## 過去の記録

### 2011年02月24日(木)

#### 応用解析セミナー

16:00-18:10   数理科学研究科棟(駒場) 002号室
Arnaud Ducrot 氏 (University of Bordeaux 2) 16:00-17:00
Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections (ENGLISH)
[ 講演概要 ]
This work is devoted to the study of travelling wave solutions for some size structured model in population dynamics. The population under consideration is also spatially structured and has a nonlocal spatial reproduction. This phenomenon may model the invasion of plants within some empty landscape. Since the corresponding unspatially structured size structured models may induce oscillating dynamics due to Hopf bifurcations, the aim of this work is to prove the existence of point to sustained oscillating solution travelling waves for the spatially structured problem. From a biological viewpoint, such solutions represent the spatial invasion of some species with spatio-temporal patterns at the place where the population is established.
Enrique Zuazua 氏 (Basque Center for Applied Mathematics) 17:10-18:10
Some open problems in PDE control (ENGLISH)
[ 講演概要 ]
The field of PDE control has experienced a great progress in the last decades, developing new theories and tools that have also influenced other disciplines as Inverse Problem and Optimal Design Theories and Numerical Analysis. PDE control arises in most applications ranging from classical problems in fluid mechanics or structural engineering to modern molecular design experiments.

From a mathematical viewpoint the problems arising in this field are extremely challenging since the existing theory of existence and uniqueness of solutions and the corresponding numerical schemes is insufficient when addressing realistic control problems. Indeed, an efficient controller requires of an in depth understanding of how solutions depend on the various parameters of the problem (shape of the domain, time of control, coefficients of the equation, location
of the controller, nonlinearity in the equation,...)

In this lecture we shall briefly discuss some important advances and some challenging open problems. All of them shear some features. In particular they are simple to state and very likely hard to solve. We shall discuss in particular:
1.- Semilinear wave equations and their control properties.
2.- Microlocal optimal design of wave processes
3.- Sharp observability estimates for heat processes.
4.- Robustness on the control of finite-dimensional systems.
5.- Unique continuation for discrete elliptic models
6.- Control of Kolmogorov equations and other hypoelliptic models.

### 2011年02月23日(水)

#### 関数解析セミナー

14:00-18:00   数理科学研究科棟(駒場) 118号室
Dimitri Yafaev 氏 (Univ. Rennes 1) 14:00-14:45
The semiclassical limit of eigenfunctions of the Schroedinger equation and the Bohr-Sommerfeld quantization condition, revisited (ENGLISH)
David Damanik 氏 (Rice University) 15:00-15:45
Uniform localization (ENGLISH)
Erik Skibsted 氏 (Aarhus University) 16:15-17:00
Global solutions to the eikonal equation (ENGLISH)
Christian Gerard 氏 (Univ. Paris Sud 11) 17:15-18:00
Applications of microlocal analysis to quantum field theory on curved space-times (ENGLISH)

### 2011年02月18日(金)

#### 作用素環セミナー

10:30-12:00   数理科学研究科棟(駒場) 122号室
Dirac families and 1-cocycles (ENGLISH)
[ 講演概要 ]
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.

#### 古典解析セミナー

11:00-15:45   数理科学研究科棟(駒場) 126号室
T. Morita 氏 (Osaka University) 11:00-12:00
Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)
M. Yamaguchi 氏 (University of Tokyo) 13:30-14:30
Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)
(ENGLISH)
L. Di Vizio 氏 (Universite Paris 7) 14:45-15:45
Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)
(ENGLISH)

#### 古典解析セミナー

10:15-10:45   数理科学研究科棟(駒場) 126号室
Y. Ohyama 氏 (Osaka University)
Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)

### 2011年02月17日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Thomas Giletti 氏 (University of Paul Cezanne (Marseilles))
Study of propagation phenomena in some reaction-diffusion systems (ENGLISH)
[ 講演概要 ]
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.

#### 古典解析セミナー

11:00-17:00   数理科学研究科棟(駒場) 126号室
L. Di Vizio 氏 (Universite Paris 7) 11:00-12:00
Overview of local theory of $q$-difference equations and summation, 1
(ENGLISH)
Y. Katsushima 氏 (University of Tokyo) 13:30-14:30
Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)
K. Matsuya 氏 (University of Tokyo) 14:45-15:45
Blow-up of solutions for a nonlinear difference equation (ENGLISH)
L. Di Vizio 氏 (Universite Paris 7) 16:00-17:00
Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)

### 2011年02月16日(水)

#### 古典解析セミナー

13:30-17:00   数理科学研究科棟(駒場) 126号室
H. Sakai 氏 (University of Tokyo) 13:30-14:30
Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)
H. Kawakami 氏 (University of Tokyo) 14:45-15:45
Degeneration scheme of 4-dimensional Painlev¥'e type equations
(Joint work with H. Sakai and A. Nakamura)

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

### 2011年02月14日(月)

#### GCOEセミナー

13:00-14:00   数理科学研究科棟(駒場) 270号室
Jin Cheng 氏 (Fudan University)
Unique continuation on the analytic curve and its application to inverse problems. (ENGLISH)
[ 講演概要 ]
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年02月10日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Alan Weinstein 氏 (UC Berkeley)
Symplectic and quantum categories (ENGLISH)

#### 応用解析セミナー

15:30-16:30   数理科学研究科棟(駒場) 002号室

Jean-Michel Coron 氏 (University of Paris 6)
Control and nonlinearity (ENGLISH)
[ 講演概要 ]
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).

#### 代数学コロキウム

11:00-12:00   数理科学研究科棟(駒場) 056号室

Joseph Ayoub 氏 (University of Zurich)
The motivic Galois group and periods of algebraic varieties (ENGLISH)
[ 講演概要 ]
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年02月04日(金)

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 122号室

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)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 122号室

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)

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 128号室

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)

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 128号室

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)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 128号室

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)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 128号室

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年02月03日(木)

#### 博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 118号室

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

#### 博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 118号室

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)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室

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)