# 東大数理セミナー情報 --- 今後の予定 2014年03月11日(火)～

## 2014年03月11日(火)

### GCOEセミナー

17:00 - 18:00 数理科学研究科棟(駒場) 118号室
Lucie Baudouin 氏 (LAAS-CNRS, equipe MAC)
『 Inverse problem for the waves : stability and convergence matters 』(ENGLISH)
This talk aims to present some recent works in collaboration with Maya de Buhan, Sylvain Ervedoza and Axel Osses regarding an inverse problem for the wave equation. More specifically, we study the determination of the potential in a wave equation with given Dirichlet boundary data from a measurement of the flux of the solution on a part of the boundary. On the one hand, we will focus on the question of convergence of the space semi-discrete inverse problems toward their continuous counterpart. Several uniqueness and stability results are available in the literature about the continuous setting of the inverse problem of determination of a potential in the wave equation. In particular, we can mention a Lipschitz stability result under a classical geometric condition obtained by Imanuvilov and Yamamoto, and a logarithmic stability result obtained by Bellassoued when the observation measurement is made on an arbitrary part of the boundary. In both situations, we can design a numerical process for which convergence results are proved. The analysis we conduct is based on discrete Carleman estimates, either for the hyperbolic or for the elliptic operator, in which case we shall use a result of Boyer, Hubert and Le Rousseau. On the other hand, still considering the same inverse problem, we will present a new reconstruction algorithm of the potential. The design and convergence of the algorithm are based on the Carleman estimates for the waves previously used to prove the Lipschitz stability. We will finally give some simple illustrative numerical simulations for 1-d problems.

## 2014年03月12日(水)

### 講演会

10:15 - 11:45 数理科学研究科棟(駒場) 470号室
Michele Triestino 氏 (Ecole Normale Superieure de Lyon)
『 Invariant distributions for circle diffeomorphisms of irrational rotation number and low regularity 』(ENGLISH)
The main inspiration of this joint work with Andrés Navas is the beautiful result of Ávila and Kocsard: if f is a C^\infty circle diffeomorphism of irrational rotation number, then the unique invariant probability measure is also the unique (up to rescaling) invariant distribution.
Using conceptual geometric arguments (Hahn-Banach...), we investigate the uniqueness of invariant distributions for C^1 circle diffeomorphisms of irrational rotation number, with particular attention to sharp regularity.
We prove that If the diffeomorphism is C^{1+bv}, then there is a unique invariant distribution of order 1. On the other side, examples by Douady and Yoccoz, and by Kodama and Matsumoto exhibit differentiable dynamical systems for which the uniqueness does not hold.

### 数理人口学・数理生物学セミナー

15:00 - 17:00 数理科学研究科棟(駒場) 126号室
Andre M. de Roos 氏 (University of Amsterdam)
『 When size does matter: Ontogenetic symmetry and asymmetry in energetics 』(ENGLISH)
Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.
http://staff.science.uva.nl/~aroos/

### GCOEセミナー

15:00 - 17:00 数理科学研究科棟(駒場) 126号室
Andre M. de Roos 氏 (University of Amsterdam)
『 When size does matter: Ontogenetic symmetry and asymmetry in energetics 』(ENGLISH)
Body size (≡ biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as “ontogenetic symmetry”. Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.
http://staff.science.uva.nl/~aroos/

## 2014年03月13日(木)

### 講演会

13:30 - 15:00 数理科学研究科棟(駒場) 470号室
Michele Triestino 氏 (Ecole Normale Superieure de Lyon)
『 Almost sure triviality of the $C^1$-centralizer of random circle diffeomorphisms with periodic points 』(ENGLISH)
By the end of the 80s, Malliavin and Shavgulidze introduced a measure on the space of C^1 circle diffeomorphisms which carries many interesting features. Perhaps the most interesting aspect is that it can be considered as an analog of the Haar measure for the group Diff^1_+(S^1).
The nature of this measure has been mostly investigated in connection to representation theory.
For people working in dynamical systems, the MS measure offers a way to quantify dynamical phenomena: for example, which is the probability that a random diffeomorphism is irrational? Even if this question have occupied my mind for a long time, it remains still unanswered, as many other interesting ones. However, it is possible to understand precisely what are the typical features of a diffeomorphism with periodic points.

### GCOEセミナー

17:00 - 18:00 数理科学研究科棟(駒場) 122号室
『 STABILITY IN THE OBSTACLE PROBLEM FOR A SHALLOW SHELL 』(ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/bm02.pdf

## 2014年03月14日(金)

### GCOEセミナー

16:00 - 16:50 数理科学研究科棟(駒場) 118号室
Kazufumi Ito 氏 (North Carolina State Univ.)
『 A new finite difference scheme based on staggered grids for Navier Stokes equations 』(ENGLISH)
We develop a new method that uses the staggered grid only for the pressure node, i.e., the pressure gird is the center of the square cell and the velocities are at the node. The advantage of the proposed method compared to the standard staggered grid methods is that it is very straight forward to treat the boundary conditions for the velocity field, the fluid structure interaction, and to deal with the multiphase flow using the immersed interface methods. We present our analysis and numerical tests.

### GCOEセミナー

17:00 - 17:50 数理科学研究科棟(駒場) 118号室
Jun Zou 氏 (The Chinese University of Hong Kong)
『 Efficient Domain Decomposition Methods for a Class of Linear and Nonlinear Inverse Problems 』(ENGLISH)
In this talk we shall present several new domain decomposition methods for solving some linear and nonlinear inverse problems. The motivations and derivations of the methods will be discussed, and numerical experiments will be demonstrated.

## 2014年04月21日(月)

### 数値解析セミナー

16:30 - 18:00 数理科学研究科棟(駒場) 056号室

『 人工血管の最適設計を目的としたNavier-Stokes方程式の周期解に対する形状最化問題 』(JAPANESE)
Stokes方程式やNavier-Stokes方程式の定常解に対する形状最適化問題は,これまで多く行われてきた.しかし, Navier-Stokes方程式の周期解に対しては十分に行われていない.本講演では,安定性理論を活用することで,Navier-Stokes方程式の周期解に対する形状最適化問題を人工血管の最適設計という現実の問題を通して考察する.
http://www.infsup.jp/utnas/

## 2014年04月24日(木)

### 幾何コロキウム

10:00 - 11:30 数理科学研究科棟(駒場) 122号室

『 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。)

## 2014年04月28日(月)

### 代数幾何学セミナー

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.