## Seminar information archive

Seminar information archive ～02/19｜Today's seminar 02/20 | Future seminars 02/21～

#### GCOE Seminars

11:15-12:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Determining moving boundaries from Cauchy data on remote surfaces

**J. Ralston**(UCLA)Determining moving boundaries from Cauchy data on remote surfaces

[ Abstract ]

We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.

We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.

### 2009/03/04

#### GCOE Seminars

15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Probing for inclusions for the heat equation with complex

spherical waves

**P. Gaitan (with H. Isozaki and O. Poisson)**(Univ. Marseille)Probing for inclusions for the heat equation with complex

spherical waves

#### GCOE Seminars

16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Coefficient reconstruction from partial measurements in a heterogeneous

equation of FKPP type

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf

**M. Cristofol**(Univ. Marseille)Coefficient reconstruction from partial measurements in a heterogeneous

equation of FKPP type

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf

### 2009/03/03

#### GCOE Seminars

16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications

**O. Poisson**(Univ. Marseille)Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications

[ Abstract ]

We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.

We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.

#### GCOE Seminars

15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Controllability of the heat equation in a stratified media : a consequence of its spectral structure.

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf

**Y. Dermenjian**(Univ. Marseille)Controllability of the heat equation in a stratified media : a consequence of its spectral structure.

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf

### 2009/03/02

#### GCOE Seminars

15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions

http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf

**Bernd Hofmann**(Chemnitz University of Technology)Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions

[ Abstract ]

Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization

[ Reference URL ]Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization

http://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf

### 2009/02/26

#### Lectures

17:00-18:30 Room #270 (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

#### GCOE Seminars

15:00-16:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Reconstruction of biological tissue conductivity by MREIT technique

**Jijun Liu**(Southeast University, P.R.China)Reconstruction of biological tissue conductivity by MREIT technique

[ Abstract ]

Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT)model, MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. In this talk, we will give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm and nonlinear integral equation algorithm. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.

Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT)model, MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. In this talk, we will give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm and nonlinear integral equation algorithm. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.

### 2009/02/24

#### Colloquium

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

相関関数の構成要素

**神保道夫**(東京大学大学院数理科学研究科)相関関数の構成要素

[ Abstract ]

2次元の可積分な格子模型や、それと等価な1次元量子スピンチェインは、ベーテ、オンサーガー以来多くの研究が重ねられ、詳細に調べられている。ハミルトニアンのスペクトルと並ぶ重要な物理量に相関関数がある。イジング模型や共形場理論では相関関数自身が微分方程式で特徴づけられるがこのような簡明な結果はそれ以外の場合には知られていない。イジング模型を超える代表的な例として1次元のXXZ模型がある。相関関数は多重積分であらわされ、その長距離漸近挙動の研究が近年フランスのグループにより大きく進展している。

講演の前半では、相関関数に焦点をあててこれまでの研究の歴史を概観する。結合定数や温度などのパラメータの関数として見た場合、相関関数は2つの要素的超越関数から原理的には有理的に決まっていることがわかる。後半ではこの話題を紹介したい。

2次元の可積分な格子模型や、それと等価な1次元量子スピンチェインは、ベーテ、オンサーガー以来多くの研究が重ねられ、詳細に調べられている。ハミルトニアンのスペクトルと並ぶ重要な物理量に相関関数がある。イジング模型や共形場理論では相関関数自身が微分方程式で特徴づけられるがこのような簡明な結果はそれ以外の場合には知られていない。イジング模型を超える代表的な例として1次元のXXZ模型がある。相関関数は多重積分であらわされ、その長距離漸近挙動の研究が近年フランスのグループにより大きく進展している。

講演の前半では、相関関数に焦点をあててこれまでの研究の歴史を概観する。結合定数や温度などのパラメータの関数として見た場合、相関関数は2つの要素的超越関数から原理的には有理的に決まっていることがわかる。後半ではこの話題を紹介したい。

### 2009/02/23

#### Lectures

13:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

TBA

**長田 博文**(九大数理)TBA

#### Lectures

14:40-16:10 Room #123 (Graduate School of Math. Sci. Bldg.)

Some problems from Statistical Mechanics linked to matrix-valued

Brownian motion

**Herbert Spohn**(ミュンヘン工科大学)Some problems from Statistical Mechanics linked to matrix-valued

Brownian motion

#### Lectures

16:20-17:50 Room #123 (Graduate School of Math. Sci. Bldg.)

Macroscopic energy transport: a weak coupling approach

**Stefano Olla**(パリ第9大学)Macroscopic energy transport: a weak coupling approach

### 2009/02/19

#### Lectures

17:00-18:30 Room #056 (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

#### Algebraic Geometry Seminar

15:50-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

・Linear Systems on Rational Surfaces; Applications (15:50--16: 50)

・Some Applications of Model Theory in Algebraic Geometry (17:00 --18:00)

**O. F. Pasarescu**(Romanian Academy)・Linear Systems on Rational Surfaces; Applications (15:50--16: 50)

・Some Applications of Model Theory in Algebraic Geometry (17:00 --18:00)

### 2009/02/18

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Non-existence theorem of periodic solutions except out-of-phase

and in-phase solutions in the coupled van der Pol equation system

**野原勉**(武蔵工業大学)Non-existence theorem of periodic solutions except out-of-phase

and in-phase solutions in the coupled van der Pol equation system

[ Abstract ]

We consider the periodic solutions of the coupled van der Pol equation system $\\Sigma$, which is quite different from the ordinary van der Pol equation. We show the necessary and sufficient condition for the periodic solutions of $\\Sigma$. Non-existence theorem of periodic solutions except out-of-phase and in-phase solutions in $\\Sigma$ is presented.

We consider the periodic solutions of the coupled van der Pol equation system $\\Sigma$, which is quite different from the ordinary van der Pol equation. We show the necessary and sufficient condition for the periodic solutions of $\\Sigma$. Non-existence theorem of periodic solutions except out-of-phase and in-phase solutions in $\\Sigma$ is presented.

#### thesis presentations

17:00-18:10 Room #122 (Graduate School of Math. Sci. Bldg.)

Finite group actions on spin 4-manifolds(四次元スピン多様体への有限群作用)

**清野和彦**(東京大学大学院数理科学研究科)Finite group actions on spin 4-manifolds(四次元スピン多様体への有限群作用)

### 2009/02/14

#### Infinite Analysis Seminar Tokyo

10:30-14:00 Room #117 (Graduate School of Math. Sci. Bldg.)

野海・山田系におけるタウ関数の関係式

ワイル群の regular な共役類に付随するドリンフェルト・ソコロフ階層とパンルヴェ型微分方程式

**藤健太**(神戸理) 10:30-11:30野海・山田系におけるタウ関数の関係式

[ Abstract ]

野海・山田系は, A型のドリンフェルト・ソコロフ階層の相似簡約から得られる高階

の常微分方程式系である.

本講演では, ドリンフェルト・ソコロフ階層を波動作用素を用いて考察することによっ

て, 野海・山田系のタウ関数の双線形方程式を求める.

野海・山田系は, A型のドリンフェルト・ソコロフ階層の相似簡約から得られる高階

の常微分方程式系である.

本講演では, ドリンフェルト・ソコロフ階層を波動作用素を用いて考察することによっ

て, 野海・山田系のタウ関数の双線形方程式を求める.

**鈴木貴雄**(神戸理) 13:00-14:00ワイル群の regular な共役類に付随するドリンフェルト・ソコロフ階層とパンルヴェ型微分方程式

[ Abstract ]

ドリンフェルト・ソコロフ階層はKdV階層のアフィン・リー代数への一般化で, ワイ

ル群の共役類(またはハイゼンベルグ部分代数)によって特徴付けられる可積分系で

ある.

本講演では, ワイル群の共役類のうち特に regular と呼ばれるものに注目し, それ

に対応するドリンフェルト・ソコロフ階層の定式化について, F.Kroode-J.Leur, Kik

uchi-Ikeda-Kakei 等の仕事を紹介しつつ解説する.

また, パンルヴェ型微分方程式との関連についても述べる.

ドリンフェルト・ソコロフ階層はKdV階層のアフィン・リー代数への一般化で, ワイ

ル群の共役類(またはハイゼンベルグ部分代数)によって特徴付けられる可積分系で

ある.

本講演では, ワイル群の共役類のうち特に regular と呼ばれるものに注目し, それ

に対応するドリンフェルト・ソコロフ階層の定式化について, F.Kroode-J.Leur, Kik

uchi-Ikeda-Kakei 等の仕事を紹介しつつ解説する.

また, パンルヴェ型微分方程式との関連についても述べる.

### 2009/02/13

#### GCOE lecture series

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

ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第3講

**Vladimir Romanov**(Sobolev Instutite of Mathematics)ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第3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

14:00-14:45 Room #270 (Graduate School of Math. Sci. Bldg.)

Direct and inverse problems in fluid-solid interaction

**Johannes Elschner**(Weierstrass Institute)Direct and inverse problems in fluid-solid interaction

[ Abstract ]

We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The direct problem is to determine the scattered pressure field in the fluid domain as well as the displacement field in the elastic body, while the inverse problem is to reconstruct the shape of the elastic body from the far field pattern of the fluid pressure. We present a variational approach to the direct problem and two reconstruction methods for the inverse problem, which are based on nonlinear optimization and regularization.

We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The direct problem is to determine the scattered pressure field in the fluid domain as well as the displacement field in the elastic body, while the inverse problem is to reconstruct the shape of the elastic body from the far field pattern of the fluid pressure. We present a variational approach to the direct problem and two reconstruction methods for the inverse problem, which are based on nonlinear optimization and regularization.

#### GCOE Seminars

16:15-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)

New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations

**Wenbin Chen**(Fudan University)New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations

[ Abstract ]

In this talk, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.

In this talk, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.

### 2009/02/12

#### Lectures

17:00-18:30 Room #056 (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

### 2009/02/10

#### GCOE Seminars

15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Carleman estimates for degenerate parabolic operators with application to null controllability

**Piermarco Cannarsa**(Univ. degli Studi Roma "Tor Vergata")Carleman estimates for degenerate parabolic operators with application to null controllability

[ Abstract ]

From the controllability viewpoint, the behavior of uniformly parabolic equations is by now well understood. On the contrary, fewer results are known for degenerate parabolic equations, even though such a class of operators arise in many applied, as well as theoretical, problems.

A fairly complete analysis of the null controllability properties of degenerate parabolic equations in one space dimension was completed in a series of recent works by the speaker and coauthors. The aim of this talk is to review the above theory and present some recent results obtained in collaboration with P. Martinez and J.Vancostenoble for higher dimensional problems. Essential tools of such an approach are adapted Carleman estimates and Hardy type inequalities.

From the controllability viewpoint, the behavior of uniformly parabolic equations is by now well understood. On the contrary, fewer results are known for degenerate parabolic equations, even though such a class of operators arise in many applied, as well as theoretical, problems.

A fairly complete analysis of the null controllability properties of degenerate parabolic equations in one space dimension was completed in a series of recent works by the speaker and coauthors. The aim of this talk is to review the above theory and present some recent results obtained in collaboration with P. Martinez and J.Vancostenoble for higher dimensional problems. Essential tools of such an approach are adapted Carleman estimates and Hardy type inequalities.

#### GCOE Seminars

16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Constructive methods in inverse problems

**Yurii Anikonov**(Sobolev Institute of Mathematics)Constructive methods in inverse problems

[ Abstract ]

New representations for solutions and coefficients of evolutionary equations are presented. On the basic of these representations theorems of solvability for inverse problems are obtained. This direction develops constructibility in the theory and applications of inverse problems to differential equations

New representations for solutions and coefficients of evolutionary equations are presented. On the basic of these representations theorems of solvability for inverse problems are obtained. This direction develops constructibility in the theory and applications of inverse problems to differential equations

### 2009/02/07

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

次数2のモジュラー群の基本領域における行列式の最小値

Siegel's fundamental domain of degree 2 and Groebner method

**河村隆**(成蹊大学) 13:30-14:30次数2のモジュラー群の基本領域における行列式の最小値

**早田孝博**(山形大学・工学部) 15:00-16:00Siegel's fundamental domain of degree 2 and Groebner method

### 2009/02/06

#### GCOE lecture series

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

ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第2講

**Vladimir Romanov**(Sobolev Instutite of Mathematics)ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第2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.

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