## Seminar information archive

Seminar information archive ～10/21｜Today's seminar 10/22 | Future seminars 10/23～

### 2010/03/09

#### PDE Real Analysis Seminar

10:30-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Shallow water waves with singularities

**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.

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.)

Protein Moduli Space

**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.

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.)

Homogenization Limit and Singular Limit of the Allen-Cahn equation

**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.

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.)

Discrete groups acting on homogeneous spaces V

**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.

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.)

Discrete groups acting on homogeneous spaces III

Discrete groups acting on homogeneous spaces IV

**Yves Benoist**(Pars Sud) 10:30-11:30Discrete 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.

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) 15:00-16:00Discrete groups acting on homogeneous spaces IV

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Von Neumann Algebras and Boundary Quantum Field Theory

**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.)

Homogenization limit of a parabolic equation with nonlinear boundary conditions

**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 $g$".

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.)

空間的に非一様な場における進行波

**俣野 博**(数理科学)空間的に非一様な場における進行波

#### GCOE Seminars

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

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

**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

#### GCOE Seminars

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

結晶界面の成長と偏微分方程式

**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

#### GCOE Seminars

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

成層の影響を考えたエクマン層の安定性について

**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

#### GCOE Seminars

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

Flow and material simulation for industrial purposes

**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.)

Discrete groups acting on homogeneous spaces I

Discrete groups acting on homogeneous spaces II

**Yves Benoist**(Paris Sud) 10:30-11:30Discrete 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.

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) 15:00-16:00Discrete groups acting on homogeneous spaces II

#### Seminar on Probability and Statistics

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

勾配写像で表される球面上の確率分布族

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

**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

[ Abstract ]

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。

[ Reference URL ]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

#### Tuesday Seminar on Topology

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Characteristic numbers of algebraic varieties

**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.

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.)

Elementary computation of ramified components of Jacobi sum Hecke characters (JAPANESE)

**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.)

Comparison between Swan conductors and characteristic cycles (JAPANESE)

**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)

**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)

#### 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)

**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)

#### 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)

**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)

#### 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)

**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)

#### 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)

**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)

#### 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)

**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)

#### 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)

**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)

#### thesis presentations

09:45-11:00 Room #128 (Graduate School of Math. Sci. Bldg.)

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)

**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)

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