## FMSP Lectures

Seminar information archive ～09/27｜Next seminar｜Future seminars 09/28～

**Seminar information archive**

### 2013/12/19

17:00-18:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hu.pdf

**Guanghui Hu**(WIAS, Germany)Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)

[ Abstract ]

In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.

Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.

In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely

determined from the near-field data corresponding to a finite number of incident elastic plane waves.

This is a joint work with J. Elschner and M. Yamamoto.

[ Reference URL ]In recent years, Schwarz reflection principles have been used to prove uniqueness in inverse scattering by bounded obstacles and unbounded periodic structures of polygonal or polyhedral type with only one or several incident plane waves.

Such a principle for the Navier equation is established by far only underthe third or fourth kind boundary conditions, and still remains unknown in the more practical case of the Dirichlet boundary condition.

In this talk we will discuss the uniqueness in inverse elastic scattering from rigid diffraction gratings of polygonal type, where the total displacement vanishes on the scattering surface. Mathematically, this can be modeled by the Dirichlet boundary value problem for the Navier equation in periodic structures. We prove that such diffraction gratings can be uniquely

determined from the near-field data corresponding to a finite number of incident elastic plane waves.

This is a joint work with J. Elschner and M. Yamamoto.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hu.pdf

### 2013/12/16

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The discrete Schrodinger equation for compact support potentials (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf

**Jon Nimmo**(Univ. of Glasgow)The discrete Schrodinger equation for compact support potentials (ENGLISH)

[ Abstract ]

We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.

Applications of this approach to the udKdV are also discussed.

[ Reference URL ]We consider the exact form of the Jost solutions of the discrete Schrodinger equation for arbitrary potentials with compact support. Remarkably, these solutions may be written in terms of certain explicitly defined polynomials in the non-trivial values of the potential. These polynomials also arise in the work of Yamada (2000) in connection with a birational representation of the symmetric group.

Applications of this approach to the udKdV are also discussed.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_%20NIMMO.pdf

### 2013/12/10

13:00-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

### 2013/12/06

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Horospheres: geometry and analysis (II) (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf

**Simon Gindikin**(Rutgers University)Horospheres: geometry and analysis (II) (ENGLISH)

[ Abstract ]

About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

[ Reference URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf

### 2013/12/04

15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Horospheres: geometry and analysis (I) (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf

**Simon Gindikin**(Rutgers University)Horospheres: geometry and analysis (I) (ENGLISH)

[ Abstract ]

About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

[ Reference URL ]About 50 years ago Gelfand suggested a concepion of horospherical transform which, he hoped, must be an universal principle unifying non commutative harmonic analysis. I want to make several historic remarks (especialy, since this year is the centenial anniversary of Gelfand). I want to discuss the evolution of this fundamental conception for 50 years and how Gelfand’s dreams are looked today. I will discuss an elementary case of hyperboloids of any signature where there were not too much progress after old initial result of Gelfand-Graev.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gindikin.pdf

### 2013/12/03

13:00-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

### 2013/11/29

10:40-12:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

### 2013/11/29

14:50-16:20 Room #126 (Graduate School of Math. Sci. Bldg.)

Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

**Erwin Bolthausen**(University of Zurich)Random walks in random environments (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Bolthausen.pdf

### 2013/11/22

10:40-11:40 Room #123 (Graduate School of Math. Sci. Bldg.)

Integrable discrete systems, an introduction Pt. 2 (ENGLISH)

**Alfred RAMANI**(École polytechnique)Integrable discrete systems, an introduction Pt. 2 (ENGLISH)

[ Abstract ]

The second part will mostly be devoted to the various integrability detectors (singularity confinement, algebraic entropy) for integrability of discrete systems, in one or more dimensions. The most important systems identified through these detectors, namely the discrete Painlev¥'e equations, will be presented in detail, through a geometric approach.

The second part will mostly be devoted to the various integrability detectors (singularity confinement, algebraic entropy) for integrability of discrete systems, in one or more dimensions. The most important systems identified through these detectors, namely the discrete Painlev¥'e equations, will be presented in detail, through a geometric approach.

### 2013/11/18

15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Integrable discrete systems, an introduction Pt.1 (ENGLISH)

**Alfred RAMANI**(École polytechnique)Integrable discrete systems, an introduction Pt.1 (ENGLISH)

[ Abstract ]

The first part will contain a general overview of the notion of integrability, starting from continuous systems with or without physical applications. The Painlev¥'e property will be discussed as an integrability detector for integrability of continuous systems. The notion of integrability of discrete systems will be introduced next. One dimensional systems will be presented as well as multidimensional ones.

The first part will contain a general overview of the notion of integrability, starting from continuous systems with or without physical applications. The Painlev¥'e property will be discussed as an integrability detector for integrability of continuous systems. The notion of integrability of discrete systems will be introduced next. One dimensional systems will be presented as well as multidimensional ones.

### 2013/09/07

15:00-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Dominating representations by Fuchsian ones (ENGLISH)

**Bertrand Deroin**(University of Paris-Sud)Dominating representations by Fuchsian ones (ENGLISH)

[ Abstract ]

We will focus on the problem of dominating the translation lengths of a representation from a surface group to the isometries of a CAT(-1) space by the lengths induced by a hyperbolic structure on the surface. This is related to the construction of 3-dimensional anti-de-Sitter compact manifolds. This is a collaboration with Nicolas Tholozan.

We will focus on the problem of dominating the translation lengths of a representation from a surface group to the isometries of a CAT(-1) space by the lengths induced by a hyperbolic structure on the surface. This is related to the construction of 3-dimensional anti-de-Sitter compact manifolds. This is a collaboration with Nicolas Tholozan.

### 2013/08/12

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Operator Algebraic Construction of Quantum Field Theory Models (ENGLISH)

**Roberto Longo**(Univ. Roma, Tor Vergata)Operator Algebraic Construction of Quantum Field Theory Models (ENGLISH)

### 2013/08/07

16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Water waves over a random bottom (ENGLISH)

**Philippe Guyenne**(Univ. of Delaware)Water waves over a random bottom (ENGLISH)

[ Abstract ]

We present a Hamiltonian formulation for nonlinear surface water waves in the presence of a variable bottom. This formulation is based on a reduction of the problem to a lower-dimensional system involving boundary variables alone. To accomplish this, we express the Dirichlet-to-Neumann operator as a Taylor series in terms of the surface and bottom variations. This expansion is convenient for both asymptotic calculations and numerical simulations. First we apply this formulation to the asymptotic description of long waves over random topography. We show that the principal component of the solution can be described by a Korteweg-de Vries equation plus random phase corrections. We also derive an asymptotic expression for the scattered component. Finally numerical simulations will be shown to illustrate the theoretical results. This is joint work with Walter Craig and Catherine Sulem.

We present a Hamiltonian formulation for nonlinear surface water waves in the presence of a variable bottom. This formulation is based on a reduction of the problem to a lower-dimensional system involving boundary variables alone. To accomplish this, we express the Dirichlet-to-Neumann operator as a Taylor series in terms of the surface and bottom variations. This expansion is convenient for both asymptotic calculations and numerical simulations. First we apply this formulation to the asymptotic description of long waves over random topography. We show that the principal component of the solution can be described by a Korteweg-de Vries equation plus random phase corrections. We also derive an asymptotic expression for the scattered component. Finally numerical simulations will be shown to illustrate the theoretical results. This is joint work with Walter Craig and Catherine Sulem.

### 2013/07/26

10:30-12:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Representations of reductive groups and L-functions (II) (ENGLISH)

**Birgit Speh**(Cornell University)Representations of reductive groups and L-functions (II) (ENGLISH)

[ Abstract ]

In the second lecture we will quickly discuss Rankin Selberg integral approach to L-factors and then Shahidi's method of constructing L-functions by relating them to intertwining operators, leading to the definition of the the L-factors of tempered non degenerate representations. The lecture closes with a discussion of L-factors for nontempered representations.

In the second lecture we will quickly discuss Rankin Selberg integral approach to L-factors and then Shahidi's method of constructing L-functions by relating them to intertwining operators, leading to the definition of the the L-factors of tempered non degenerate representations. The lecture closes with a discussion of L-factors for nontempered representations.

### 2013/07/18

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Representations of reductive groups and L-functions (I) (ENGLISH)

**Birgit Speh**(Cornell University)Representations of reductive groups and L-functions (I) (ENGLISH)

[ Abstract ]

This is an introduction to the theory of L-functions and in particular of the local L-factors of representations in real and complex groups. Some familiarity with infinite dimensional representations would be very helpful, but I will not assume any knowledge of number theory. We will start in the first lecture by considering L-functions for Groessen characters and classical automorphic forms, in other words for automorphic representations of G(1) and GL(2). This will motivate the definition of the local L-factors of representations of GL(1,R) and GL(2,R). Then we will discuss Rankin convolutions and define the L-factors for infinite dimensional tempered representations of GL(n,R).

This is an introduction to the theory of L-functions and in particular of the local L-factors of representations in real and complex groups. Some familiarity with infinite dimensional representations would be very helpful, but I will not assume any knowledge of number theory. We will start in the first lecture by considering L-functions for Groessen characters and classical automorphic forms, in other words for automorphic representations of G(1) and GL(2). This will motivate the definition of the local L-factors of representations of GL(1,R) and GL(2,R). Then we will discuss Rankin convolutions and define the L-factors for infinite dimensional tempered representations of GL(n,R).

### 2013/07/08

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

Two-dimensional Calderon problems for Navier-Stokes equations and Lame system (ENGLISH)

**Oleg Emanouilov**(Colorado State Univ.)Two-dimensional Calderon problems for Navier-Stokes equations and Lame system (ENGLISH)

[ Abstract ]

We will prove the uniqueness in determining viscosity in two-dimensional Navier-Stokes equations by Dirichlet-to-Neumann map.

Moreover, without any smallness assumption, we establish the uniqueness in determining two Lame coefficients in two-dimensional isotropic Lame system Dirichlet-to-Neumann map.

We will prove the uniqueness in determining viscosity in two-dimensional Navier-Stokes equations by Dirichlet-to-Neumann map.

Moreover, without any smallness assumption, we establish the uniqueness in determining two Lame coefficients in two-dimensional isotropic Lame system Dirichlet-to-Neumann map.

### 2013/07/05

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric applications of Wasserstein distance,

Lecture (IV) Applications to differential geometry and foliations (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

**Szymon M. Walczak**(University of Lodz, Poland)Geometric applications of Wasserstein distance,

Lecture (IV) Applications to differential geometry and foliations (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

### 2013/06/28

16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Mathematical model for the electrodiffusion of ions, Lecture II (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

**Yoichiro Mori**(University of Minnesota)Mathematical model for the electrodiffusion of ions, Lecture II (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

### 2013/06/27

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric applications of Wasserstein distance,

Lecture (III) Curvature of metric measure spaces II

(ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

**Szymon M. Walczak**(University of Lodz, Poland)Geometric applications of Wasserstein distance,

Lecture (III) Curvature of metric measure spaces II

(ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

### 2013/06/27

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Mathematical model for the electrodiffusion of ions, Lecture I (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

**Yoichiro Mori**(University of Minnesota)Mathematical model for the electrodiffusion of ions, Lecture I (JAPANESE)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~fmsp/files/FMSPLectures_Mori.pdf

### 2013/06/20

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric applications of Wasserstein distance,

Lecture (II) Curvature of metric measure spaces I (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

**Szymon M. Walczak**(University of Lodz, Poland)Geometric applications of Wasserstein distance,

Lecture (II) Curvature of metric measure spaces I (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

### 2013/06/19

14:40-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Geometric applications of Wasserstein distance,

Lecture (I) Wasserstein distance and optimal transportation

(ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

**Szymon M. Walczak**(University of Lodz, Poland)Geometric applications of Wasserstein distance,

Lecture (I) Wasserstein distance and optimal transportation

(ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Walczak.pdf

### 2013/06/13

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Boundary Rigidity for Riemannian Manifolds (ENGLISH)

**Fikret Golgeleyen**(Bulent Ecevit University)Boundary Rigidity for Riemannian Manifolds (ENGLISH)

### 2013/06/06

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Real-valued and circle-valued Morse theory:

an introduction

(ENGLISH)

**Andrei Pajitnov**(Univ. de Nantes)Real-valued and circle-valued Morse theory:

an introduction

(ENGLISH)

[ Abstract ]

Classical Morse theory relates the number of critical points of a Morse

function f on a manifold M to the topology of M. The main technical

ingredient of this theory is a chain complex generated by the critical points

of the function. In 1981 S.P. Novikov generalized this theory to the case of

circle-valued Morse functions. In this talk we describe the construction of

both chain complexes, based on the idea of E. Witten (1982), which allows, in

particular, to compute the boundary operators in the Morse complex from

the count of flow lines of the gradient of f. We discuss geometric applications

of these constructions.

Classical Morse theory relates the number of critical points of a Morse

function f on a manifold M to the topology of M. The main technical

ingredient of this theory is a chain complex generated by the critical points

of the function. In 1981 S.P. Novikov generalized this theory to the case of

circle-valued Morse functions. In this talk we describe the construction of

both chain complexes, based on the idea of E. Witten (1982), which allows, in

particular, to compute the boundary operators in the Morse complex from

the count of flow lines of the gradient of f. We discuss geometric applications

of these constructions.

### 2013/05/30

13:00-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Low-dimensional linear representations of mapping class groups (III) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups (III) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf