## Seminar information archive

Seminar information archive ～09/22｜Today's seminar 09/23 | Future seminars 09/24～

#### GCOE Seminars

16:15-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Inverse problems and observability inequalities for plate equations and Schrodinger equations.

**G. Yuan**(Northeast Normal Univ.)Inverse problems and observability inequalities for plate equations and Schrodinger equations.

[ Abstract ]

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.

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

#### Lectures

17:00-18:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Introduction to Coherent Risk Measure

**Freddy DELBAEN**(チューリッヒ工科大学名誉教授)Introduction to Coherent Risk Measure

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Heat transfer in composite materials with Stenfen-Boltzmann conditions and related inverse problems

**Jin CHENG (程 晋)**(復旦大学)Heat transfer in composite materials with Stenfen-Boltzmann conditions and related inverse problems

[ Abstract ]

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.

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.

#### thesis presentations

15:45-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

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)

**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)

#### thesis presentations

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

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)

**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)

#### thesis presentations

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

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)

**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)

#### thesis presentations

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

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)

**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)

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

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)

**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

#### Seminar on Probability and Statistics

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

Non-Parametric Statistics for a partial sums of iid observations: New Trials

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/13.html

**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

[ Abstract ]

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.

[ Reference URL ]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.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/13.html

#### Seminar on Probability and Statistics

16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

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)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/14.html

**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)

[ Abstract ]

(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.

[ Reference URL ](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.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/14.html

#### Lectures

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Traveling waves of a curvature flow in almost periodic media

**Bendong LOU (婁 本東)**(同済大学)Traveling waves of a curvature flow in almost periodic media

[ Abstract ]

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.

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.

#### Seminar on Probability and Statistics

13:40-14:50 Room #128 (Graduate School of Math. Sci. Bldg.)

Applications of Iterated Function Systems to Inference and Simulation

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/12.html

**Stefano Maria Iacus**(Universita degli Studi di Milano)Applications of Iterated Function Systems to Inference and Simulation

[ Abstract ]

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.

[ Reference URL ]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.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/12.html

### 2009/02/03

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**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)

[ Abstract ]

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.

[ Reference URL ]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.

https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009/02/02

#### Lectures

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

On a perceptron version of the Generalized Random Energy Model

**Erwin Bolthausen**(University of Zurich)On a perceptron version of the Generalized Random Energy Model

### 2009/01/30

#### GCOE Seminars

16:15-17:15 Room #370 (Graduate School of Math. Sci. Bldg.)

Faber-Krahn Type Inequalities in Inverse Scattering Theory

**F. Cakoni**(University of Delaware)Faber-Krahn Type Inequalities in Inverse Scattering Theory

[ Abstract ]

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.

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.

#### GCOE Seminars

15:10-16:10 Room #370 (Graduate School of Math. Sci. Bldg.)

Use of Carleman estimates for stability in some inverse problems

**Lucie Baudouin**(LAAS-CNRS groupe MAC)Use of Carleman estimates for stability in some inverse problems

[ Abstract ]

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).

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

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Extension and Unification of Singular Perturbation Methods for ODE's Based on the Renormalization Gourp Method

**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

[ Abstract ]

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.

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

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #122 (Graduate School of Math. Sci. Bldg.)

電場による配管損傷評価法について

**吉野 伸**(東京電力)電場による配管損傷評価法について

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On the p-adic local Langlands correspondence

**Pierre Colmez**(École polytechnique)On the p-adic local Langlands correspondence

### 2009/01/27

#### Tuesday Seminar on Topology

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Lagrangian Floer homology and quasi homomorphism

from the group of Hamiltonian diffeomorphism

**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

[ Abstract ]

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).

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

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

高次順像層のホッジ計量の正値性

**高山 茂晴**(東大数理)高次順像層のホッジ計量の正値性

#### GCOE lecture series

17:15-18:15 Room #470 (Graduate School of Math. Sci. Bldg.)

ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講

**Vladimir Romanov**(Sobolev Instutite of Mathematics)ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講

[ Abstract ]

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.

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.

#### GCOE Seminars

16:00-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Ingham-Beurling type inequalities

**Vilmos Komornik**(University of Strasbourg)Ingham-Beurling type inequalities

[ Abstract ]

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.

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

#### Infinite Analysis Seminar Tokyo

11:00-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)

一般化されたヤング図形の q-Hook formula

Catalan numbers and level 2 weight structures of $A^{(1)}_{p-1}$

On a dimer model with impurities

**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

[ Abstract ]

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。

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) 13:30-14:30Catalan numbers and level 2 weight structures of $A^{(1)}_{p-1}$

[ Abstract ]

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.

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) 15:00-16:00On a dimer model with impurities

[ Abstract ]

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.

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

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50 Room #128 (Graduate School of Math. Sci. Bldg.)

防衛電子技術についてⅡ

**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

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