, we will begin with an overview of thin film theory and present a number of examples from the natural sciences and industrial process engineering. Similarity solutions play an important role in understanding the dynamics of general thin film motion and we shall use them to investigate the dynamics of an archetypal (degenerate high-order parabolic) thin film equation. In this context, we will encounter self-similarity of the first and second kind, undertake an investigation of a four-dimensional phase space and discover a surprisingly rich set of stable sign-changing solutions for the intermediate asymptotics of a generalised problem.
2006/06/14
10:30 - 11:30Room #056 (Mathematics building)
Qing-Ming Cheng (Saga University)
"Bounds on eigenvalues of Dirichlet aplacian"
In this talk, I shall consider the eigenvalue problem of the Dirichlet Laplacian. I shall mention the Weyl asymptotic formula,
Polya conjecture and its partial solution. Furthermore, I shall talk about Bochner-Kac problem.
For universal inequalities for eigenvalues, I shall consider
conjectures of Payne, Polya and Weinberger and their development. In the final, I shall talk the universal bounds for eigenvalues as main part of my talk, which is my recent joint work with rofessor Yang.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/06/13
16:30 - 18:00Room #056 (Mathematics building)
田中 心 (東京大学大学院数理科学研究科)
"A note on C1-moves"
鎌田氏によりチャートという概念が定義された。これは二次元円板上の 有向ラベル付きグラフであり、二次元ブレイドを記述する際に用いられる。 彼はチャートに対してC変形と呼ばれる三種類の変形(C1変形、C2変形、C3変形) を定義し、曲面ブレイドの同値類とチャートのC変形同値類の間に一対一対応が ある事を示した。 カーター氏と斎藤氏は、任意のC1変形は七種類の基本C1変形の列で得られる 事を示したが、その証明には曖昧な部分がある事が知られていた。本講演では 彼らとは異なるアプローチにより、彼らの主張に対して正しい証明を与える。
16:30 - 18:00Room #126 (Mathematics building)
織田 寛 (拓殖大学工学部)
"古典型複素Lie環の一般Verma加群に対する最小多項式"
古典型複素Lie環 g の自然表現から自然に定まる U(g) 係数の正方行列を F とする.g のスカラー一般Verma加群 $M_Θ(λ)$ に対して,複素モニック多項式 q(x) で q(F) の各成分が全て Ann $M_Θ(λ)$ に属するような最小次数のものを “$M_Θ(λ)$ の最小多項式” とよぶ.M(λ) を $M_Θ(λ)$ を商加群とするVerma加群とし,q(F) の各成分と Ann M(λ) が生成する U(g) の両側イデアルを $I_Θ(λ)$ とすると,最近
(1) 各λに対する $M_Θ(λ)$ の最小多項式の明示公式
(2) $M_Θ(λ)= M(λ)/I_Θ(λ)M(λ)$ が成り立つためのλの 必要十分条件
が得られた(これらは大島により g = gln の場合には既に得られている).セミナーでは(2)を示すための q(F) の各成分の Harish-Chandra 準同型像の計算法を主に説明する.
2006/06/12
10:30 - 12:00Room #128 (Mathematics building)
赤堀隆夫 (兵庫県立大学)
"The Rumin complex and Hamiltonian mechanism"
http://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf
2006/06/10
13:30 - 16:00Room #117 (Mathematics building)
Boris Feigin (Landau Institute for Theoretical Physics) 13:30 - 14:30
""Critical" level for Vertex Algebras"
In the talk I present the construction of "VOA" on a critical level using fermionic screenings.Then I discuss the geometric background behind such algebras and applications - Langlands correspondence and related things
坂井 穣 (北陸先端科学技術大学院大学) 15:00 - 16:00
"酸化物非線形素子とその展開"
半導体からなるダイオード、超伝導体からなるジョセフソン素子 などは、それぞれに特徴的な非線形電流電圧 (I-V) 特性をもつがゆえに素子としての機能を発現する。本講演では、主にセラミックス 材料からなるいくつかの薄膜素子において最近観測された、電界誘起金 属転移や不揮発性抵抗変化といった興味深い非線形 I-V 特性を 紹介し、それらをメモリやロジック素子へ展開する可能性を探る。
2006/06/07
14:00 - 15:00Room #270 (Mathematics building)
Youjin Zhang (Tsinghua Univ.)
"On deformations of bihamiltonian structures of hydrodynamic type"
I will talk about the properties of deformations bihamiltonian structures of hydrodynamic type and the related integrable hierarchies, and the problem of classification of such deformations.
10:30 - 11:30Room #056 (Mathematics building)
高坂 良史 (室蘭工業大学)
"On phase boundary motion by surface diffusion with triple junction"
The phase boundary motion by a geometrical evolution law in a bounded domain is studied in this talk. We consider the surface diffusion flow equation, which has the gradient flow structure with respect to $H^{-1}$-inner product and the area-preserving property. This equation was derived by Mullins to model the motion of interfaces in the case that the motion of interfaces is governed purely by mass diffusion within the interfaces. We study the three-phase problem with triple junction in a bounded domain and analyze the stability of the stationary solutions for this problem.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/022.html
16:30 - 17:30Room #117 (Mathematics building)
廣惠 一希 (東京大学大学院数理科学研究科)
"Hecke-Siegel's pull back formula for the Epstein zeta function with spherical"
16:00 - 18:00Room #002 (Mathematics building)
Marek FILA (Bratislava, スロバキア) 16:00 - 17:00
"Slow convergence to zero for a supercritical parabolic equation"
柴田 良弘 (早稲田大学・理工学部数理科学科) 17:00 - 18:00
"未定"
2006/06/06
16:30 - 18:00Room #056 (Mathematics building)
三好 重明 (中央大学理工学部)
"Thurston's inequality for a foliation with Reeb components"
The Euler class of a Reebless foliation or a tight contact structure on a closed 3-manifold satisfies Thurston's inequality, i.e. its (dual) Thurston norm is less than or equal to 1. It should be significant to study Thurston's inequality in both of foliation theory and contact topology. We investigate conditions for a spinnable foliation one of which assures that Thurston's inequality holds and also another of which implies the violation of the inequality.
13:30 - 14:30Room #117 (Mathematics building)
Leon Takhtajan (SUNY)
"A local index theorem for families of $\bar\partial$-operators and moduli of parabolic vector bundles"
We extend our previous work on local index theorem for families of $\bar\partial$-operators on punctured Riemann surfaces (Comm. Math. Phys. 137 (1991), 399-426) and for families of $\bar\partial$-operators on endomorphism bundles of stable vector bundles over a compact Riemann surface (Math. USSR Izvestia 35 (1990), 83-100) to the case of stable parabolic vector bundles over a Riemann surface. The result is an explicit formula for the first Chern form of the canonical line bundle to the moduli space stable parabolic bundles with the Quillen's type metric. The derivation uses Mehta-Seshadri theorem and spectral theory of automorphic functions on the Lobatchevsky plane with the unitary representation. This is a joint work with P. Zograf.
2006/06/05
10:30 - 12:00Room #128 (Mathematics building)
Wolfram Bauer (東京理科大)
"Integral formulas for infinite dimensional domains with arbitrary boundary"
http://www.ms.u-tokyo.ac.jp/~hirachi/scv/Bauer.pdf
2006/05/31
16:20 - 17:30Room #128 (Mathematics building)
津田 美幸 (統計数理研究所)
"Bhattacharyya inequality for quantum state estimation II"
前回導出した三種類(S型, R型, L型)の量子Bhattacharyya不等式を量子ガウス状態の複素振幅θの多項式g(θ)の推定問題に応用する. 量子ガウス状態は, レーザ光の量子状態の典型的なモデルであり, 量子光学や量子情報で重要な研究対象である. 未知の複素振幅θを推定する方法としては, θが実軸にある場合はホモダイン測定, 一般の複素数の場合はヘテロダイン測定が知られており, それぞれS型とR型の量子Cramer-Rao不等式の下限を達成するUMVUEである. さらにここでは, θが実数の場合に (1), (2)を示し, θが複素数の場合に (3), (4)を示す.
(1) g(θ)=θ^2に対するUMVUEは存在してS型Bhattacharyya下限を達成する. その推定量は, 物理系にスクイジングと呼ばれる操作を施した後の個数測定によって与えられる.
(2) g(θ)=θ^3に対するUMVUEは, 生成消滅作用素の多項式の形では存在しない.
(3) g(θ)が正則, 或いは反正則, ならば, ヘテロダイン測定によってUMVUEが与えられ, それぞれR型, L型のBhattacharyya下限を達成する.
(4) g(θ)が実数値ならば, ある測定によりUMVUEが与えられ, R型, L型両方の下限を達成する.
量子ガウス状態は古典の正規分布に似ている. しかし, 古典では, 平均の多項式は Hermite多項式により常にUMVUEを構成できるが, 量子では上記のように事情が異なる.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/04.html
2006/05/30
16:30 - 18:00Room #052 (Mathematics building)
山崎 晋 (日大理工)
"Fuchs 型偏微分方程式の超分布解に対する割算定理について"
16:30 - 18:00Room #056 (Mathematics building)
佐藤 隆夫 (東京大学大学院数理科学研究科)
"自由群の自己同型群のJohnson準同型の余核について"
本講演では,まず次数が2,3の場合に自由群の自己同型群の Johnson準同型の余核の構造を決定する.さらに,次数1の元たちが生成する部分に定義域を制限することで,奇数次のJohnson準同型の全射性に関して新しい障害が得られたことを紹介する.
2006/05/29
16:00 - 17:00Room #056 (Mathematics building)
池 周一郎 (帝京大学文学部社会学科)
"拡散モデルによる夫婦の子ども数の低下"
10:30 - 12:00Room #128 (Mathematics building)
Marco Brunella (Bourgogne)
"Uniformisation of Holomorphic Foliations by Curves II"
13:30 - 15:00Room #128 (Mathematics building)
大沢 健夫 (名古屋大学)
"Hodge theory with bounds and its application to foliations"
2006/05/27
13:30 - 16:00Room #117 (Mathematics building)
首藤 啓 (首都大学東京理工学研究科) 13:30 - 14:30
"複素WKB理論を用いた非可積分系の量子トンネル現象の解析"
インスタントン軌道により記述される1次元系のトンネル効果とは対照的に、多数の複素経路が関与することが非可積分系のトンネル効果の特徴である。
(1)簡単な離散写像系(エノン写像)においては,この複素軌道はジュリア集合と密接な関係があること、
(2)トンネル軌道の選別に,完全WKB解析の手法(特に高階微分方程式に対する)が有効であること、
などを示す。
南 和彦 (名古屋大学多元数理科学研究科) 15:00 - 16:00
"可解模型、特に six-vertex 模型におけるフラクタル構造と、確率過程との関連"
Six-vertex 模型は数理的には量子群、物質としては量子 XXZ スピン鎖に関連し、 Yang-Baxter 関係式によって対角化される可解模型の典型例である。この模型に現れるフラクタル構造、特に graph-directed IFS フラクタルについて議論し、確率過程その他との関連に言及する。
2006/05/25
16:30 - 18:00Room #052 (Mathematics building)
松井 宏樹 (千葉大・自然科学)
"カントール極小$Z^d$系のコホモロジー"
17:00 - 18:30Room #123 (Mathematics building)
佐藤 健一 (和算研究所)
"和算の遊び"
日本には飛鳥時代から数学が伝わり、律令制の中で多少の学習はされていたのであろうが、ほとんど発達する事もなく、ソロバンが伝わるまでは一部の計算を職業とする人を除けば無いに等しかったと思われる。数学が芽を吹き出したのは江戸時代になってからで、それ以前のソロバンのマニュアルとも考えられる『算用記』の類から脱却したのが『塵劫記』からと言われている。『塵劫記』は寛永4 年(1627)が初版であるが、ここでは、生活数学の本で、ソロバンを実生活での数の処理にどのように使うのかを丁寧に書いている。遊びは入っていない。それが、『塵劫記』の海賊版の刊行に対抗して次々と生活数学ではないものを取り入れていった。遊びもいくつも入ったのである。「入れ子算」「まま子立て」「ねずみ算」「からす算」「百五減算」「油分け算」「薬師算」「目付け字」などである。その後数学は遺題の継承が流行し、数学は発達する。関孝和や建部賢弘の時代では一般の人では全く理解出来ないレベルに到達した。関や建部は江戸で活動していたが、ほとんど同じ時代に関西では別の数学を考えて、書物にして発表していた。著者たちは関や建部と較べてもそれほど劣るという人ではなく、興味が違っていただけである。
江戸でも興味が無かったというのではなく、同じようなことを書いているのだが、それ自体の本としては刊行しなかった、ということは考え方に違いがあったと、言えるであろう。
江戸時代の数学の特徴として、遊びの気持ちの現れも一つの要素であったと考え、今回は取り上げることにした。
同時代のヨーロッパでも同じような遊びが残っているが、これも和算の誕生はキリシタンと決め付ける材料になっている。
2006/05/24
16:20 - 17:30Room #128 (Mathematics building)
津田 美幸 (統計数理研究所)
"Bhattacharyya inequality for quantum state estimation I"
量子状態推定のBhattacharyya不等式の導出とその応用例を前後二回に分けて紹介する. 今回は, 一般的な形で問題設定を行い, 量子Cramer-Rao不等式と量子 Bhattacharyya不等式について述べる.
量子状態推定は量子力学系の未知の状態に関する統計的推定問題である. 古典的な統計モデルの推定問題との違いは, データを観測するための測定を, 量子力学的に可狽ネ範囲で, 選択する点にある. 実数または複素数でパラメトライズされたモデルに対しては, 不偏推定量の分散の最小化が基本的な問題である. ただしここでは, 複素パラメータz=x+iyの分散とは, (x,y)の二次元の共分散行列のトレースをさす. この問題に対しては Yuen and Lax (1973) 等により, パラメータの一階微分に基づいた量子Cramer-Rao不等式が導出されており, 量子ガウス状態の複素振幅θのUMVUEが知られている. 二階以上の微分に基づくBhattacharyya型の不等式は, Brody and Hughston (1998) により, ある特殊なモデルにおいて導入され, 漸近論へ応用された. ここではより一般的なモデルに適用可能な形で量子Bhattacharyya不等式を三種類定式化する.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/03.html
16:30 - 18:45Room #117 (Mathematics building)
Kai Köehler (Düesseldorf 大学) 16:30 - 17:30
"Quaternionic analytic torsion and arithmetic geometry"
Thomas Geisser (南カリフォルニア大学) 17:45 - 18:45
"Duality via cycle complexes"
2006/05/23
16:30 - 18:00Room #056 (Mathematics building)
笠川 良司 (日本大学理工学部)
"On crossed homomorphisms on symplectic mapping class groups"
We consider a symplectic manifold M. For a relation between Chern classes of M and the cohomology class of the symplectic form, we construct a crossed homomorphism on the symplectomorphism group of M with values in the cohomology group of M. We show an application of it to the flux homomorphism. Then we see that it induces a one on the symplectic mapping class group of M and show a nontrivial example of it.
2006/05/22
10:30 - 12:00Room #128 (Mathematics building)
Marco Brunella (Bourgogne)
"Uniformisation of Holomorphic Foliations by Curves I (Part II on May 29)"
In the first lecture, we give a definition of "leaf" for a singular holomorphic one-dimensional foliation on a projective manifold. The definition is such that the leaves of a foliation glue together in a nice way, giving a "covering tube" which is a sort of semi-global flow box. This is, in some sense, the topological part of the theory. In the second lecture, we prove some convexity property of this covering tube. As a corollary we obtain that, when there are hyperbolic leaves, the leafwise Poincare' metric has some remarkable positivity property. In the third lecture, we study foliations all of whose leaves are parabolic. Using a suitable extension theorem for certain meromorphic maps, we show how to generalise the above positivity property to this degenerate class of foliations.
15:00 - 16:30Room #470 (Mathematics building)
Nessim Sibony (Paris Sud)
"Laminations with Singularities by Riemann Surfaces II"
2006/05/20
13:30 - 15:45Room #123 (Mathematics building)
水野 義紀 (慶應大学COE研究員) 13:30 - 14:30
"The Koecher-Maass series for real analytic Siegel-Eisenstein series"
非正則のジーゲル保型形式に対して、そのKoecher-Maass級数を定義し、その解析接続・関数等式を得ることは、正則のときMaassが発展させた方法でうまくいくかどうかはわかっていないと思われます。一変数半整数の実解析的Eisenstein級数のRankin-Selberg convolutionの解析接続、関数等式を示し、伊吹山・桂田の明示公式を用いた実解析的Siegel-Eisenstein級数のKoecher-Maass級数への応用(解析接続、関数等式)を述べます。
石井 卓 (東京大学大学院数理科学研究科) 14:45 - 15:45
"Standard L-functions for generic cusp forms on GSp(2)"
Whittaker模型を持つようなGSp(2)の尖点保型表現に付随するスタンダードL関数(5次のオイラー積)を、Ginzburg-Rallis-Soudry ('97)やBump-Friedberg-Ginzburg ('99)によって与えれたゼータ積分を通じて解析接続する方法について、これまでに得られた結果を紹介する。
2006/05/18
16:00 - 17:30Room #056 (Mathematics building)
石井 仁司 (早稲田大学 教育学部 理学科 数学専修)
"Asymptotic behavior for large-time of solutions of Hamilton-Jacobi equations in n space"
2006/05/17
16:20 - 17:30Room #128 (Mathematics building)
Arnak DALALYAN (Universite Paris 6, France)
"Second-order efficiency in the semiparametric problem of estimating the shift of a signal"
2006/05/16
17:00 - 18:30Room #056 (Mathematics building)
Laurentiu Maxim (University of Illinois at Chicago)
"Fundamental groups of complements to complex hypersurfaces"
I will survey various Alexander-type invariants of hypersurface complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to affine hypersurfaces.
16:30 - 18:00Room #126 (Mathematics building)
大島 利雄 (東京大学大学院数理科学研究科)
"確定特異点型の可換な微分作用素系について"
実簡約Lie群やその対称空間をコンパクト多様体に実現すると,不変微分作用素系はその境界に沿って確定特異点を持つ可換微分作用素系となる.
可換微分作用素系がただ一つの作用素から特徴づけられることを基に,境界の近傍で多価解析的な同時固有関数の一般的構成を考察し,表現論,特にWhittaker模型などへの応用を論じる(Harish-Chandra同型やGoodman-Wallach作用素の微分方程式論の立場からの解釈などを含む).
2006/05/15
10:30 - 12:00Room #128 (Mathematics building)
Nessim Sibony (Paris Sud)
"Laminations with Singularities by Riemann Surfaces I (Part II on May 22)"
The basic example of a lamination, possibly with singularites, by Riemann surfaces, is the closure of a leaf of a holomorphic foliation in the complex projective plane.There are also many examples arising from the theory of iteration of a holomorphic map. The goal is to introduce tools in order to understand the globalproperties of leaves of a holomorphic lamination, mostly in compact Kaehler manifolds. We will develop the following topics.
-Poincare metric on a hyperbolic lamination.
-Positive cycles and positive harmonic currents directed by a lamination.
-Ahlfors construction of positive harmonic currents.
-Cohomological and geometrical intersection of positive harmonic currents.
2006/05/12
16:30 - 17:30Room #123 (Mathematics building)
浜窪 隆雄 氏, 油谷 浩幸 (東京大学先端科学技術センター)
"ポストゲノム時代のシステム生物学の問題について"
ヒトゲノム30億塩基対のシークエンスは解読されましたが、その遺伝暗号の意味がわかっている部分はほんの数パーセントにすぎません。DNAチップや質量分析機の発達とコンピューターの進歩により、細胞や組織で読まれている遺伝子の量や生ずるタンパク質の種類を網羅的に解析する手段ができています。これらのトランスクリプトーム解析やプロテオーム解析により多数の遺伝子あるいはタンパク質の挙動を調べることが可能になってくると、生命現象の基礎となっている調節メカニズムが単一分子の相互作用だけで説明できないのではないかと思われてきました。多数分子の挙動とそれらの相互作用をどのように解析することができるかということが、生命現象を分子から生体システムとして理解するために必要なのではないかと感じています。これまで、我々の解析で得られているデータをお示しし、現在の生命科学が直面しつつある問題点を説明できればと思います。
2006/05/10
16:20 - 17:30Room #128 (Mathematics building)
Arnak DALALYAN (Universite Paris 6, France)
"Asymptotic statistical equivalence for diffusion processes II"
We consider the experiment of a continuously observed scalar diffusion process with unknown drift function. In the stationary case, we prove that this experment is locally asymptotically equivalent to a simple Gaussian white noise experiment. We also derive the rate of convergence of the Le Cam's distance and describe the Markov kernel attaining this rate of convergence. These results are obtained in collaboration with Markus Reiss.
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/01.html
2006/05/08
10:30 - 12:00Room #128 (Mathematics building)
大沢 健夫 (名古屋大学)
"Real-analytic Levi-flats in complex tori"
2006/04/27
16:00 - 17:30Room #056 (Mathematics building)
西原 健二 (早稲田大学・政治経済学術院)
"消散型波動方程式のコーシー問題の解の挙動"
17:00 - 18:30Room #152 (Mathematics building)
川原 秀城 (東京大学大学院人文社会系研究科、東アジア思想文化、(兼)韓国朝鮮言語思想)
"九数略──17・18世紀の朝鮮数学"
『九数略』は,当時の代表的な政治家兼経学者、崔錫鼎(1645- 1715)が著した数学書。内容自体は伝統の実用算術のレベルを超えていないけれども、形而上学的な易学思想をもって、朝鮮の計算術と実用数学の構造を理論的に位置づけている。また数学の基本的構造自体に西洋の3数法の深い影響があることも、この数学書の特徴の1つである。
今回は特に『九数略』の思想史的な意味に注目してその内容を紹介したい。
2006/04/26
16:30 - 17:30Room #117 (Mathematics building)
伴 克馬 (東京大学大学院数理科学研究科)
"Differential Operators of Rankin-Cohen-Ibukiyama Type for Automorphic Forms of Several Variables"
16:20 - 17:30Room #128 (Mathematics building)
Arnak DALALYAN (Universite Paris 6, France)
"Asymptotic statistical equivalence for diffusion processes I"
This is the first talk of a series of three talks devoted to the asymptotic statistical equivalence for diffusion processes. We will introduce the notion of Le Cam's distance between statistical experiments and will present its properties with some easy examples. Then we will show that the experiment of a discretely observed diffusion process with unknown drift is asymptoically equivalent to the experiment of continuously observed diffusion process provided that the step of discretisation is small enough (this result is due to Milstein and Nussbaum).
2006/04/25
16:30 - 18:00Room #056 (Mathematics building)
合田 洋 (東京農工大学)
"Counting closed orbits and flow lines via Heegaard splittings"
Let K be a fibred knot in the 3-sphere. It is known that the Alexander polynomial of K is essentially equal to a Lefschetz zeta function obtained from the monodromy map of the fibre structure. In this talk, we discuss the non-fibred knot case. We introduce "monodromy matrix" by making use of Heegaard splitting for sutured manifolds of a knot K, and then observe a method of counting closed orbits and flow lines, which gives the Alexander polynomial of K. This observation is based on works of Donaldson and Mark. (joint work with Hiroshi Matsuda and Andrei Pajitnov)
16:30 - 18:00Room #052 (Mathematics building)
松井 優 (東大数理)
"構成可能関数のRadon変換の像の特徴付けと射影双対性への応用について"
http://agusta.ms.u-tokyo.ac.jp/seminarphotos/Matsui2006/matsui2006_1.html
2006/04/24
10:30 - 12:00Room #128 (Mathematics building)
Jonas Wiklund (名古屋大学, JSPS fellow)
"Monge-Ampére mass at the boundary on some domains with corner"
The Monge-Ampére operator is a highly non-linear operator that assigns a positive measure to every plurisubharmonic function and the null-measure to every maximal plurisubharmonic measure, whenever it is well defined. We discuss the sweeping out of this measure to the boundary for functions that essentially vanish on the boundary, and show two examples that this boundary measure vanish outside the distinguished boundary. Namely for analytic polyhedrons and for the cross product of two hyperconvex domains. Some related open problems are also mentioned.
2006/04/21
16:30 - 17:30Room #123 (Mathematics building)
Dmitri Orlov (Steklov Institute)
"Homological mirror symmetry"
Homological mirror symmetry is a relation between algebraic and symplectic sides of a geometric object. Original mirror symmetry came from physics, but homological mirror symmetry conjecture formulated by M.Kontsevich for Calabi-Yau varieties is an attempt to give a mathematical explanation of this phenomenon. We will try to describe main principles of homological mirror symmetry and the extension to a non-Calabi-Yau case.
2006/04/20
16:00 - 18:15Room #123 (Mathematics building)
杉原 厚吉 (東京大学大学院情報理工学系研究科) 16:00 - 17:00
"立体イリュージョンの世界"
人は写真や絵の中に3次元的な奥行きを感じ取ることができるが,実は,同一の投影図をもつ立体は無限に多く存在する.人間の立体知覚にかかわるイリュージョンをコンピュータビジョンの立場から数理的に眺めてみると,さまざまな面白い発見が得られる.たとえば,だまし絵の中だけに存在して,実際にはありえないと思われている立体が作れたりもする.
新井 仁之 (東京大学大学院数理科学研究科) 17:15 - 18:15
"色彩と明暗が生む錯視"
錯視は視覚における錯覚である.しかし,じつは錯視は視覚がどのように情報処理を行っているかを知るための重要な鍵の一つである.本講演ではウェーブレットという数学的道具を用いて,視覚情報処理の非線形数理モデルを作り,色や明暗に関するさまざまな錯視発生のメカニズムに迫りたい.
16:30 - 18:00Room #052 (Mathematics building)
戸松 玲治 (東大数理・COE)
"Compact Kac 環の極小作用の分類 I"
2006/04/19
16:30 - 17:30Room #117 (Mathematics building)
谷口 隆 (東京大学大学院数理科学研究科)
"Distributions of discriminants of cubic algebras"
10:30 - 11:30Room #056 (Mathematics building)
横山 悦郎 (学習院大学)
"Oscillatory growth of a crystal controlled by interface kinetics and transport process"
Periodic texture in a crystal -such as growth banding and growth striations- are believed to be caused by oscillatory growth. The origin of oscillatory growth falls into two categories, i.e., external and internal. Since the growth rate of a crystal depends strongly on the growth conditions, periodic changes of external conditions, such as temperature, concentration, convection etc., are common reasons for explaining oscillatory growth. On the other hand, it is thought that oscillatory growth can also have an internal cause, but there is no clear understanding. In this talk we propose the hypothesis of a hysteresis behaviour of growth rate to explain the formation of periodic structures of a growing crystal without a change of external conditions. Recently, evidence for our hypothesis is observed not only in the growth of a crystal but also in the motion of steps on the surface of crystals. Possibly such self-oscillatory growth can be controlled in experiments in near future.
http://coe.math.sci.hokudai.ac.jp/sympo/various/005.html
2006/04/18
16:30 - 18:00Room #056 (Mathematics building)
Vladimir Turaev (Univ. Louis Pasteur Strasbourg)
"Topology of words"
There is a parallel between words, defined as finite sequences of letters, and curves on surfaces. This allows to treat words as geometric objects and to analyze them using techniques from low-dimensional topology. I will discuss basic ideas in this direction and the resulting topological invariants of words.
16:30 - 18:00Room #126 (Mathematics building)
伴 克馬 (東京大学大学院数理科学研究科)
"Rankin-Cohen-伊吹山型の微分作用素について"
正則保型形式の正則微分は一般に保型形式ではなくなるが、それらを組み合わせることで新たな正則保型形式を与えることもできる。
楕円モジュラー形式に対するRankin-Cohen微分作用素はその最も簡単な例である。伊吹山はSiegelモジュラー形式に対するこのようなタイプの微分作用素がどのような形をしているかについて、一般的な記述を与えた。
今回のセミナーでは、伊吹山による結果を表現論的な命題として捉え直し、その命題が自然にSU(p,q)やO*(2p)上の正則保型形式にも拡張されることを説明する。
2006/04/17
10:30 - 12:00Room #128 (Mathematics building)
C. Robin Graham (University of Washington)
"Dirichlet-to-Neumann map for Poincaré-Einstein metrics"
This talk will describe an analogue of a Dirichlet to Neumann map for Poincaré-Einstein metrics, also known as asymptotically hyperbolic Einstein metrics. An explicit identification of the linearization of the map at the sphere will be given for even interior dimensions, together with applications to the structure of the map near the sphere and to the positive frequency conjecture of LeBrun which was resolved by Biquard.
2006/04/15
13:30 - 15:45Room #123 (Mathematics building)
軍司 圭一 (東京大学大学院数理科学研究科) 13:30 - 14:30
"On the dimension of the space of Siegel Eisenstein series of weight one."
一般に低いweightのSiegel保型形式の空間の次元を求めるのは難しく、特にcusp形式についてはほとんど分かっていない。この講演では素数レベルの主合同部分群に対して、Siegel-Eisenstein級数と呼ぶべき、cusp形式
の補空間の一部の次元を、有限群の表現論及びSatakeコンパクト化の境界の様子を調べることによって計算する方法を与える。
森山 知則 (東京大学大学院数理科学研究科) 14:45 - 15:45
"L-functions for $GSp(2)\times GL(2)$: archimedean theory and applications"
$\Pi$ を $GSp(2)$のWhittaker模型を持つ尖点保型表現で,実素点で大きい離散系列表現を生成するものとする。$\Pi$と$\GL(2)$の尖点保型表現$\sigma$の組からテンソル積 L-関数が定義される。
このL-関数の関数等式を,ゼータ積分を使って証明する。
証明のいくつかの副産物($\Pi$ のspinor L-関数への応用など)についてもお話したい。
13:30 - 16:00Room #117 (Mathematics building)
坂本 玲峰 (東大理) 13:30 - 14:30
"Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection."
Kerov-Kirillov-Reshetikhin bijection とは、フェルミ型公式の 証明に関して 1986 年に導入された組み合わせ的な写像であり、 rigged configurations と highest paths の間の全単射を与える。 この写像を、結晶基底の組み合わせ R 行列のみを用いた代数的な 形式に書き直すことができる [1,2]。証明には、アフィン組み合わせ R 行列の構造を rigged configurations に導入することが必要となる。 これらの結果は箱玉系と呼ばれるソリトンセルオートマトンの 逆散乱形式ともなっている。
REFERENCE:
[1] A.Kuniba, M.Okado, R.Sakamoto, T.Takagi, Y.Yamada, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection" Nuclear Physics B 740 (2006) 299-327, math.QA/0601630.
[2] R.Sakamoto, "Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection II. Proof for sl_n case", math.QA/0601697.
塩田 翠 (東大数理) 15:00 - 16:00
"ダブルアファインヘッケ代数と楕円ヘッケ代数について"
ダブルアファインヘッケ代数と楕円ヘッケ代数の比較について話します。 楕円ヘッケ代数は、マーキング付き楕円ルート系のディンキン図形から 生成元と関係式を読み取って定義される代数です。マーキング付き楕円 ルート系は、2つのアファインルート系を部分ルート系として含むので そのヘッケ代数がダブルアファインヘッケ代数と何かしらの関係がある ことは想像がつきます。ここでは、楕円ヘッケ代数がダブルアファイン ヘッケ代数の部分代数になっていること、およびダブルアファインヘッケ 代数を楕円ヘッケ代数上の加群と見たときの自由基底について説明します。
2006/04/13
16:30 - 18:00Room #118 (Mathematics building)
勝良 健史 (北大理・学振SPD)
"A construction of finite group actions on Kirchberg algebras"
2006/04/12
14:40 - 18:00Room #056 (Mathematics building)
三鍋 聡司 (名古屋大学大学院多元数理科学研究科) 14:40 - 16:10
"Topological Vertex とその応用"
この講演の内容は小西由紀子さんとの共同研究に基づきます.
まず,3次元 toric Calabi--Yau 多様体の Gromov--Witten 不変量の分配関数を計算する Topological Vertex と呼ばれる方法について説明します.その応用として,分配関数のフロップに関する不変性や,3次曲面の局所 Gromov--Witten 不変量の分配関数の公式が求められることを説明したいと思います.
安井 幸則 (大阪市立大学物理学科) 16:30 - 18:00
"Kerr Black Holes and Compact Einstein Manifolds"
1978 年 Page は,4次元 AdS Kerr ブラックホール解からある種の極限操作を使って S^2 上の S^2 束に inhomogeneous Einstein 計量を構成しました.この計量はコンパクトな空間上の inhomogeneous Einstein 計量として顕に書き下された最初の例です.ここでは、Page の手法を高次元に拡張することにより,Hawking たちによって発見された5次元 AdS Kerr ブラックホール解から,S^2 上の S^3 束に無限個のアインシュタイ ン計量を誘導します.関連する話題として, 5次元佐々木アインシュタイン計量および AdS/CFT 対応についても言及したいと思います.
2006/04/11
16:30 - 18:00Room #056 (Mathematics building)
Martin Arkowitz (Dartmouth College)
"Homotopy actions, cyclic maps and their Eckmann-Hilton duals."
We study the homotopy action of a based space A on a based space X. The resulting map A--->X is called cyclic. We classify actions on an H-space which are compatible with the H-structure. In the dual case we study coactions X--->X v B and the resulting cocyclic map X--->B. We relate the cocyclicity of a map to the Lusternik-Schnirelmann category of the map.
2006/04/04
16:30 - 17:30Room #128 (Mathematics building)
Maria Reznikoff (Department of Mathematics, Princeton University)
"Thermally-Driven Rare Events and Action Minimization"
http://coe.math.sci.hokudai.ac.jp/sympo/various/004.html
2006/03/30
10:30 - 11:30Room #118 (Mathematics building)
Herbert Heyer (Tuebingen University)
"Heyer教授特別講演会:Polynomial hypergroups of several variables"
2006/01/30
10:30 - 12:00Room #128 (Mathematics building)
藤木 明 (大阪大学)
"Compact non-kaehler threefolds associated to hyperbolic 3-manifolds"
2006/01/23
10:30 - 12:00Room #128 (Mathematics building)
金子 宏 (東京理科大)
"Stochastic processes and Besov spaces on local field"
2006/01/18
10:30 - 11:30Room #056 (Mathematics building)
Juergen Saal (TU Darmstadt)
"Analyticity of the interface of the classical two-phase Stefan problem"
The Stefan problem is a model for phase transitions in liquid-solid systems, as e.g. ice surrounded by water, and accounts for heat diffusion and exchange of latent heat in a homogeneous medium.
The strong formulation of this model corresponds to a free boundary problem involving a parabolic diffusion equation for each phase and a transmission condition prescribed at the interface separating the phases.
We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a unique solution that is analytic in space and time.
The result is based on $L_p$ maximal regularity for a linearized problem, which is proved first, and the implicit function theorem.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/01/11
10:30 - 11:30Room #056 (Mathematics building)
伊東 一文 (North Carolina State University) 10:30 - 11:30
"On Fluid Mechanics Formulation of Monge-Kantorovich Mass Transfer Problem"
The Monge-Kantorovich mass transfer problem is equivalently formulated as an optimal control problem for the mass transport equation. The equivalency of the two problems is establish using the Lax-Hopf formula and the optimal control theory arguments. Also, it is shown that the optimal solution to the equivalent control problem is given in a gradient form in terms of the potential solution to the Monge-Kantorovich problem. It turns out
that the control formulation is a dual formulation of the Kantrovich distance problem via the Hamilton-Jacobi equations.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Oleg Yu. Imanuvilov (Colorado State University) 11:45 - 12:45
"Local and Global Exact Controllability of Evolution Equations"
We discuss rcent global and local controlability results for the Navier-Stokes system and Bousinesq system. The control is acting on the part of the boundary or locally distributed over subdomain.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/12/05
10:30 - 12:00Room #128 (Mathematics building)
Sebastien Boucksom (ParisVII / Univ. of Tokyo)
"Positive cones of hyper-Keahler manifold"
2005/11/28
10:30 - 12:00Room #128 (Mathematics building)
上田哲生 (京都大学)
"Schroeder equation and Abel equation"
2005/11/22
16:30 - 17:30Room #128 (Mathematics building)
Hans Heesterbeek (University of Utrecht)
"Mathematics in the epidemiology and control of infectious diseases"
In this lecture I will give examples of the way in which mathematics helps in getting insight into the spread and control of infectious diseases. I will do this by discussing the population phenomena that are observed after an infectious agent enters a population (invasion, epidemic, recurrent epidemic, endemic, regulation, control). Along the way I will also give insight into the historical development of mathematical modelling in infectious disease epidemiology. Examples will be taken from human and animal infections. Special topics treated in some detail are threshold quantities such as the basic reproduction number R_0, the importance of understanding the structure of contacts in a population, the use of R_0 to estimate control effort with vaccines. In the last part of the lecture a number of important epidemiological problems will be discussed where input of new mathematical theory is needed.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2005/11/21
10:30 - 12:00Room #128 (Mathematics building)
Andreas Cap (Univ. of Vienna)
"On CR-invariant differential operators "
My talk will be devoted to questions about differential operators which are intrinsic to non--degenerate CR structures of hypersurface type. Restricting to the subclass of spherical CR structures, this question admits an equivalent formulation in terms of representation theory, which leads to several surprising consequences.
Guided by the ideas from representation theory and using the canonical Cartan connection which is available in this situation, one obtains a construction for a large class of such operators, which continues to work for non--spherical structures, and even for a class of almost CR structures. In the end of the talk I will discuss joint work with V. Soucek which shows that in the integrable case many of the operators obtained in this way form complexes.
2005/11/14
10:30 - 12:00Room #128 (Mathematics building)
Raphael Pong (Ohio State Univ)
"New invariants for CR and contact manifolds "
In this talk I will explain the construction of several new invariants for CR and contact manifolds as noncommutative residue traces of various geometric pseudodifferential projections. In the CR setting these operators arise from the ∂b-complex and include the Szegö projections. In the contact setting they stem from the generalized Szegö projections at arbitrary integer levels of Epstein-Melrose and from the contact complex of Rumin. In particular, we recover and extend recent results of Hirachi and Boutet de Monvel and answer a question of Fefferman.
2005/11/09
10:30 - 11:30Room #056 (Mathematics building)
藤田安啓 (富山大学)
"Asymptotic solutions and Aubry sets for Hamilton-Jacobi equations"
In this talk, we consider the asymptotic behavior of the viscosity solution of the Cauchy problem for the Hamilton-Jacobi equation $u_t + \alpha x\cdot Du + H(Du) =f(x)$ in ${\rm I}\!{\rm R}^N \times (0,\infty)$, where $\alpha$ is a positive constant and $H$ is a convex function on ${\rm I} \!{\rm R}^N$. We show that, under some assumptions, $u(x,t) - ct - v(x)$ converges to $0$ locally uniformly in ${\rm I}\!{\rm R}^N$ as $t \to \infty$, where $c$ is a constant and $v$ is a viscosity solution of the Hamilton-Jacobi equation $c + \alpha x\cdot Dv + H(Dv) = f(x)$ in ${\rm I}\!{\rm R}^N$. A set in ${\rm I}\!{\rm R}^N$, which is called the {\it Aubry set}, gives a concrete representation of the viscosity solution $v$. We also discuss convergence rates of this asymptotic behavior. This is a joint work with Professors H. Ishii and P. Loreti.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/11/07
10:30 - 12:00Room #128 (Mathematics building)
難波誠 (追手門学院大学)
"Moduli of Galois coverings of the complex projective line"
2005/10/26
10:30 - 11:30Room #056 (Mathematics building)
利根川吉廣 (北海道大学)
"On Mullins-Sekerka as singular limit of Cahn-Hilliard, some mathematical progress and open problems"
The Cahn-Hilliard equation and its variants have been widely used in materials science community to model coarse graining phenomena in mesoscopic scale. The equation has a parameter corresponding the order of thickness of phase boundaries. When the parameter is close to zero, the phase boundary and the chemical potential field are known to evolve by the so-called Mullins-Sekerka problem. The rigorous justification for the latter statement is known only for short-time so far. I describe some recent progress as well as some difficulties on the long-time case, relateing my recent works and those by M. Roeger and R. Schaetzle.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/10/24
10:30 - 12:00Room #128 (Mathematics building)
平地健吾 (東大数理)
"Ambient metrics for even dimensional conformal structures"
2005/10/18
16:30 - 17:30Room #128 (Mathematics building)
Rainer Kress (Goettingen 大学)
"Hybrid methods for inverse boundary problems"
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2005/10/17
10:30 - 12:00Room #128 (Mathematics building)
吉川謙一 (東大数理)
"On the discriminant of certain K3 surfaces"
2005/09/28
10:30 - 11:30Room #056 (Mathematics building)
Matthias Geissert (ダルムシュタット工科大学)
"The Navier-Stokes flow in the exterior of a rotating obstacle"
We show the existence of solutions of the Navier-Stokes flow in the exterior of a rotating obstacle. In the first step we transform the Navier-Stokes equations to a problem in a time independent domain. In this talk we present two different change of coordinates to do this. Finally, we discuss the advantages of both approaches and show the local existence and uniqueness of mild and strong $L^p$ solutions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/07/22
10:30 - 12:00Room #128 (Mathematics building)
倉西正武 (コロンビア大学)
"Szeg\"o kernel の構成について"
15:30 - 17:00Room #128 (Mathematics building)
Dan Popovici (JSPS, 名古屋大学多元数理)
"Effective Local Finite Generation of Multiplier Ideal Sheaves"
2005/07/20
10:30 - 11:30Room #056 (Mathematics building)
相川弘明 (島根大学)
"Equivalence between the boundary Harnack principle and the Carleson estimate"
Both the boundary Harnack principle and the Carleson estimate describe the boundary behavior of positive harmonic functions vanishing on a portion of the boundary. These notions are inextricably related and have been obtained simultaneously for domains with specific geometrical conditions. The main aim of this talk is to show that the boundary Harnack principle and the Carleson estimate are equivalent for arbitrary domains.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/07/13
10:30 - 11:30Room #122 (Mathematics building)
Yonggeun Cho (北海道大学)
"On classical solutions of the compressible Navier-Stokes equation with nonnegative density"
In this talk, we discuss a recent progress on the regularity of solution of compressible Navier-Stokes equations with nonnegative density. The nonnegativity of density cauases a problem in using the usual parabolicity of momentum equations and hence in general makes it hard to gain a regularity of solution. To overcome the difficulty, we develop a natural compatibility condition. Then observing a smoothing effect for positive time, we obtain classical solutions of the compressible Navier-Stokes equations.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/07/11
10:30 - 12:00Room #128 (Mathematics building)
青柳美輝 (上智大理工)
"学習理論のゼータ関数と特異点解消"
2005/07/04
10:30 - 12:00Room #128 (Mathematics building)
辻 元 (上智大理工)
"Variation of Bergman kernel of projective manifolds"
2005/06/27
10:30 - 12:00Room #128 (Mathematics building)
相原義弘 (沼津高専)
"Uniqueness problem of analytic coverng spaces"
2005/06/22
16:30 - 17:30Room #056 (Mathematics building)
Y. H. Richard Tsai (University of Texas)
"Threshold Dynamics for the Piecewise Constant"
We propose an efficient algorithm for minimizing the piecewise constant Mumford-Shah functional of image segmentation. It is based on the threshold dynamics of Merriman, Bence, and Osher for evolving an interface by its mean curvature. We show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding. We discuss our current work of extending this line of work to higher order accuracy and to applications involving Willmore flow.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2005/06/15
10:30 - 11:30Room #056 (Mathematics building)
中井英一 (大阪教育大学)
"Singular and fractional integral operators on function spaces related to Morrey spaces"
It is known that the Hardy-Littlewood maximal operator, singular integral operators and fractional integral operators are bounded on L^p spaces and Morrey spaces. We extend the boundedness to generalized Morrey spaces, Orlicz-Morrey spaces, etc.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/06/08
10:30 - 11:30Room #056 (Mathematics building)
宮地晶彦 (東京女子大学)
"Weighted Hardy spaces on an interval and Jacobi series"
For the classical Hardy class consisting of functions holomorphic in the unit disc, the Burkholder-Gundy-Silverstein theorem gives a characterization of the class in terms of certain maximal functions. We give a variant of this theorem related to weighted Hardy spaces on the interval(0,$\pi$) and generalized holomorphic functions efined through ultraspherical (Gegenbauer) polynomials.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/06/06
10:30 - 12:00Room #128 (Mathematics building)
大沢健夫 (名大多元数理)
"Application of Hartogs type extension theorems to Levi flats in Kaehler manifolds"
2005/06/01
10:30 - 11:30Room #056 (Mathematics building)
Jong-Shenq-Guo (国立台湾師範大学)
"Annihilation of wave fronts of a reaction-diffusion equation"
We shall present some recent results on the existence and uniqueness of 2-front entire solutions of a reaction-diffusion equation. These entire solutions behave as two opposite wave fronts approaching each other from both sides of the x-axis and then annihilating in a finite time.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/05/30
10:30 - 12:00Room #128 (Mathematics building)
宮岡礼子 (九大数理)
"全曲率有限な完備極小曲面のガウス写像の除外値について"
2005/05/25
10:30 - 11:30Room #056 (Mathematics building)
Vincenzo Vespri (Dipartimento di Matematica Ulisse Dini Viale Morgagni) 10:30 - 11:30
"Some regularity results for Stefan equation"
We consider the eqation $\beta (u)_t = A(u)$ where $A$ is an elliptic operator and $\beta$ is a maximal graph. Under suitable hypothesis on $\beta$ and $A$ we prove the continuity of local solutions extendind some techniques introduced in the 80's.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Paolo Marcellini (Università degli Studi di Firenze) 11:45 - 12:45
"Nonlinear elliptic systems with general growth"
We prove \textit{local Lipschitz-continuity} and, as a consequence, $C^{k}$%\textit{\ and }$C^{\infty }$\textit{\ regularity} of \textit{weak} solutions $u$ for a class of \textit{nonlinear elliptic differential systems} of the form $\sum_{i=1}^{n}\frac{\partial }{\partial x_{i}}a_{i}^{\alpha}(Du)=0,\;\alpha =1,2\dots m$. The \textit{growth conditions} on the dependence of functions $a_{i}^{\alpha }(\cdot )$ on the gradient $Du$ are so mild to allow us to embrace growths between the \textit{linear} and the \textit{exponential} cases, and they are more general than those known in the literature.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/05/23
10:30 - 12:00Room #128 (Mathematics building)
赤堀隆夫 (兵庫県立大物質理学)
"A-branes from CR-geometry"
2005/05/18
10:30 - 11:30Room #056 (Mathematics building)
剣持信幸 (千葉大学)
"A model of damage evolution in viscous locking material."
A model problem, describing the damage evolution for instance in some composite materials, is considered. The model is a system of nonlinear PDEs, which are kinetic equations for the displacement and damage quantity in the material. They are both heavily nonlinear parabolic equations, and one of them is of degenerate type. In this talk, the existence of a global in time solution is shown with some key ideas.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/05/16
10:30 - 12:00Room #128 (Mathematics building)
野口潤次郎 (東大数理)
"Algebraic degeneracy of holomorphic curves"
2005/05/09
10:30 - 12:00Room #128 (Mathematics building)
林本厚志 (長野高専)
"レビ形式が退化する、あるクラスの実超曲面の定義関数について"
2005/04/25
10:30 - 12:00Room #128 (Mathematics building)
藤川英華 (東工大情報理工)
"停留的写像類群とタイヒミュラー空間への作用"
2005/04/20
10:30 - 11:30Room #056 (Mathematics building)
酒井 良 (都立大学)
"Small modifications of quadrature domains around a cusp"
A flow which is produced by injection of fluid into the narrow gap between two parallel planes is called a Hele-Shaw flow. We regard the flow as an increasing family of plane domains and discuss the case that the initial domain has a cusp on the boundary. We give sufficient conditions for the cusp to be a laminar-flow point.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/04/18
10:30 - 12:00Room #128 (Mathematics building)
厚地 淳 (慶大経済)
"エネルギー有限な有理形関数の除外点の個数について"
2005/03/23
10:30 - 11:30Room #122 (Mathematics building)
Helmut Abels (Max Planck Institute)
"Pseudodifferential Boundary Value Problems with Non-Smooth Coefficients"
We discuss an operator class that models elliptic differential boundary value problems as well as their solution operators and is closed under compositions. It was introduced by Boutet de Monvel in 1971 and provides a powerful tool to calculate with symbols associated to these operators. But the standard calculus and most of its further developments require that the symbols have smooth coefficient in the space and phase variable. We present some results which extend the calculus to symbols which have limited smoothness in the space variable. Such an extension is nescessary to apply the calculus to nonlinear partial differential boundary value problems and free boundary value problems.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/03/02
10:30 - 11:30Room #270 (Mathematics building)
Italo Capuzzo-Dolcetta (Universita di Roma) 10:30 - 11:30
"The maximum principle in unbounded domains"
The issue of the talk is the validity of the Weak Maximum Principle for functions u satisfying a second-order partial differential inequality of the form
(*) F(x,u,Du,D^2u) ≧ 0
in a domain A of the n-dimensional euclidean space.
The main result presented in the lecture is that for bounded above upper semicontinuous functions verifying
(*) in the viscosity sense, the inequality u≦ 0 on the boundary ∂A is propagated in the interior of the domain itself, under suitable conditions on F and A.
These conditions include ellipticity of F, a general geometric condition on the (possibly) unbounded domain A and a joint requirement involving the spread of A and the decay of first order terms at infinity.
This result, contained in I.C.D, A.Leoni, A.Vitolo "The Alexandrov-Bakelman-Pucci weak Maximum Principle for fully nonlinear equations in unbounded domains", to appear in Comm.in PDE's, extends previous results due to X.Cabré and L.Caffarelli-X.Cabré.
In the second part of the talk we present different versions of Weak Maximum Principle, namely for solutions growing exponentially fast of (*) in narrow domains and for solutions of
(**) F(x,u,Du,D^2u) + c(x)u ≧ 0
(c changing sign) in domains of small measure.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Antonio Siconolfi (Universita di Roma) 11:45 - 12:45
"Aubry set and applications"
For given Hamiltonian H(x, p) continuous and quasiconvex in the second argument, defined in Rn × Rn or on the cotangent bundle of a compact boundaryless manifold, we consider the equation
H= c
with c critical value, i.e. for which the equation admits locally Lipschitzcontinuous a.e. subsolutions, but not strict subsolutions. We show that there is a subset of the state variable space, called Aubry set and denoted by A, where the obstruction to the existence of such subsolutions is concentrated. We give a metric characterization of A, and we discuss its main properties.
They are applied to a projection problem in a Banach space, to the study of the largetime behaviour of subsolutions to a timedependent HamiltonJacobi equation, and to construct a Lyapunov function for a perturbed dynamics, under suitable stability assumptions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/01/26
10:30 - 11:30Room #122 (Mathematics building)
Matthias Hieber (ダルムシュタット工科大学)
"L^p-Theory of the Navier-Stokes flow past rotating or moving obstacles"
In this talk we consider the equation of Navier-Stokes in the exterior of a rotating or moving domain. Using techniques from the analysis of Ornstein-Uhlenbeck operators it is shown that, after rewriting the problem on a fixed domain $\Omega$, the solution of the linearized equation is governed by a $C_0$-semigroup on $L^p_\sigma(\Omega)$ for $1
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2005/01/24
10:30 - 12:00Room #128 (Mathematics building)
金子 宏 (東京理科大)
"Hausdorff measure and exceptional sets in Dirichlet space theory on local fields"
2005/01/17
10:30 - 12:00Room #128 (Mathematics building)
中川健治 (長岡技術科学大学)
"複素函数論の情報ネットワーク特性評価への応用 "
情報ネットワークの特性評価を目的として,離散型 および連続型確率変数 X の裾確率 P(X > x) の指数的 減少について調べる。特に X が連続型の場合,X の確率 分布関数 F(x) = P(X ≧ x)のLaplace-Stieltjes変換を φ(s) とし,φ(s) の収束座標を σ とする。 -∞ < σ < 0 を仮定する。φ(s) の収束軸上の 特異点が高々有限個の極のみならば P(X > x) が指数的に 減少することを示す。その解析のために Ikehara による Tauber 型定理を拡張して適用する。
2004/12/17
10:30 - 12:00Room #126 (Mathematics building)
D. Popovici (Warwick)
"A simple proof of a theorem by Uhlenbeck and Yau"
10:30 - 12:00Room #126 (Mathematics building)
Min Ru (Houston)
"Holomorphic curves into algebraic varieties"
2004/12/15
10:30 - 12:45Room #122 (Mathematics building)
Andrzej Swiech (ジョージア工科大学) 10:30 - 11:30
"Hamilton-Jacobi-Bellman equations for optimal control of stochastic Navier-Stokes equations."
We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Francesca Da Lio (Dipartimento di Matematica P. e A.Universit di Padova researcher) 11:45 - 12:45
"A GEOMETRICAL APPROACH TO FRONT PROPAGATION PROBLEMS IN BOUNDED DOMAINS WITH NEUMANN-TYPE BOUNDARY AND APPLICATIONS"
We talk about a new definition of weak solution for the global-in-time motion of a front in bounded domains with normal velocity depending not only on its curvature but also on the measure of the set it encloses and with a contact angle boundary condition. We apply this definition to study the asymptotic behaviour of the solutions of some local and nonlocal reaction-diffusion equations.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/12/13
10:30 - 12:00Room #126 (Mathematics building)
野口潤次郎 (東大数理)
"正則曲線、小林双曲性とアーベル多様体の川又特徴付け"
2004/12/01
10:30 - 11:30Room #122 (Mathematics building)
岡本 久 (京都大学)
"A remark on continuous, nowhere differentiable functions"
We consider a parameterized family of continuous functions, which containsas its members Bourbai's and Perkins's nowhere differentiable functions as well as the Cantor-Lebesgue singular functions.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/10/20
10:30 - 11:30Room #122 (Mathematics building)
Hermann Sohr (University of Paderborn)
"Some recent results on the Navier-Stokes equations"
The aim of this talk is to explain some new results in particular on local regularity properties of Hopf type weak solutions to the Navier-Stokes equations for arbitrary domains. Further we explain a new existence result for nonhomogeneous data and a result for global regular solutions with "slightly" modified forces.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/10/13
10:30 - 11:30Room #128 (Mathematics building)
Philippe G. LeFloch (University of Paris 6)
"Existence, uniqueness, and continuous dependence of entropy solutions to hyperbolic systems"
I will review the well-posedness theory of nonlinear hyperbolic systems, in conservative or in non-conservative form, by focusing attention on the existence and properties of entropy solutions with sufficiently small total variation.
New results and perspectives on the following issues will be discussed: Glimm's existence theorem,
Bressan-LeFloch's uniqueness theorem,and the L1 continuous dependence property (established by Bressan, LeFloch, Liu, and Yang).
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/09/29
10:30 - 11:30Room #117 (Mathematics building)
Alex Mahalov (Arizona State University)
"Global Regularity of the 3D Navier-Stokes with Uniformly Large Initial Vorticity"
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity with periodic boundary conditions and in bounded cylindrical domains; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold.
The global existence is proven using techniques of fast singular oscillating limits and the Littlewood-Paley dyadic decomposition. The approach is based on the computation of singular limits of rapidly oscillating operators and cancellation of oscillations in the nonlinear interactions for the vorticity field. With nonlinear averaging methods in the context of almost periodic functions, we obtain fully 3D limit resonant Navier-Stokes equations. Using Lemmas on restricted convolutions, we establish the global regularity of the latter without any restriction on the size of 3D initial data.
With strong convergence theorems, we bootstrap this into the global regularity of the 3D Navier-Stokes Equations with uniformly large initial vorticity.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2004/07/05
16:30 - 18:00Room #002 (Mathematics building)
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2004/01/30
10:30 - 12:00Room #128 (Mathematics building)
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