## 過去の記録

#### 講演会

14:40-16:10   数理科学研究科棟(駒場) 123号室
Herbert Spohn 氏 (ミュンヘン工科大学)
Some problems from Statistical Mechanics linked to matrix-valued
Brownian motion

#### 講演会

16:20-17:50   数理科学研究科棟(駒場) 123号室
Stefano Olla 氏 (パリ第9大学)
Macroscopic energy transport: a weak coupling approach

### 2009年02月19日(木)

#### 講演会

17:00-18:30   数理科学研究科棟(駒場) 056号室
Freddy DELBAEN 氏 (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure

#### 代数幾何学セミナー

15:50-18:00   数理科学研究科棟(駒場) 128号室
O. F. Pasarescu 氏 (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年02月18日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Non-existence theorem of periodic solutions except out-of-phase
and in-phase solutions in the coupled van der Pol equation system
[ 講演概要 ]
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.

#### 博士論文発表会

17:00-18:10   数理科学研究科棟(駒場) 122号室

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

### 2009年02月14日(土)

#### 東京無限可積分系セミナー

10:30-14:00   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]

の常微分方程式系である.

て, 野海・山田系のタウ関数の双線形方程式を求める.

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
[ 講演概要 ]
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.

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年02月13日(金)

#### GCOEレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 370号室

Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第3講
[ 講演概要 ]
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セミナー

14:00-14:45   数理科学研究科棟(駒場) 270号室
Johannes Elschner 氏 (Weierstrass Institute)
Direct and inverse problems in fluid-solid interaction
[ 講演概要 ]
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セミナー

16:15-17:00   数理科学研究科棟(駒場) 270号室
Wenbin Chen 氏 (Fudan University)
New Energy-conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations
[ 講演概要 ]
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年02月12日(木)

#### 講演会

17:00-18:30   数理科学研究科棟(駒場) 056号室
Freddy DELBAEN 氏 (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure

### 2009年02月10日(火)

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室

Piermarco Cannarsa 氏 (Univ. degli Studi Roma "Tor Vergata")
Carleman estimates for degenerate parabolic operators with application to null controllability
[ 講演概要 ]
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セミナー

16:15-17:15   数理科学研究科棟(駒場) 270号室

Yurii Anikonov 氏 (Sobolev Institute of Mathematics)
Constructive methods in inverse problems
[ 講演概要 ]
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年02月07日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

Siegel's fundamental domain of degree 2 and Groebner method

### 2009年02月06日(金)

#### GCOEレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 370号室

Vladimir Romanov 氏 (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第2講
[ 講演概要 ]
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.

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 118号室

Brauer Groups,Mackey and Tambara functors on profinite groups,and 2-dimensional homological algebra(Brauer群、プロ有限群上のMackey及び丹原関手と2次元ホモロジー代数)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 118号室

Generalized Whittaker functions for degenerate principal series of GL(4,R)(GL(4,R)の退化主系列表現の一般Whittaker関数)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 118号室

On the existence of homomorphisms between principal series of complex semisimple Lie groups(複素半単純リー群の主系列表現の間の準同型の存在について)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 122号室

Surface links which are coverings of a trivial torus knot(自明なトーラスの被覆の形をした曲面結び目の研究)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 122号室

Compactification of the homeomorphism group of a graph(グラフの同相群のコンパクト化について)

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 126号室

Large deviations and theorems of law of large numbers' type for the processes related to the interface models(

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 126号室

On the Navier-Stokes equations in a rotating frame and the functional-differential equations of advanced type - a Fourier analysis approach(フーリエ解析的手法による回転場内の流体方程式と進み型関数微分方程式の考察)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 128号室

Short time asymptotic behavior and large deviations for Brownian motion on scale irregular Sierpinski gaskets(非正規なシェルピンスキーガスケット上のブラウン運動に対する熱核の短時間漸近挙動と大偏差原理)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 128号室

Rumor Transmission Models and Persistence Analysis(流言伝播モデルとパーシステンス解析)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 128号室

Generalized Okubo systems and the middle convolution(一般大久保型方程式とミドルコンボルーション)