## Lectures

Seminar information archive ～12/01｜Next seminar｜Future seminars 12/02～

**Seminar information archive**

### 2014/03/10

15:15-16:45 Room #123 (Graduate School of Math. Sci. Bldg.)

Energy fluctuations in the disordered harmonic chain (ENGLISH)

**Marielle Simon**(ENS Lyon, UMPA)Energy fluctuations in the disordered harmonic chain (ENGLISH)

[ Abstract ]

We study the energy diffusion in the disordered harmonic chain of oscillators: the usual Hamiltonian dynamics is provided with random masses and perturbed by a degenerate energy conserving noise. After rescaling space and time diffusively, we prove that energy fluctuations evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and an equivalent definition through the Green-Kubo formula. Since the model is non gradient, and the perturbation is very degenerate, the standard Varadhan's approach is reviewed under new perspectives.

We study the energy diffusion in the disordered harmonic chain of oscillators: the usual Hamiltonian dynamics is provided with random masses and perturbed by a degenerate energy conserving noise. After rescaling space and time diffusively, we prove that energy fluctuations evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and an equivalent definition through the Green-Kubo formula. Since the model is non gradient, and the perturbation is very degenerate, the standard Varadhan's approach is reviewed under new perspectives.

### 2014/02/17

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

Canceled!! (ENGLISH)

**Ratnasingham Shivaji**(The University of North Carolina at Greensboro)Canceled!! (ENGLISH)

[ Abstract ]

Canceled!!

Canceled!!

### 2013/12/19

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

Inverse elastic wave scattering from rigid diffraction gratings (ENGLISH)

**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.

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.

### 2013/07/25

13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

)

Quantum Chern-Simons field theory (ENGLISH)

**Joergen E Andersen**(Centre for Quantum Geometry of Moduli Spaces (QGM), Aarhus University, Denmark)

Quantum Chern-Simons field theory (ENGLISH)

### 2013/07/23

13:00-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)

)

Moduli space approach for protein structures (ENGLISH)

**Joergen E Andersen**(Centre for Quantum Geometry of Moduli Spaces (QGM), Aarhus University, Denmark)

Moduli space approach for protein structures (ENGLISH)

### 2013/07/22

13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

)

Moduli space approach for RNA structure analysis (ENGLISH)

**Joergen E Andersen**(Centre for Quantum Geometry of Moduli Spaces (QGM), Aarhus University, Denmark)

Moduli space approach for RNA structure analysis (ENGLISH)

### 2013/07/08

10:40-12:10 Room #128 (Graduate School of Math. Sci. Bldg.)

Meiji University)

Aggregation mechanism of biological species : from microscopic

and macroscopic viewpoints (JAPANESE)

**Hirofumi Izuhara**(Meiji Institute for Advanced Study of Mathematical Sciences,Meiji University)

Aggregation mechanism of biological species : from microscopic

and macroscopic viewpoints (JAPANESE)

[ Abstract ]

There are a lot of organisms which form aggregation in nature. In order to describe the dynamics of such biological species, a particle model is often proposed, which is based on the random walk from the microscopic point of view. On the other hand, when we take population densities of biological species into account, the dynamics is expressed as partial differential equations. We see that different models are proposed according to the viewpoints which we are focusing on. In this talk, we take aggregation phenomena of biological species as an example, and introduce a relation between a microscopic particle model and a macroscopic partial differential equation model.

There are a lot of organisms which form aggregation in nature. In order to describe the dynamics of such biological species, a particle model is often proposed, which is based on the random walk from the microscopic point of view. On the other hand, when we take population densities of biological species into account, the dynamics is expressed as partial differential equations. We see that different models are proposed according to the viewpoints which we are focusing on. In this talk, we take aggregation phenomena of biological species as an example, and introduce a relation between a microscopic particle model and a macroscopic partial differential equation model.

### 2013/06/13

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

Introduction to inter-universal Teichmueller theory, extended version (JAPANESE)

**Shinichi Mochizuki**(Kyoto University, RIMS)Introduction to inter-universal Teichmueller theory, extended version (JAPANESE)

### 2013/05/24

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

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (JAPANESE)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (JAPANESE)

### 2013/05/21

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

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

### 2013/05/14

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

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

### 2013/05/10

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

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

### 2013/04/22

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Thermal conductivity and weak coupling (ENGLISH)

**Stefano Olla**(Univ. Paris-Dauphine)Thermal conductivity and weak coupling (ENGLISH)

[ Abstract ]

We investigate the macroscopic thermal conductivity of a chain of anharmonic oscillators and more general systems, under weak coupling limits and energy conserving stochastic perturbations of the dynamics. In particular we establish a series expansion in the coupling parameter.

We investigate the macroscopic thermal conductivity of a chain of anharmonic oscillators and more general systems, under weak coupling limits and energy conserving stochastic perturbations of the dynamics. In particular we establish a series expansion in the coupling parameter.

### 2013/04/15

15:00-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Two-sided bounds for the Dirichlet heat kernel on inner uniform domains (ENGLISH)

**Janna Lierl**(University of Bonn)Two-sided bounds for the Dirichlet heat kernel on inner uniform domains (ENGLISH)

[ Abstract ]

I will present sharp two-sided bounds for the heat kernel in domains with Dirichlet boundary conditions. The domain is assumed to satisfy an inner uniformity condition. This includes any convex domain, the complement of any convex domain in Euclidean space, and the interior of the Koch snowflake.

The heat kernel estimates hold in the abstract setting of metric measure spaces equipped with a (possibly non-symmetric) Dirichlet form. The underlying space is assumed to satisfy a Poincare inequality and volume doubling.

The results apply, for example, to the Dirichlet heat kernel associated with a divergence form operator with bounded measurable coefficients and symmetric, uniformly elliptic second order part.

This is joint work with Laurent Saloff-Coste.

I will present sharp two-sided bounds for the heat kernel in domains with Dirichlet boundary conditions. The domain is assumed to satisfy an inner uniformity condition. This includes any convex domain, the complement of any convex domain in Euclidean space, and the interior of the Koch snowflake.

The heat kernel estimates hold in the abstract setting of metric measure spaces equipped with a (possibly non-symmetric) Dirichlet form. The underlying space is assumed to satisfy a Poincare inequality and volume doubling.

The results apply, for example, to the Dirichlet heat kernel associated with a divergence form operator with bounded measurable coefficients and symmetric, uniformly elliptic second order part.

This is joint work with Laurent Saloff-Coste.

### 2013/04/15

16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)

Persistence Probabilities (ENGLISH)

**Amir Dembo**(Stanford University)Persistence Probabilities (ENGLISH)

[ Abstract ]

Persistence probabilities concern how likely it is that a stochastic process has a long excursion above fixed level and of what are the relevant scenarios for this behavior. Power law decay is expected in many cases of physical significance and the issue is to determine its power exponent parameter. I will survey recent progress in this direction (jointly with Jian Ding, Fuchang Gao, and Sumit Mukherjee), dealing with random algebraic polynomials of independent coefficients, iterated partial sums and other auto-regressive sequences, and with the solution to heat equation initiated by white noise.

Persistence probabilities concern how likely it is that a stochastic process has a long excursion above fixed level and of what are the relevant scenarios for this behavior. Power law decay is expected in many cases of physical significance and the issue is to determine its power exponent parameter. I will survey recent progress in this direction (jointly with Jian Ding, Fuchang Gao, and Sumit Mukherjee), dealing with random algebraic polynomials of independent coefficients, iterated partial sums and other auto-regressive sequences, and with the solution to heat equation initiated by white noise.

### 2013/03/06

16:00-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)

**Frederic Le Roux**(Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie)The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)

[ Abstract ]

We propose two definitions of a local rotation set. As applications, one

gets some criteria for the existence of periodic orbits, and a clear

explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:

for surface diffeomorphisms, the rotation number of the derivative at a

fixed point which is not a sink nor a source is a topological invariant.

Tha local rotation set also provide an unexpected topological

characterization for the parabolic fixed points of holomorphic maps.

We propose two definitions of a local rotation set. As applications, one

gets some criteria for the existence of periodic orbits, and a clear

explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:

for surface diffeomorphisms, the rotation number of the derivative at a

fixed point which is not a sink nor a source is a topological invariant.

Tha local rotation set also provide an unexpected topological

characterization for the parabolic fixed points of holomorphic maps.

### 2013/02/08

10:30-11:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Strong and weak solutions to stochastic Landau-Lifshitz equations (ENGLISH)

**Zdzislaw Brzezniak**(University of York)Strong and weak solutions to stochastic Landau-Lifshitz equations (ENGLISH)

[ Abstract ]

I will speak about the existence of weak solutions (and the existence and uniqueness of strong solutions) to the stochastic Landau-Lifshitz equations for multi (and one)-dimensional spatial domains. I will also describe the corresponding Large Deviations principle and it's applications to a ferromagnetic wire.

The talk is based on a joint work with B. Goldys and T. Jegaraj.

I will speak about the existence of weak solutions (and the existence and uniqueness of strong solutions) to the stochastic Landau-Lifshitz equations for multi (and one)-dimensional spatial domains. I will also describe the corresponding Large Deviations principle and it's applications to a ferromagnetic wire.

The talk is based on a joint work with B. Goldys and T. Jegaraj.

### 2013/01/30

17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

**Antonio Degasperis**(La Sapienza, University of Rome)Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

[ Abstract ]

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

### 2013/01/30

17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

**Antonio Degasperis**(La Sapienza, University of Rome)Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

[ Abstract ]

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

### 2013/01/30

17:30-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

**Antonio Degasperis**(La Sapienza, University of Rome)Integrable nonlinear wave equations, nonlocal interaction and spectral methods (ENGLISH)

[ Abstract ]

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

A general class of integrable nonlinear multi-component wave equations are discussed to show that integrability, as implied by Lax pair, does not necessarily imply solvability of the initial value problem by spectral methods. A simple instance of this class, with applicative relevance to nonlinear optics, is discussed as a prototype model. Conservation laws and special solutions of this model are displayed to underline the integrability issue.

### 2013/01/30

09:45-10:45 Room #123 (Graduate School of Math. Sci. Bldg.)

Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)

**Marzieh Forough**(Ferdowsi Univ. Mashhad)Stability of Fredholm property of regular operators on Hilbert $C^*$-modules (ENGLISH)

### 2013/01/30

11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)

**Gerardo Morsella**(Univ. Roma II)Scaling algebras, superselection theory and asymptotic morphisms (ENGLISH)

### 2013/01/30

13:30-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)

**Joav Orovitz**(Ben-Gurion Univ.)Tracially $\\mathcal{Z}$-absorbing $C^*$-algebras (ENGLISH)

### 2013/01/30

14:45-15:45 Room #118 (Graduate School of Math. Sci. Bldg.)

Noncommutative covering dimension (ENGLISH)

**Nicola Watson**(Univ. Toronto)Noncommutative covering dimension (ENGLISH)

### 2013/01/30

16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)

**Marcel Bischoff**(Univ. G\"ottingen)Construction of models in low dimensional QFT using operator algebraic methods (ENGLISH)