## Seminar information archive

Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～

### 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 ]

https://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 ]

https://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.

### 2007/02/21

#### 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

13:30-15:00 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.

### 2007/02/20

#### Lectures

10:30-17:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Exit distributions for random walks in random environments

Quasi one-dimensional random walks in random environments

Large deviation principle for currents generated by stochasticline integrals

on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)

Interacting Brownian motions related to Ginibre random point field

**Erwin Bolthausen**(University of Zurich) 10:30-12:00Exit distributions for random walks in random environments

**Erwin Bolthausen**(University of Zurich) 14:00-15:30Quasi one-dimensional random walks in random environments

**田村要造**(慶応大理工) 15:50-16:30Large deviation principle for currents generated by stochasticline integrals

on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)

**長田博文**(九大数理) 16:40-17:20Interacting Brownian motions related to Ginibre random point field

#### Tuesday Seminar of Analysis

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

On the dynamics of the Gross-Pitaevskii equation

**Patrick G¥'erard**(パリ南大学)On the dynamics of the Gross-Pitaevskii equation

### 2007/02/17

#### Infinite Analysis Seminar Tokyo

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

Finite-dimensional representations of the small quantum algebras

Combinatorics of Young walls and crystal bases

**阿部 友紀**(上智理工数学) 13:30-14:30Finite-dimensional representations of the small quantum algebras

[ Abstract ]

量子代数は定義にパラメーターを一つ含み、量子代数の表現論は、

そのパラメーターが1のべき根であるか、そうでないかによって大きく異なる。

さらに、1のべき根の場合は、Lusztig氏によって定義された「制限型量子代数」と、

De Conini-Kac氏らによって定義された「非制限型量子代数」の2種類が存在し、

それぞれ表現論が異なる。

また、制限型量子代数は、「小型量子代数(=small quantum algebra)」と

呼ばれる真部分代数を含み、その表現論は、制限型量子代数と非制限型量子代数の

どちらの表現論においても重要な役割を果たしている。

今回の講演では、主に以下の3点について説明したい:

●小型量子代数が、非制限型量子代数のある商代数と同型になることを、

有限型とループ型の場合に示す。

●A, B, C, D, G型の小型量子代数の有限次元既約表現を、

Schnizer表現の部分表現として構成する。

●A型の小型ループ量子代数のevaluation表現の性質を調べる。

量子代数は定義にパラメーターを一つ含み、量子代数の表現論は、

そのパラメーターが1のべき根であるか、そうでないかによって大きく異なる。

さらに、1のべき根の場合は、Lusztig氏によって定義された「制限型量子代数」と、

De Conini-Kac氏らによって定義された「非制限型量子代数」の2種類が存在し、

それぞれ表現論が異なる。

また、制限型量子代数は、「小型量子代数(=small quantum algebra)」と

呼ばれる真部分代数を含み、その表現論は、制限型量子代数と非制限型量子代数の

どちらの表現論においても重要な役割を果たしている。

今回の講演では、主に以下の3点について説明したい:

●小型量子代数が、非制限型量子代数のある商代数と同型になることを、

有限型とループ型の場合に示す。

●A, B, C, D, G型の小型量子代数の有限次元既約表現を、

Schnizer表現の部分表現として構成する。

●A型の小型ループ量子代数のevaluation表現の性質を調べる。

**Seok-Jin Kang**(Seoul National University) 15:00-16:00Combinatorics of Young walls and crystal bases

[ Abstract ]

We introduce combinatorics of Young walls and give a realization of crystal bases in terms of reduced Young walls. We also discuss their connection with representation theory of Hecke algebras.

We introduce combinatorics of Young walls and give a realization of crystal bases in terms of reduced Young walls. We also discuss their connection with representation theory of Hecke algebras.

### 2007/02/16

#### Colloquium

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

トポロジーと私の思い出

**松本幸夫**(東京大学・大学院数理科学研究科)トポロジーと私の思い出

[ Abstract ]

大学院に入ったのが1967年ですから、ちょうど40年前の

ことになります。それから「多様体のトポロジー」の分野で研究を

してきましたが、この40年間にトポロジーもずいぶん変化した

ように思います。自分の思い出話を交えて、その変化の様子をお話

できればと思います。私的な観点のものですので、それほど大所

高所からの話ではありません。

大学院に入ったのが1967年ですから、ちょうど40年前の

ことになります。それから「多様体のトポロジー」の分野で研究を

してきましたが、この40年間にトポロジーもずいぶん変化した

ように思います。自分の思い出話を交えて、その変化の様子をお話

できればと思います。私的な観点のものですので、それほど大所

高所からの話ではありません。

#### Applied Analysis

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

Multiple positive solutions for classes of elliptic systems with combined nonlinear effects

**Ratnasingham SHIVAJI**(ミシシッピ州立大学)Multiple positive solutions for classes of elliptic systems with combined nonlinear effects

[ Abstract ]

We study the existence of multiple positive solutions to systems of the form

-\\Delta u = \\lambda f(v)

-\\Delta v = \\lambda g(u)

in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.

We study the existence of multiple positive solutions to systems of the form

-\\Delta u = \\lambda f(v)

-\\Delta v = \\lambda g(u)

in a bounded domain in R^N under the Dirichlet boundary conditions. Here f, g belong to a class of positive functions having a combined sublinear effect at infinity. Our result also easily extends to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.

### 2007/02/01

#### Lectures

15:00-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On Calderon's inverse conductivity problem in the plane.

**Lassi Paivarinta**(Helsinki University of Technology, Finland)On Calderon's inverse conductivity problem in the plane.

#### Lectures

16:15-17:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Finland)

Locating transparent cavities in optical absorption and scattering

tomography

**Nuuti Huyvonen**(Helsinki University of Technology,Finland)

Locating transparent cavities in optical absorption and scattering

tomography

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