## Seminar information archive

Seminar information archive ～02/21｜Today's seminar 02/22 | Future seminars 02/23～

### 2011/02/16

#### Classical Analysis

13:30-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)

Degeneration scheme of 4-dimensional Painlev¥'e type equations

(Joint work with H. Sakai and A. Nakamura)

(ENGLISH)

Solvability of difference Riccati equations (ENGLISH)

**H. Sakai**(University of Tokyo) 13:30-14:30Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)

**H. Kawakami**(University of Tokyo) 14:45-15:45Degeneration scheme of 4-dimensional Painlev¥'e type equations

(Joint work with H. Sakai and A. Nakamura)

(ENGLISH)

**S. Nishioka**(University of Tokyo) 16:00-17:00Solvability of difference Riccati equations (ENGLISH)

### 2011/02/14

#### GCOE Seminars

13:00-14:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Unique continuation on the analytic curve and its application to inverse problems. (ENGLISH)

**Jin Cheng**(Fudan University)Unique continuation on the analytic curve and its application to inverse problems. (ENGLISH)

[ Abstract ]

The unique continuation is one of the important properties for the partial differential equations, which is applied to the study of inverse problems for PDE. In this talk, we will show the unique continuation on the analytic curve for the elliptic equations with analytic coefficients. Some applications to inverse problems are mentioned.

The unique continuation is one of the important properties for the partial differential equations, which is applied to the study of inverse problems for PDE. In this talk, we will show the unique continuation on the analytic curve for the elliptic equations with analytic coefficients. Some applications to inverse problems are mentioned.

### 2011/02/10

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Symplectic and quantum categories (ENGLISH)

**Alan Weinstein**(UC Berkeley)Symplectic and quantum categories (ENGLISH)

#### Applied Analysis

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Control and nonlinearity (ENGLISH)

**Jean-Michel Coron**(University of Paris 6)Control and nonlinearity (ENGLISH)

[ Abstract ]

We present methods to study the controllability and the stabilizability of nonlinear control systems. The emphasis is put on specific phenomena due to the nonlinearities. In particular we study cases where the nonlinearities are essential for the controllability or the stabilizability.

We illustrate these methods on control systems modeled by ordinary differential equations or partial differential equations (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg de Vries equations).

We present methods to study the controllability and the stabilizability of nonlinear control systems. The emphasis is put on specific phenomena due to the nonlinearities. In particular we study cases where the nonlinearities are essential for the controllability or the stabilizability.

We illustrate these methods on control systems modeled by ordinary differential equations or partial differential equations (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg de Vries equations).

#### Number Theory Seminar

11:00-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)

The motivic Galois group and periods of algebraic varieties (ENGLISH)

**Joseph Ayoub**(University of Zurich)The motivic Galois group and periods of algebraic varieties (ENGLISH)

[ Abstract ]

We give a construction of the motivic Galois group of $\\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.

We give a construction of the motivic Galois group of $\\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.

### 2011/02/04

#### thesis presentations

09:45-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p(総実代数体の羃指数p型非可換p拡大に対するp-進ゼータ関数の帰納的構成) (JAPANESE)

**Takashi HARA**(Graduate School of Mathematical Sciences University of Tokyo)Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p(総実代数体の羃指数p型非可換p拡大に対するp-進ゼータ関数の帰納的構成) (JAPANESE)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Galois extensions,pls closure,and maps on local cohomology(ガロア拡大、プラス閉包、及び局所コホモロジー間の射について) (JAPANESE)

**Akiyoshi SANNAI**(Graduate School of Mathematical Sciences University of Tokyo)Galois extensions,pls closure,and maps on local cohomology(ガロア拡大、プラス閉包、及び局所コホモロジー間の射について) (JAPANESE)

#### thesis presentations

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

Fast lattice reduction algorithms for optimizing F2-linear pseudorandom number generators(F2-線形擬似乱数発生法の最適化のための高速格子簡約アルゴリズム) (JAPANESE)

**Shin HARASE**(Graduate School of Mathematical Sciences University of Tokyo)Fast lattice reduction algorithms for optimizing F2-linear pseudorandom number generators(F2-線形擬似乱数発生法の最適化のための高速格子簡約アルゴリズム) (JAPANESE)

#### thesis presentations

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

Non-commutative Reidemeister torsion, Morse-Novikov theory and homology cylinders of higher-order(非可換ライデマイスタートーション,モース‐ノビコフ理論及び高次のホモロジーシリンダー) (JAPANESE)

**Takahiro KITAYAMA**(Graduate School of Mathematical Sciences University of Tokyo)Non-commutative Reidemeister torsion, Morse-Novikov theory and homology cylinders of higher-order(非可換ライデマイスタートーション,モース‐ノビコフ理論及び高次のホモロジーシリンダー) (JAPANESE)

#### thesis presentations

14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Uniform Estimates for Distributions of Sums of i.i.d Random Variables with Fat Tail(分布がファットテールをもつ場合の独立同分布の和の分布の一様評価について) (JAPANESE)

**Kenji NAKAHARA**(Graduate School of Mathematical Sciences University of Tokyo)Uniform Estimates for Distributions of Sums of i.i.d Random Variables with Fat Tail(分布がファットテールをもつ場合の独立同分布の和の分布の一様評価について) (JAPANESE)

#### thesis presentations

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

Regularity of two dimensional steady capillary gravity water waves(二次元定常表面張力重力波の正則性) (JAPANESE)

**Zhang Guanghui**(Graduate School of Mathematical Sciences University of Tokyo)Regularity of two dimensional steady capillary gravity water waves(二次元定常表面張力重力波の正則性) (JAPANESE)

#### thesis presentations

11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Singular Problems Related to Curvature Flow and Hamilton-Jacobi Equations(曲率流とハミルトン・ヤコビ方程式における特異問題) (JAPANESE)

**Liu Qing**(Graduate School of Mathematical Sciences University of Tokyo)Singular Problems Related to Curvature Flow and Hamilton-Jacobi Equations(曲率流とハミルトン・ヤコビ方程式における特異問題) (JAPANESE)

#### thesis presentations

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

Hydrodynamic limit and equilibrium fluctuation for nongradient systems(非勾配型の系に対する流体力学極限と平衡揺動) (JAPANESE)

**Makiko SASADA**(Graduate School of Mathematical Sciences University of Tokyo)Hydrodynamic limit and equilibrium fluctuation for nongradient systems(非勾配型の系に対する流体力学極限と平衡揺動) (JAPANESE)

#### thesis presentations

14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Coefficient inverse problems for partial differential equations in the viscoelasticity, the material science and population studies by Carleman estimates(カーレマン評価を用いた、粘弾性論・材料科学・人口学における偏微分方程式系の係数決定問題について) (JAPANESE)

**Masaaki UESAKA**(Graduate School of Mathematical Sciences University of Tokyo)Coefficient inverse problems for partial differential equations in the viscoelasticity, the material science and population studies by Carleman estimates(カーレマン評価を用いた、粘弾性論・材料科学・人口学における偏微分方程式系の係数決定問題について) (JAPANESE)

### 2011/02/03

#### thesis presentations

09:45-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Generators of modules in tropical geometry(トロピカル幾何における加群の生成元) (JAPANESE)

**Shuhei YOSHITOMI**(Graduate School of Mathematical Sciences the University of Tokyo)Generators of modules in tropical geometry(トロピカル幾何における加群の生成元) (JAPANESE)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Finite Symplectic Actions on the K3 Lattice(K3格子への有限シンプレクティック作用) (JAPANESE)

**Kenji HASHIMOTO**(Graduate School of Mathematical Sciences University of Tokyo)Finite Symplectic Actions on the K3 Lattice(K3格子への有限シンプレクティック作用) (JAPANESE)

#### thesis presentations

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

Weyl modules, Demazure modules and finite crystals for non-simply laced type(Bn, Cn, F4, G2型のワイル加群、デマズール加群および有限クリスタルについて) (JAPANESE)

**Katsuyuki NAOI**(Graduate School of Mathematical Sciences University of Tokyo)Weyl modules, Demazure modules and finite crystals for non-simply laced type(Bn, Cn, F4, G2型のワイル加群、デマズール加群および有限クリスタルについて) (JAPANESE)

#### thesis presentations

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

Extensions between finite-dimensional simple modules over a generalized current Lie algebra(一般化されたカレントリー代数上の有限次元単純加群の間の拡大) (JAPANESE)

**Ryosuke KODERA**(Graduate School of Mathematical Sciences University of Tokyo )Extensions between finite-dimensional simple modules over a generalized current Lie algebra(一般化されたカレントリー代数上の有限次元単純加群の間の拡大) (JAPANESE)

#### thesis presentations

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

Rigidity theorems for universal and symplectic universal lattices(普遍格子と斜交普遍格子の剛性定理) (JAPANESE)

**Masato MIMURA**(Graduate School of Mathematical Sciences University of Tokyo)Rigidity theorems for universal and symplectic universal lattices(普遍格子と斜交普遍格子の剛性定理) (JAPANESE)

#### thesis presentations

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

Deformation of torus equivariant spectral triples(トーラス同変なスペクトラル三つ組の変形) (JAPANESE)

**Makoto YAMASHITA**(Graduate School of Mathematical Sciences University of Tokyo)Deformation of torus equivariant spectral triples(トーラス同変なスペクトラル三つ組の変形) (JAPANESE)

#### thesis presentations

14:15-15:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Noncommutative Maximal Ergodic Inequality For Non-tracial L1-spaces(非トレース的L1空間に対する非可換極大エルゴード不等式) (JAPANESE)

**Zhang Qin**(Graduate School of Mathematical Sciences University of Tokyo)Noncommutative Maximal Ergodic Inequality For Non-tracial L1-spaces(非トレース的L1空間に対する非可換極大エルゴード不等式) (JAPANESE)

#### thesis presentations

14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Dispersive and Strichartz estimates for Schrödinger equations(シュレディンガー方程式に対する分散型及びストリッカーツ評価) (JAPANESE)

**Haruya MIZUTANI**(Graduate School of Mathematical Sciences University of Tokyo)Dispersive and Strichartz estimates for Schrödinger equations(シュレディンガー方程式に対する分散型及びストリッカーツ評価) (JAPANESE)

#### thesis presentations

15:45-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Conditional stability by Carleman estimates for inverse problems : coefficient inverse problems for the Dirac equation, the determination of subboundary by the heat equation and the continuation of solution of the Euler equation(逆問題に対するカーレマン評価による条件付き安定性: ディラック方程式に対する係数逆問題,熱方程式による部分境界の決定とオイラー方程式に対する解の接続性) (JAPANESE)

**Atsushi KAWAMOTO**(Graduate School of Mathematical Sciences University of Tokyo)Conditional stability by Carleman estimates for inverse problems : coefficient inverse problems for the Dirac equation, the determination of subboundary by the heat equation and the continuation of solution of the Euler equation(逆問題に対するカーレマン評価による条件付き安定性: ディラック方程式に対する係数逆問題,熱方程式による部分境界の決定とオイラー方程式に対する解の接続性) (JAPANESE)

### 2011/02/02

#### Lectures

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

Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities (ENGLISH)

**Yong Jung Kim**(Korea Advanced Institute of Science and Technology (KAIST))Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities (ENGLISH)

[ Abstract ]

The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.

The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.

#### Lectures

15:15-16:15 Room #002 (Graduate School of Math. Sci. Bldg.)

Regularity of two dimensional capillary gravity water waves (ENGLISH)

**Guanghui ZHANG**(Graduate School of Mathematical Sciences, the University of Tokyo)Regularity of two dimensional capillary gravity water waves (ENGLISH)

[ Abstract ]

We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.

We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.

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