東大数理セミナー情報 --- 今後の予定 2014年04月22日(火)~



16:30 - 18:00 数理科学研究科棟(駒場) 128号室
筒井 容平 氏 (東大 数理)
『 拡散性を有しない誘因因子に対する走化性方程式の小さな有界な解 』(JAPANESE)
We consider a chemotaxis system with a logarithmic
sensitivity and a non-diffusive chemical substance. For some chemotactic
sensitivity constants, Ahn and Kang proved the existence of bounded
global solutions to the system. An entropy functional was used in their
argument to control the cell density by the density of the chemical
substance. Our purpose is to show the existence of bounded global
solutions for all the chemotactic sensitivity constants. Assuming the
smallness on the initial data in some sense, we can get uniform
estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu
Univ.) and Juan J. L. Vel\'azquez (Univ. of Bonn).



14:50 - 16:20 数理科学研究科棟(駒場) 128号室
中田行彦 氏 (東京大学大学院数理科学研究科)
『 Age-structured epidemic model with infection during transportation 』(JAPANESE)
現代、航空路を手段とした大陸間移動が身近であるがゆえに、多くの感染症が世界中に蔓延することが容易となっている。本発表では、Volterra型積分方程式と遅延微分方程式を用いて、感染者個体の感染齢(age since infection)を連続的なパラメータとして組み込みながら、複数領域に広がる感染病の伝染ダイナミクスを記述する数理モデルを紹介する。領域間の個体群移動を記述するために、非自励な遅延微分方程式の解が陰的に用いられる。最後に、領域間の移動においては、それぞれの感染個体の発生状態がその交通機関内での滞在時間に連続的に依存することから、無限次元のVolterra型積分方程式が得られることを示したい。本研究はD.H.KniplおよびG. Röstとの共同研究となっている。


16:30 - 18:00 数理科学研究科棟(駒場) 122号室
武石拓也 氏 (東大数理)
『 Bost-Connes system for local fields of characteristic zero 』(ENGLISH)


16:40 - 17:40 数理科学研究科棟(駒場) 002号室
三枝洋一 氏 (東京大学数理科学研究科)
『 Non-tempered A-packets and the Rapoport-Zink spaces 』(JAPANESE)



10:00 - 11:30 数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
野澤 啓 氏 (立命館大学)
『 Lie葉層構造の剛性について 』(JAPANESE)
Lie葉層の葉たちが高実階非コンパクト型対称空間と計量同型であるとき、そのLie葉層のホロノミー群は超剛性や数論性などの高実階半単純群Lie群の一様格子と似た剛性を持つことが、Zimmerの定理により知られている。本講演では、Mostow剛性の変種の応用による、実階数1の場合を含むZimmerの定理の拡張について述べる。(Ga¥"el Meigniezとの共同研究。)



13:30 - 16:00 数理科学研究科棟(駒場) 123号室
岡崎龍太郎 氏 (元・同志社大学) 13:30 - 14:30
『 実数上既約な、整数係数斉次4次形式$F(X,Y)$ に対する、$F(X,Y)=1$の解の個数の評価 』(JAPANESE)
岡崎龍太郎 氏 (元・同志社大学) 15:00 - 16:00
『 種数2の代数曲線と、その不分岐7次拡大の組のモジュライ 』(JAPANESE)



10:30 - 12:00 数理科学研究科棟(駒場) 128号室
斎藤俊輔 氏 (東大数理)
『 On the existence problem of K\"ahler-Ricci solitons 』(JAPANESE)


15:30 - 17:00 数理科学研究科棟(駒場) 122号室
Alexandru Dimca 氏 (Institut Universitaire de France )
『 Syzygies of jacobian ideals and Torelli properties 』(ENGLISH)
Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.



16:40 - 17:40 数理科学研究科棟(駒場) 056号室
丸山拓也 氏 (東京大学数理科学研究科)
『 An effective upper bound for the number of principally polarized Abelian schemes 』(JAPANESE)



16:30 - 17:30 数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:00~16:30 (コモンルーム)。
A.P. Veselov 氏 (Loughborough, UK and Tokyo, Japan)
『 From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way 』(ENGLISH)
Gaudin subalgebras are abelian Lie subalgebras of maximal
dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,
associated to A-type hyperplane arrangement.
It turns out that Gaudin subalgebras form a smooth algebraic variety
isomorphic to the Deligne-Mumford moduli space \bar M_{0,n+1} of
stable genus zero curves with n+1 marked points.
A real version of this result allows to describe the
moduli space of integrable n-dimensional tops and
separation coordinates on the unit sphere
in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.



10:00 - 11:30 数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
小野 肇 氏 (埼玉大学)
『 非ハミルトン体積最小なハミルトン安定ラグランジュトーラスについて 』(JAPANESE)
Y. –G. Oh はケーラー多様体内のラグランジュ部分多様体について、ハミルトン変形のもとでの体積の極小性(ハミルトン安定性)や最小性(ハミルトン体積最小性)について考察した。これは等周問題の1つの一般化と考えられ、例えば、複素ユークリッド空間内の標準的トーラスや複素射影空間たちの直積のトーラス軌道などはハミルトン安定であることが知られていた。本講演では次の2つの結果について紹介する:
1. 3次元以上の複素ベクトル空間のほとんどの標準的トーラスはハミルトン体積最小ではない。
2. 3次元以上の任意のコンパクトトーリックケーラー多様体のトーラス軌道にはハミルトン体積最小ではないものが数多く存在する。



10:30 - 12:00 数理科学研究科棟(駒場) 128号室
神本 丈 氏 (九州大学)
『 Resolution of singularities via Newton polyhedra and its application to analysis 』(JAPANESE)
In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.


15:30 - 17:00 数理科学研究科棟(駒場) 122号室
Andrés Daniel Duarte 氏 (Institut de Mathématiques de Toulouse)
『 Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem 』(ENGLISH)
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.


16:30 - 18:00 数理科学研究科棟(駒場) 002号室
Chien-Hong Cho 氏 (National Chung Cheng University)
『 On the finite difference approximation for blow-up solutions of the nonlinear wave equation 』(JAPANESE)
We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\alpha}$ $(\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.



13:00 - 14:10 数理科学研究科棟(駒場) 052号室
Selma Chaker 氏 (Bank of Canada)
『 On High Frequency Estimation of the Frictionless Price: The Use of Observed Liquidity Variables 』(ENGLISH)
Observed high-frequency prices are always contaminated with liquidity costs or market microstructure noise. Inspired by the market microstructure literature, I explicitly model this noise and remove it from observed prices to obtain an estimate of the frictionless price. I then formally test whether the prices adjusted for the estimated liquidity costs are either totally or partially free from noise. If the liquidity costs are only partially removed, the residual noise is smaller and closer to an exogenous white noise than the original noise is. To illustrate my approach, I use the adjusted prices to improve volatility estimation in the presence of noise. If the noise is totally absorbed, I show that the sum of squared returns - which would be inconsistent for return variance when based on observed returns - becomes consistent when based on adjusted returns.


16:30 - 18:00 数理科学研究科棟(駒場) 128号室
岡田 靖則 氏 (千葉大学大学院理学研究科)
『 Ultra-differentiable classes and intersection theorems 』(JAPANESE)
There are two ways to define notions of
ultra-differentiability: one in terms of estimates on derivatives, and
the other in terms of growth properties of Fourier transforms of
suitably localized functions.
In this talk, we study the relation between BMT-classes and
inhomogeneous Gevrey classes, which are examples of such two kinds of
notions of ultra-differentiability.
We also mention intersection theorems on these classes.
This talk is based on a joint work with Otto Liess (Bologna University).


16:30 - 18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
足助 太郎 氏 (東京大学大学院数理科学研究科)
『 Transverse projective structures of foliations and deformations of the Godbillon-Vey class 』(JAPANESE)
Given a smooth family of foliations, we can define the derivative of the Godbillon-Vey class
with respect to the family. The derivative is known to be represented in terms of the projective
Schwarzians of holonomy maps. In this talk, we will study transverse projective structures
and connections, and show that the derivative is in fact determined by the projective structure
and the family.



10:00 - 11:30 数理科学研究科棟(駒場) 122号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
只野 誉 氏 (大阪大学)
『 Gap theorems for compact gradient Sasaki Ricci solitons 』(JAPANESE)
In this talk we give some necessary and sufficient conditions for compact gradient Sasaki-Ricci solitons to be Sasaki-Einstein. Our result may be considered as a Sasaki geometry version of recent works by H. Li, and M. Fern¥'andez-L¥'opez-E. Garc¥'ia-Rio.



10:30 - 12:00 数理科学研究科棟(駒場) 126号室
高山 茂晴 氏 (東京大学)
『 On degenerations of Ricci-flat Kaehler manifolds 』(JAPANESE)



16:30 - 18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
黒木 慎太郎 氏 (東京大学大学院数理科学研究科)
『 An application of torus graphs to characterize torus manifolds with extended actions 』(JAPANESE)
A torus manifold is a compact, oriented 2n-dimensional T^n-
manifolds with fixed points. This notion is introduced by Hattori and
Masuda as a topological generalization of toric manifolds. For a given
torus manifold, we can define a labelled graph called a torus graph (
this may be regarded as a generalization of some class of GKM graphs).
It is known that the equivariant cohomology ring of some nice class of
torus manifolds can be computed by using a combinatorial data of torus
graphs. In this talk, we study which torus action of torus manifolds can
be extended to a non-abelian compact connected Lie group. To do this, we
introduce root systems of (abstract) torus graphs and characterize
extended actions of torus manifolds. This is a joint work with Mikiya



17:30 - 18:30 数理科学研究科棟(駒場) 056号室
Shenghao Sun 氏 (Mathematical Sciences Center of Tsinghua University)
『 Parity of Betti numbers in étale cohomology 』(ENGLISH)
By Hodge symmetry, the Betti numbers of a complex projective smooth variety in odd degrees are even. When the base field has characteristic p, Deligne proved the hard Lefschetz theorem in etale cohomology, and the parity result follows from this. Suh has generalized this to proper smooth varieties in characteristic p, using crystalline cohomology.
The purity of intersection cohomology group of proper varieties suggests that the same parity property should hold for these groups in characteristic p. We proved this by investigating the symmetry in the categorical level.
In particular, we reproved Suh's result, using merely etale cohomology. Some related results will be discussed. This is joint work with Weizhe Zheng.

(本講演は「東京北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, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)



16:40 - 17:40 数理科学研究科棟(駒場) 056号室
Gantsooj Batzaya 氏 (東京大学数理科学研究科)
『 On simultaneous approximation to powers of a real number by rational numbers 』(ENGLISH)



10:30 - 12:00 数理科学研究科棟(駒場) 126号室
林本 厚志 氏 (長野工業高等専門学校)