## Seminar information archive

Seminar information archive ～02/19｜Today's seminar 02/20 | Future seminars 02/21～

#### FMSP Lectures

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

II_1 factors with a unique Cartan subalgebra (ENGLISH)

**Stefaan Vaes**(KU Leuven)II_1 factors with a unique Cartan subalgebra (ENGLISH)

#### GCOE Seminars

16:00-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Exact insensitizing controls for scalar wave equations and control of coupled systems (ENGLISH)

**Fatiha Alabau-Boussouira**(Université de Lorraine)Exact insensitizing controls for scalar wave equations and control of coupled systems (ENGLISH)

[ Abstract ]

The control of scalar PDE's such as the wave or heat equation is by now well-understood.

It consists in building a source term which can drive the solution from a given initial state to a final (reachable) desired state.

Exact insensitizing control are exact controls which should satisfy an additional requirement:

they should be robust to small unknown perturbations of the initial data. More precisely, they should, as exact controls, drive the solution to the desired state, but they also should insensitize a given measure of the solution to such perturbations. One can show that the existence of exact insensitizing controls for a scalar wave equation is equivalent to the exact controllability by a single control of a system of two wave equations coupled in cascade.

We shall present in this talk the challenging issues and give some recent results and perspectives for the exact insensitizing control of scalar wave equations. We shall also give some more general results on the controllability of coupled systems by a reduced number of controls.

The control of scalar PDE's such as the wave or heat equation is by now well-understood.

It consists in building a source term which can drive the solution from a given initial state to a final (reachable) desired state.

Exact insensitizing control are exact controls which should satisfy an additional requirement:

they should be robust to small unknown perturbations of the initial data. More precisely, they should, as exact controls, drive the solution to the desired state, but they also should insensitize a given measure of the solution to such perturbations. One can show that the existence of exact insensitizing controls for a scalar wave equation is equivalent to the exact controllability by a single control of a system of two wave equations coupled in cascade.

We shall present in this talk the challenging issues and give some recent results and perspectives for the exact insensitizing control of scalar wave equations. We shall also give some more general results on the controllability of coupled systems by a reduced number of controls.

#### GCOE Seminars

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

Carleman estimates and Lipschitz stability for Grushin-type operators (ENGLISH)

**Piermarco Cannarsa**(Univ. Roma II)Carleman estimates and Lipschitz stability for Grushin-type operators (ENGLISH)

[ Abstract ]

The Baouendi-Grushin operator is an important example of a degenerate elliptic operator that has strong connections with almost-riemannian structures. It is also the infinitesimal generator of a strongly continuous semigroup on Lebesgue spaces with very interesting properties from the point of view of control theory. Such properties will be discussed in this lecture, starting with approximate and null controllability.

We will then address the inverse source problem for these operators deriving a Lipschitz stability result.

The Baouendi-Grushin operator is an important example of a degenerate elliptic operator that has strong connections with almost-riemannian structures. It is also the infinitesimal generator of a strongly continuous semigroup on Lebesgue spaces with very interesting properties from the point of view of control theory. Such properties will be discussed in this lecture, starting with approximate and null controllability.

We will then address the inverse source problem for these operators deriving a Lipschitz stability result.

### 2013/02/21

#### FMSP Lectures

15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)

)

Monte Carlo Methods for Partial Differential Equations: Computing Permeability

(ENGLISH)

**Michael Mascagni**(Florida State University)

Monte Carlo Methods for Partial Differential Equations: Computing Permeability

(ENGLISH)

[ Abstract ]

We present a brief overview of Monte Carlo methods for the solution of elliptic and parabolic partial differential equations (PDEs). We begin with a review of the Feynman-Kac formula, and its use in the probabilistic representation of the solutions of elliptic and parabolic PDEs. We then consider some specific Monte Carlo methods used for obtaining the solution of simple elliptic partial differential equations (PDEs) as part of exterior boundary value problems that arise in electrostatics and flow through porous media. These Monte Carlo methods use Feynman-Kac to represent the solution of the elliptic PDE at a point as the expected value of functionals of Brownian motion trajectories started at the point of interest. We discuss the rapid solution of these equations, in complex exterior geometries, using both the "walk on spheres" and "Greens function first-passage" algorithms. We then concentrate on methods for quickly computing the isotropic permeability using the "unit

capacitance" and "penetration depth'' methods. The first of these methods, requires computing a linear functional of the solution to an exterior elliptic PDE. Both these methods for computing permeability are simple, and provide accurate solutions in a few seconds on laptop-scale computers. We then conclude with a brief look at other Monte Carlo methods and problems that arise on related application areas.

We present a brief overview of Monte Carlo methods for the solution of elliptic and parabolic partial differential equations (PDEs). We begin with a review of the Feynman-Kac formula, and its use in the probabilistic representation of the solutions of elliptic and parabolic PDEs. We then consider some specific Monte Carlo methods used for obtaining the solution of simple elliptic partial differential equations (PDEs) as part of exterior boundary value problems that arise in electrostatics and flow through porous media. These Monte Carlo methods use Feynman-Kac to represent the solution of the elliptic PDE at a point as the expected value of functionals of Brownian motion trajectories started at the point of interest. We discuss the rapid solution of these equations, in complex exterior geometries, using both the "walk on spheres" and "Greens function first-passage" algorithms. We then concentrate on methods for quickly computing the isotropic permeability using the "unit

capacitance" and "penetration depth'' methods. The first of these methods, requires computing a linear functional of the solution to an exterior elliptic PDE. Both these methods for computing permeability are simple, and provide accurate solutions in a few seconds on laptop-scale computers. We then conclude with a brief look at other Monte Carlo methods and problems that arise on related application areas.

### 2013/02/19

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On the ring of Fricke characters of free groups (JAPANESE)

**Eri Hatakenaka**(Tokyo University of Agriculture and Technology)On the ring of Fricke characters of free groups (JAPANESE)

[ Abstract ]

This is a joint work with Takao Satoh (Tokyo University of Science). We study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of the free group naturally acts. Then by using it, we define a descending filtration of the automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.

This is a joint work with Takao Satoh (Tokyo University of Science). We study a descending filtration of the ring of Fricke characters of a free group consisting of ideals on which the automorphism group of the free group naturally acts. Then by using it, we define a descending filtration of the automorphism group of a free group, and investigate a relation between it and the Andreadakis-Johnson filtration.

### 2013/02/18

#### GCOE Seminars

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

Institute of Mining Siberian Branch of Russian Academy of Sciences)

INVERSE PROBLEMS OF GEOMECHANICS AND ITS APPLICATION IN MINING AND GEOPHYSICS (ENGLISH)

**Larisa A. Nazarova**(DepartmentInstitute of Mining Siberian Branch of Russian Academy of Sciences)

INVERSE PROBLEMS OF GEOMECHANICS AND ITS APPLICATION IN MINING AND GEOPHYSICS (ENGLISH)

[ Abstract ]

The communication devotes to the boundary, coefficient and mixed inverse problems in modeling solid mineral mining processes.

Direct and indirect methods for estimation of natural stress field components were compared.

Based on GPS data (South Siberia, 2000-2003) interpretation the possible indicator (sharp increase of horizontal strains increment in epicenter vicinity) of future strong seismic event was established.

The theoretical approach for evaluation of future earthquake focal parameters (hypocentre depth and fractal dimension of fault anomalous zone) was proposed. The approach is found on inverse problem solution by variation of daylight surface strains.

Using a viscoelastic model, a method is proposed to evaluating the equation-of-state parameters that describe deformation of structural units of the room-and-pillar implementation in bedded deposits composed of rocks developing rheological properties. The method is based on the inverse coefficient problem solution with the data on roof and floor convergence in stopes.

A method of day-to-day qualitative assessment of elastic and strength properties of backfill in flat bedded deposits has been developed on the basis of the solution of the coefficient inverse problem for a set of equations (quasi-static formulation) which describe deformation and failure of filling mass. Uniqueness of the solution only requires simultaneous minimization of two objective functions.

The communication devotes to the boundary, coefficient and mixed inverse problems in modeling solid mineral mining processes.

Direct and indirect methods for estimation of natural stress field components were compared.

Based on GPS data (South Siberia, 2000-2003) interpretation the possible indicator (sharp increase of horizontal strains increment in epicenter vicinity) of future strong seismic event was established.

The theoretical approach for evaluation of future earthquake focal parameters (hypocentre depth and fractal dimension of fault anomalous zone) was proposed. The approach is found on inverse problem solution by variation of daylight surface strains.

Using a viscoelastic model, a method is proposed to evaluating the equation-of-state parameters that describe deformation of structural units of the room-and-pillar implementation in bedded deposits composed of rocks developing rheological properties. The method is based on the inverse coefficient problem solution with the data on roof and floor convergence in stopes.

A method of day-to-day qualitative assessment of elastic and strength properties of backfill in flat bedded deposits has been developed on the basis of the solution of the coefficient inverse problem for a set of equations (quasi-static formulation) which describe deformation and failure of filling mass. Uniqueness of the solution only requires simultaneous minimization of two objective functions.

### 2013/02/16

#### Infinite Analysis Seminar Tokyo

13:30-15:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Generalized Calogero-Moser type systems and Cherednik Algebras (ENGLISH)

**Alexey Silantyev**(Tokyo. Univ.)Generalized Calogero-Moser type systems and Cherednik Algebras (ENGLISH)

[ Abstract ]

Calogero-Moser systems can be obtained using Dunkl operators, which

define the polynomial representation of the corresponding rational

Cherednik algebra. Parabolic ideals invariant under the action of the

Dunkl operators give submodules of Cherednik algebra. Considering the

corresponding quotient-modules one yields the generalized (or deformed)

Calogero-Moser systems. In the same way we construct the generalized

elliptic Calogero-Moser systems using the elliptic Dunkl operators

obtained by Buchstaber, Felder and Veselov. The Macdonald-Ruijsenaars

systems (difference (relativistic) Calogero-Moser type systems) can be

considered in terms of Double Affine Hecke Algebra (DAHA). We construct

appropriate submodules in the polynomial representation of DAHA, which

were obtained by Kasatani for some affine root systems. Considering the

corresponding quotient representation we derive the generalized

(deformed) Macdonald-Ruijsenaars systems for any affine root system,

which where obtained by Sergeev and Veselov for the A series. This is

joint work with Misha Feigin.

Calogero-Moser systems can be obtained using Dunkl operators, which

define the polynomial representation of the corresponding rational

Cherednik algebra. Parabolic ideals invariant under the action of the

Dunkl operators give submodules of Cherednik algebra. Considering the

corresponding quotient-modules one yields the generalized (or deformed)

Calogero-Moser systems. In the same way we construct the generalized

elliptic Calogero-Moser systems using the elliptic Dunkl operators

obtained by Buchstaber, Felder and Veselov. The Macdonald-Ruijsenaars

systems (difference (relativistic) Calogero-Moser type systems) can be

considered in terms of Double Affine Hecke Algebra (DAHA). We construct

appropriate submodules in the polynomial representation of DAHA, which

were obtained by Kasatani for some affine root systems. Considering the

corresponding quotient representation we derive the generalized

(deformed) Macdonald-Ruijsenaars systems for any affine root system,

which where obtained by Sergeev and Veselov for the A series. This is

joint work with Misha Feigin.

### 2013/02/08

#### Lectures

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.

#### thesis presentations

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

Stability of Navier-Stokes-Boussinesq Type Systems (JAPANESE)

**Hajime KOBA**(Guraduate School of Mathematical Sciences the University of Tokyo)Stability of Navier-Stokes-Boussinesq Type Systems (JAPANESE)

#### thesis presentations

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

Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

**Yoshiki OSHIMA**(Guraduate School of Mathematical Sciences the University of Tokyo)Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

#### thesis presentations

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

Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

**Yoshiki OSHIMA**(Guraduate School of Mathematical Sciences the University of Tokyo)Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

#### thesis presentations

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

Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

**Yoshiki OSHIMA**(Guraduate School of Mathematical Sciences the University of Tokyo)Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)

#### thesis presentations

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

Motivic Homology and Class Field Theory over p-adic Fields (JAPANESE)

**Uzun Mecit Kerem**(Guraduate School of Mathematical Sciences the University of Tokyo)Motivic Homology and Class Field Theory over p-adic Fields (JAPANESE)

#### thesis presentations

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

Uniform Representability of the Brauer Group of Diagonal Cubic Surfaces (JAPANESE)

**Tetsuya UEMATSU**(Guradate School of Mathematical Sciences the University of Tokyo)Uniform Representability of the Brauer Group of Diagonal Cubic Surfaces (JAPANESE)

#### thesis presentations

09:30-10:45 Room #128 (Graduate School of Math. Sci. Bldg.)

Nuclearity of reduced free product C*-algebras (JAPANESE)

**Qinlong LI**(Guraduate School of Mathematical Sciences the University of Tokyo)Nuclearity of reduced free product C*-algebras (JAPANESE)

#### thesis presentations

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

Construction of holomorphic local conformal framed nets (JAPANESE)

**Suthichitranont Noppakhun**(Guraduate School of Mathematical Sciences the University of Tokyo)Construction of holomorphic local conformal framed nets (JAPANESE)

#### thesis presentations

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

Topology, symplectic geometry and complex geometry of solvmanifolds -From nilpotent to solvable- (JAPANESE)

**Hisashi KASUYA**(Guraduate School of Mathematical Sciences the University of Tokyo)Topology, symplectic geometry and complex geometry of solvmanifolds -From nilpotent to solvable- (JAPANESE)

#### thesis presentations

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

Discretization and ultradiscretization of differential equations preserving characters of their solutions (JAPANESE)

**Keisuke MATSUYA**(Guraduate School of Mathematical Sciences the University of Tokyo)Discretization and ultradiscretization of differential equations preserving characters of their solutions (JAPANESE)

### 2013/02/07

#### Operator Algebra Seminars

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

Combinatorial independence, amenability, and sofic entropy (ENGLISH)

**David Kerr**(東大数理/Texas A&M Univ.)Combinatorial independence, amenability, and sofic entropy (ENGLISH)

#### thesis presentations

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

Lie foliations transversely modeled on nilpotent Lie algebras

(JAPANESE)

**Naoki KATO**(Guraduate School of Mathematical Sciences the University of Tokyo)Lie foliations transversely modeled on nilpotent Lie algebras

(JAPANESE)

#### thesis presentations

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

Mathematical Analysis for Epidemic Models with Heterogeneity (JAPANESE)

**Toshikazu KUNIYA**(Guradate School of Mathematical Sciences the University of Tokyo)Mathematical Analysis for Epidemic Models with Heterogeneity (JAPANESE)

#### thesis presentations

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

MONOMIAL DEFORMATIONS OF CERTAIN HYPERSURFACES AND TWO HYPERGEOMETRIC FUNCTIONS

(JAPANESE)

**Kazuaki MIYATANI**(Guraduate School of Mathematical Sciences the University of Tokyo)MONOMIAL DEFORMATIONS OF CERTAIN HYPERSURFACES AND TWO HYPERGEOMETRIC FUNCTIONS

(JAPANESE)

#### thesis presentations

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

Proper actions and designs on homogeneous spaces (JAPANESE)

**Takayuki OKUDA**(Guraduate School of Mathematical Sciences the University of Tokyo)Proper actions and designs on homogeneous spaces (JAPANESE)

#### thesis presentations

15:45-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Symmetrized Max-Plus Algebra and Ultradiscrete sine-Gordon Equation (JAPANESE)

**Kenichi KONDO**(Guraduate School of Mathematical Sciences the University of Tokyo)Symmetrized Max-Plus Algebra and Ultradiscrete sine-Gordon Equation (JAPANESE)

#### thesis presentations

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

Asymptotic analysis of Bergman kernels for linear series and its application to Kahler Geometry (JAPANESE)

**Tomoyuki HISAMOTO**(Guraduate School of Mathematical Sciences the University of Tokyo)Asymptotic analysis of Bergman kernels for linear series and its application to Kahler Geometry (JAPANESE)

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