## Seminar information archive

Seminar information archive ～11/14｜Today's seminar 11/15 | Future seminars 11/16～

### 2011/02/18

#### Operator Algebra Seminars

10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Dirac families and 1-cocycles (ENGLISH)

**Pedram Hekmati**(Univ. Adelaide)Dirac families and 1-cocycles (ENGLISH)

[ Abstract ]

Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.

Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.

#### Classical Analysis

11:00-15:45 Room #126 (Graduate School of Math. Sci. Bldg.)

Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)

Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)

(ENGLISH)

Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)

(ENGLISH)

**T. Morita**(Osaka University) 11:00-12:00Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)

**M. Yamaguchi**(University of Tokyo) 13:30-14:30Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)

(ENGLISH)

**L. Di Vizio**(Universite Paris 7) 14:45-15:45Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)

(ENGLISH)

#### Classical Analysis

10:15-10:45 Room #126 (Graduate School of Math. Sci. Bldg.)

Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)

**Y. Ohyama**(Osaka University)Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)

### 2011/02/17

#### Applied Analysis

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

Study of propagation phenomena in some reaction-diffusion systems (ENGLISH)

**Thomas Giletti**(University of Paul Cezanne (Marseilles))Study of propagation phenomena in some reaction-diffusion systems (ENGLISH)

[ Abstract ]

This talk deals with the existence and qualitative properties of traveling wave solutions of a nonlinear reaction-diffusion system with losses inside the domain, which has numerous applications in various fields ranging from chemical and biological contexts to combusion. Under some KPP type hypotheses, the existence of a continuum of admissible speeds for traveling waves can be shown, thus generalizing the single equation case. Lastly, by considering losses concentrated near the edge of the domain, those results can be compared with those of the boundary losses case.

This talk deals with the existence and qualitative properties of traveling wave solutions of a nonlinear reaction-diffusion system with losses inside the domain, which has numerous applications in various fields ranging from chemical and biological contexts to combusion. Under some KPP type hypotheses, the existence of a continuum of admissible speeds for traveling waves can be shown, thus generalizing the single equation case. Lastly, by considering losses concentrated near the edge of the domain, those results can be compared with those of the boundary losses case.

#### Classical Analysis

11:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Overview of local theory of $q$-difference equations and summation, 1

(ENGLISH)

Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)

Blow-up of solutions for a nonlinear difference equation (ENGLISH)

Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)

**L. Di Vizio**(Universite Paris 7) 11:00-12:00Overview of local theory of $q$-difference equations and summation, 1

(ENGLISH)

**Y. Katsushima**(University of Tokyo) 13:30-14:30Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)

**K. Matsuya**(University of Tokyo) 14:45-15:45Blow-up of solutions for a nonlinear difference equation (ENGLISH)

**L. Di Vizio**(Universite Paris 7) 16:00-17:00Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)

### 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)

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