## Seminar information archive

### 2010/03/12

#### Colloquium

15:00-17:30   Room #050 (Graduate School of Math. Sci. Bldg.)

ガルニエ系の数理
[ Abstract ]
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。

[ Abstract ]
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

#### PDE Real Analysis Seminar

10:30-11:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Joachim Escher (Leibniz University of Hanover)
Shallow water waves with singularities
[ Abstract ]
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

#### Lectures

15:00-16:30   Room #370 (Graduate School of Math. Sci. Bldg.)
Robert Penner (Aarhus University / University of Southern California)
Protein Moduli Space
[ Abstract ]
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

#### Lectures

14:00-15:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Bendong LOU (同済大学)
Homogenization Limit and Singular Limit of the Allen-Cahn equation
[ Abstract ]
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

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (Orsay)
Discrete groups acting on homogeneous spaces V
[ Abstract ]
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

#### GCOE lecture series

10:30-17:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
[ Abstract ]
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

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Roberto Longo (University of Rome, Tor Vergata)
Von Neumann Algebras and Boundary Quantum Field Theory

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Bendong LOU (同済大学)
Homogenization limit of a parabolic equation with nonlinear boundary conditions
[ Abstract ]
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 $g$".

#### GCOE Seminars

10:10-11:00   Room #122 (Graduate School of Math. Sci. Bldg.)

#### GCOE Seminars

11:00-11:50   Room #122 (Graduate School of Math. Sci. Bldg.)

#### GCOE Seminars

13:20-14:10   Room #122 (Graduate School of Math. Sci. Bldg.)

#### GCOE Seminars

14:10-14:40   Room #122 (Graduate School of Math. Sci. Bldg.)

#### GCOE Seminars

14:50-15:40   Room #122 (Graduate School of Math. Sci. Bldg.)
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

#### GCOE lecture series

10:30-16:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (Paris Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces I
[ Abstract ]
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

#### Seminar on Probability and Statistics

15:00-16:10   Room #128 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/14.html

### 2010/02/16

#### Tuesday Seminar on Topology

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Dieter Kotschick (Univ. M\"unchen)
Characteristic numbers of algebraic varieties
[ Abstract ]
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

#### thesis presentations

09:45-11:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Takahiro Tsushima (University of Tokyo)
Elementary computation of ramified components of Jacobi sum Hecke characters (JAPANESE)

#### thesis presentations

11:00-12:15   Room #118 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Abe (University of Tokyo)
Comparison between Swan conductors and characteristic cycles (JAPANESE)

#### thesis presentations

13:00-14:15   Room #118 (Graduate School of Math. Sci. Bldg.)

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)

#### thesis presentations

14:15-15:30   Room #118 (Graduate School of Math. Sci. Bldg.)

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)

#### thesis presentations

09:45-11:00   Room #122 (Graduate School of Math. Sci. Bldg.)

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)

#### thesis presentations

11:00-12:15   Room #122 (Graduate School of Math. Sci. Bldg.)

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)

#### thesis presentations

11:00-12:15   Room #126 (Graduate School of Math. Sci. Bldg.)

Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)

#### thesis presentations

13:00-14:15   Room #126 (Graduate School of Math. Sci. Bldg.)

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)

#### thesis presentations

14:15-15:30   Room #126 (Graduate School of Math. Sci. Bldg.)

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)