## Seminar information archive

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

### 2007/04/24

#### Tuesday Seminar on Topology

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

Realization of twisted $K$-theory and

finite-dimensional approximation of Fredholm operators

**五味 清紀**(東京大学大学院数理科学研究科)Realization of twisted $K$-theory and

finite-dimensional approximation of Fredholm operators

[ Abstract ]

A problem in twisted $K$-theory is to realize twisted $K$-groups generally by means of finite-dimensional geometric objects, like vector bundles. I would like to talk about an approach toward the problem by means of Mikio Furuta's generalized vector bundles. By using a twisted version of the generalized vector bundle and a finite-dimensional approximation of Fredholm operators, I construct a group into which there exists a natural injection from the twisted $K$-group twisted by any third integral cohomology class.

A problem in twisted $K$-theory is to realize twisted $K$-groups generally by means of finite-dimensional geometric objects, like vector bundles. I would like to talk about an approach toward the problem by means of Mikio Furuta's generalized vector bundles. By using a twisted version of the generalized vector bundle and a finite-dimensional approximation of Fredholm operators, I construct a group into which there exists a natural injection from the twisted $K$-group twisted by any third integral cohomology class.

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino

**Taro Yoshino (吉野太郎)**(University of Tokyo)Existence problem of compact Clifford-Klein forms of the infinitesimal homogeneous space of indefinite Stiefle manifolds

[ Abstract ]

The existence problem of compact Clifford-Klein forms is important in the study of discrete groups. There are several open problems on it, even in the reductive cases, which is most studied. For a homogeneous space of reductive type, one can define its `infinitesimal' homogeneous space.

This homogeneous space is easier to consider the existence problem of compact Clifford-Klein forms.

In this talk, we especially consider the infinitesimal homogeneous spaces of indefinite Stiefel manifolds. And, we reduce the existence problem of compact Clifford-Klein forms to certain algebraic problem, which was already studied from other motivation.

[ Reference URL ]The existence problem of compact Clifford-Klein forms is important in the study of discrete groups. There are several open problems on it, even in the reductive cases, which is most studied. For a homogeneous space of reductive type, one can define its `infinitesimal' homogeneous space.

This homogeneous space is easier to consider the existence problem of compact Clifford-Klein forms.

In this talk, we especially consider the infinitesimal homogeneous spaces of indefinite Stiefel manifolds. And, we reduce the existence problem of compact Clifford-Klein forms to certain algebraic problem, which was already studied from other motivation.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2007.html#20070424yoshino

### 2007/04/23

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Generalization of Q-curvature in CR geometry

**平地健吾**(東京大学)Generalization of Q-curvature in CR geometry

### 2007/04/19

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Graph algebras, Exel-Laca algebras and ultragraph algebras

**勝良健史**(東大数理)Graph algebras, Exel-Laca algebras and ultragraph algebras

### 2007/04/17

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Some $L^r$-decomposition of $3D$-vector fields and its application to the stationary Navier-Stokes equations in multi-connected domains.

**小薗 英雄**(東北大学・大学院理学研究科)Some $L^r$-decomposition of $3D$-vector fields and its application to the stationary Navier-Stokes equations in multi-connected domains.

#### Tuesday Seminar on Topology

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

Existence Problem of Compact Locally Symmetric Spaces

**小林 俊行**(東京大学大学院数理科学研究科)Existence Problem of Compact Locally Symmetric Spaces

[ Abstract ]

The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

In this talk, I will give a survey on the recent developments on the question about how the local geometric structure affects the global nature of non-Riemannian manifolds with emphasis on the existence problem of compact models of locally symmetric spaces.

The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

In this talk, I will give a survey on the recent developments on the question about how the local geometric structure affects the global nature of non-Riemannian manifolds with emphasis on the existence problem of compact models of locally symmetric spaces.

### 2007/04/16

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Joyce計量のツイスター空間の具体的な構成方法

**本多 宣博**(東京工業大学)Joyce計量のツイスター空間の具体的な構成方法

#### Lectures

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

Rearrangement inequalities and isoperimetric eigenvalue problems for second-order differential operators

**Francois Hamel**(エクス・マルセーユ第3大学 (Universite Aix-Marseille III))Rearrangement inequalities and isoperimetric eigenvalue problems for second-order differential operators

[ Abstract ]

The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. We show that, to each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types.

The results are new even for symmetric operators or in dimension 1. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new rearrangement technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.

The talk is concerned with various optimization results for the principal eigenvalues of general second-order elliptic operators in divergence form with Dirichlet boundary condition in bounded domains of R^n. We show that, to each operator in a given domain, we can associate a radially symmetric operator in the ball with the same Lebesgue measure, with a smaller principal eigenvalue. The constraints on the coefficients are of integral, pointwise or geometric types.

The results are new even for symmetric operators or in dimension 1. In particular, we generalize the Rayleigh-Faber-Krahn inequality for the principal eigenvalue of the Dirichlet Laplacian. The proofs use a new rearrangement technique, different from the Schwarz symmetrization. This talk is based on a joint work with N. Nadirashvili and E. Russ.

### 2007/04/14

#### Infinite Analysis Seminar Tokyo

13:00-16:30 Room #117 (Graduate School of Math. Sci. Bldg.)

q-Fock空間と非対称Macdonald多項式

The Quantum Knizhnik-Zamolodchikov Equation

and Non-symmetric Macdonald Polynomials

**長尾健太郎**(京大理) 13:00-14:30q-Fock空間と非対称Macdonald多項式

[ Abstract ]

斎藤-竹村-Uglov,Varagnolo-Vasserotによって,q-Fock空間に

A型量子トロイダル代数のレベル(0,1)表現の構造が入ることが知られています.

この表現をある可換部分代数に制限して得られる作用の同時固有ベクトルを,

非対称Macdonald多項式を用いて構成することができます.

さらにこの同時固有ベクトルをq-Fock空間の基底とすることで,

量子トロイダル代数の作用を組合せ論的に記述することができます.

今回のセミナーでは,斎藤-竹村-Uglov,Varagnolo-Vasserotの構成を

振り返ったあとで,同時固有ベクトルの構成法を紹介します.

最後に箙多様体の同変K群との関連について少しだけ言及します.

斎藤-竹村-Uglov,Varagnolo-Vasserotによって,q-Fock空間に

A型量子トロイダル代数のレベル(0,1)表現の構造が入ることが知られています.

この表現をある可換部分代数に制限して得られる作用の同時固有ベクトルを,

非対称Macdonald多項式を用いて構成することができます.

さらにこの同時固有ベクトルをq-Fock空間の基底とすることで,

量子トロイダル代数の作用を組合せ論的に記述することができます.

今回のセミナーでは,斎藤-竹村-Uglov,Varagnolo-Vasserotの構成を

振り返ったあとで,同時固有ベクトルの構成法を紹介します.

最後に箙多様体の同変K群との関連について少しだけ言及します.

**笠谷昌弘**(京大理) 15:00-16:30The Quantum Knizhnik-Zamolodchikov Equation

and Non-symmetric Macdonald Polynomials

[ Abstract ]

We construct special solutions of the quantum Knizhnik-Zamolodchikov equation

on the tensor product of the vector representation of

the quantum algebra of type $A_{N-1}$.

They are constructed from non-symmetric Macdonald polynomials

through the action of the affine Hecke algebra.

As special cases,

(i) the matrix element of the vertex operators

of level one is reproduced, and

(ii) we give solutions of level $\\frac{N+1}{N}-N$.

(ii) is a generalization of the solution of

level $-\\frac{1}{2}$ by V.Pasquier and me.

This is a jount work with Y.Takeyama.

We construct special solutions of the quantum Knizhnik-Zamolodchikov equation

on the tensor product of the vector representation of

the quantum algebra of type $A_{N-1}$.

They are constructed from non-symmetric Macdonald polynomials

through the action of the affine Hecke algebra.

As special cases,

(i) the matrix element of the vertex operators

of level one is reproduced, and

(ii) we give solutions of level $\\frac{N+1}{N}-N$.

(ii) is a generalization of the solution of

level $-\\frac{1}{2}$ by V.Pasquier and me.

This is a jount work with Y.Takeyama.

### 2007/04/12

#### Seminar on Mathematics for various disciplines

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

Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability

http://coe.math.sci.hokudai.ac.jp/

**Boris Khesin**(University of Toronto)Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability

[ Abstract ]

We describe a simple relation between curvatures of the group of volume-preserving diffeomorphisms (responsible for Lagrangian instability of ideal fluids via Arnold's approach) and the generation of shocks for potential solutions of the inviscid

Burgers equation (important in mass transport). For this we characterize focal points of the group of volume-preserving diffeomorphism, regarded as a submanifold in all diffeomorphisms and the corresponding conjugate points along geodesics in the Wasserstein space of densities.

Further, we consider the non-holonomic optimal transport problem,

related to the following non-holonomic version of the classical Moser theorem: given a bracket-generating distribution on a manifold two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution.

[ Reference URL ]We describe a simple relation between curvatures of the group of volume-preserving diffeomorphisms (responsible for Lagrangian instability of ideal fluids via Arnold's approach) and the generation of shocks for potential solutions of the inviscid

Burgers equation (important in mass transport). For this we characterize focal points of the group of volume-preserving diffeomorphism, regarded as a submanifold in all diffeomorphisms and the corresponding conjugate points along geodesics in the Wasserstein space of densities.

Further, we consider the non-holonomic optimal transport problem,

related to the following non-holonomic version of the classical Moser theorem: given a bracket-generating distribution on a manifold two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution.

http://coe.math.sci.hokudai.ac.jp/

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

ミラー対称性

**小西由紀子**(東大数理)ミラー対称性

### 2007/04/11

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The numerical treatment of pricing early exercise options under L'evy processes

http://coe.math.sci.hokudai.ac.jp/

**C. W. Oosterlee**(Delft University of Technology)The numerical treatment of pricing early exercise options under L'evy processes

[ Abstract ]

In this presentation we will discuss the pricing of American and Bermudan options under L'evy process dynamics.

Two different approaches will be discussed: First of all, modelling with differential operators gives rise to the numerical solution of a partial-integro differential equation for obtaining European option prices. For American prices a linear complementarity problem with the partial integro-differential operator needs to be solved. We outline the difficulties and possible solutions in this context.

At the same time we would also like to present a different pricing approach based on numerical integration and the fast Fourier Transform. Both approaches are compared in terms of accuracy and efficiency.

[ Reference URL ]In this presentation we will discuss the pricing of American and Bermudan options under L'evy process dynamics.

Two different approaches will be discussed: First of all, modelling with differential operators gives rise to the numerical solution of a partial-integro differential equation for obtaining European option prices. For American prices a linear complementarity problem with the partial integro-differential operator needs to be solved. We outline the difficulties and possible solutions in this context.

At the same time we would also like to present a different pricing approach based on numerical integration and the fast Fourier Transform. Both approaches are compared in terms of accuracy and efficiency.

http://coe.math.sci.hokudai.ac.jp/

#### Number Theory Seminar

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

l進層の暴分岐と特性サイクル

**斎藤 毅**(東京大学大学院数理科学研究科)l進層の暴分岐と特性サイクル

### 2007/04/10

#### Lectures

15:00-16:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Applications of the Generalised Pauli Group in Quantum Information

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf

**Thomas DURT**(ブリユッセル自由大学・VUB)Applications of the Generalised Pauli Group in Quantum Information

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf

### 2007/04/05

#### Applied Analysis

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Acoustic Modeling and Osteoporotic Evaluation of Bone

**Robert P. GILBERT**(デラウェア大学・数学教室)Acoustic Modeling and Osteoporotic Evaluation of Bone

[ Abstract ]

In this talk we discuss the modeling of the acoustic response of cancellous bone using the methods of homogenization.

This can lead to Biot type equations or more generalized equations. We develop the effective acoustic equations for cancellous bone. It is assumed that the bone matrix is elastic and the interstitial blood-marrow can be modeled as a Navier-Stokes system.

We also discuss the use of the Biot model and consider its applicability to cancellous bone. One of the questions this talk addresses is whether the clinical experiments customarily performed can be used to determine the parameters of the Biot or other bone models. A parameter recovery algorithm which uses parallel processing is developed and tested.

In this talk we discuss the modeling of the acoustic response of cancellous bone using the methods of homogenization.

This can lead to Biot type equations or more generalized equations. We develop the effective acoustic equations for cancellous bone. It is assumed that the bone matrix is elastic and the interstitial blood-marrow can be modeled as a Navier-Stokes system.

We also discuss the use of the Biot model and consider its applicability to cancellous bone. One of the questions this talk addresses is whether the clinical experiments customarily performed can be used to determine the parameters of the Biot or other bone models. A parameter recovery algorithm which uses parallel processing is developed and tested.

### 2007/03/26

#### Algebraic Geometry Seminar

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Existence of minimal models and flips (3rd talk of three)

**Professor Caucher Birkar**(University of Cambridge)Existence of minimal models and flips (3rd talk of three)

### 2007/03/22

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

A semidiscrete scheme for the Perona Malik equation

http://coe.math.sci.hokudai.ac.jp/

**Matteo Novaga**(Hokkaido University / Universita di Pisa)A semidiscrete scheme for the Perona Malik equation

[ Abstract ]

We discuss the convergence of the spatial semidiscrete scheme for the one-dimensional Perona-Malik equation. If the initial datum is 1-Lipschitz out of a finite number of jump points, we haracterize the problem satisfied by the limit solution. In the general case, we construct a solution by a careful inspection of the behaviour of the approximating solutions in a space-time neighbourhood of the jump points.

[ Reference URL ]We discuss the convergence of the spatial semidiscrete scheme for the one-dimensional Perona-Malik equation. If the initial datum is 1-Lipschitz out of a finite number of jump points, we haracterize the problem satisfied by the limit solution. In the general case, we construct a solution by a careful inspection of the behaviour of the approximating solutions in a space-time neighbourhood of the jump points.

http://coe.math.sci.hokudai.ac.jp/

#### Algebraic Geometry Seminar

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On boundedness of log Fano varieties (2nd talk of three)

**Professor Caucher Birkar**(University of Cambridge)On boundedness of log Fano varieties (2nd talk of three)

### 2007/03/20

#### Algebraic Geometry Seminar

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

)

Singularities and termination of flips (1st talk of three)

**Professor Caucher Birkar**(University of Cambridge)

Singularities and termination of flips (1st talk of three)

### 2007/03/17

#### Infinite Analysis Seminar Tokyo

13:30-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Calogero model and Quantum Benjamin-Ono Equation

**Paul Wiegmann**(Chicago Univ.)Calogero model and Quantum Benjamin-Ono Equation

[ Abstract ]

TBA

TBA

### 2007/03/09

#### Lectures

10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Nonsmooth Optimization and Applications in PDEs

**Kazufumi Ito**(North Carolina State University)Nonsmooth Optimization and Applications in PDEs

[ Abstract ]

Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.

Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.

Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.

Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.

### 2007/03/08

#### Lectures

15:30-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Nonsmooth Optimization and Applications in PDEs

**Kazufumi Ito**(North Carolina State University)Nonsmooth Optimization and Applications in PDEs

[ Abstract ]

Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.

Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.

Semismooth Newton method for solving nonlinear non-smooth equations in Banach spaces is discussed.

Applications include complementarity problems, variational inequalities and optimal control problems with control or state constraints, Black Scholes model with American option and imaging analysis.

### 2007/03/07

#### Seminar on Mathematics for various disciplines

14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Stability theory in L^p for the space-inhomogeneous Boltzmann equation

http://coe.math.sci.hokudai.ac.jp/index.html.en

**Seung Yeal Ha**(Seoul National University)Stability theory in L^p for the space-inhomogeneous Boltzmann equation

[ Abstract ]

In this talk, I will present kinetic nonlinear funtionals which are similar in sprit to Glimm type functionals in one-dimensional hyperbolic conservation laws. These functionals measures the dispersive mechanism of the Boltzmann equation near vacuum and can be used to the study of the large-time behavior and L^p-stability of the Boltzmann equation near vacuum. This is a joint work with M. Yamazaki (Univ. of Tsukuba) and Seok-Bae Yun (Seoul National Univ.)

[ Reference URL ]In this talk, I will present kinetic nonlinear funtionals which are similar in sprit to Glimm type functionals in one-dimensional hyperbolic conservation laws. These functionals measures the dispersive mechanism of the Boltzmann equation near vacuum and can be used to the study of the large-time behavior and L^p-stability of the Boltzmann equation near vacuum. This is a joint work with M. Yamazaki (Univ. of Tsukuba) and Seok-Bae Yun (Seoul National Univ.)

http://coe.math.sci.hokudai.ac.jp/index.html.en

### 2007/02/22

#### Lectures

10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The level set method, multivalued solutions and image science

**Stan Osher**(UCLA)The level set method, multivalued solutions and image science

[ Abstract ]

During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.

During the past two decades variational and partial differential based methods have greatly affected the fields of image processing, computer vision and graphics (image science in general). Almost simultaneously the level set method for computing moving interfaces has impacted many areas of mathematics, engineering and applied science, including image science. I will try to give an overview of the basics and recent advances in these topics.

#### Lectures

13:00-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Optimal control of semilinear parabolic equations and an application to laser material treatments

**Dietmar Hoemberg**(Berlin Technical University)Optimal control of semilinear parabolic equations and an application to laser material treatments

[ Abstract ]

Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.

However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.

The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.

Many technological processes can be described by partial differential equations. For many years the role of industrial mathematics was mainly to try to understand the respective process, to derive an appropriate PDE or ODE model for it and to simulate it using, e.g., a finite-element code.

However, the ultimate goal usually is to try to optimize the process. Mathematically, this requires the solution of an optimal control problem, i.e., a constrained nonlinear optimization problem in which the constraints are PDEs.

The goal of these two talks is to give an overview of the theory and numerics of optimal control of PDEs for the case of parabolic state equations including an application in laser material treatments. More specifically, I will focus on the following topics.

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