過去の記録

過去の記録 ~02/21本日 02/22 | 今後の予定 02/23~

トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
小林 俊行 氏 (東京大学大学院数理科学研究科)
Existence Problem of Compact Locally Symmetric Spaces
[ 講演概要 ]
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年04月16日(月)

複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
本多 宣博 氏 (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

講演会

16:30-17:30   数理科学研究科棟(駒場) 056号室
Francois Hamel 氏 (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
[ 講演概要 ]
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年04月14日(土)

東京無限可積分系セミナー

13:00-16:30   数理科学研究科棟(駒場) 117号室
長尾健太郎 氏 (京大理) 13:00-14:30
q-Fock空間と非対称Macdonald多項式
[ 講演概要 ]
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 氏 (京大理) 15:00-16:30
The Quantum Knizhnik-Zamolodchikov Equation
and Non-symmetric Macdonald Polynomials
[ 講演概要 ]
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年04月12日(木)

諸分野のための数学研究会

16:30-17:30   数理科学研究科棟(駒場) 056号室
Boris Khesin 氏 (University of Toronto)
Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
小西由紀子 氏 (東大数理)
ミラー対称性

2007年04月11日(水)

諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
C. W. Oosterlee 氏 (Delft University of Technology)
The numerical treatment of pricing early exercise options under L'evy processes
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/

代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室
斎藤 毅 氏 (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年04月10日(火)

講演会

15:00-16:00   数理科学研究科棟(駒場) 370号室
Thomas DURT 氏 (ブリユッセル自由大学・VUB)
Applications of the Generalised Pauli Group in Quantum Information
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~willox/abstractDurt.pdf

2007年04月05日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室
Robert P. GILBERT 氏 (デラウェア大学・数学教室)
Acoustic Modeling and Osteoporotic Evaluation of Bone
[ 講演概要 ]
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年03月26日(月)

代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge)
Existence of minimal models and flips (3rd talk of three)

2007年03月22日(木)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Matteo Novaga 氏 (Hokkaido University / Universita di Pisa)
A semidiscrete scheme for the Perona Malik equation
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/

代数幾何学セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge)
On boundedness of log Fano varieties (2nd talk of three)

2007年03月20日(火)

代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Professor Caucher Birkar 氏 (University of Cambridge
)
Singularities and termination of flips (1st talk of three)

2007年03月17日(土)

東京無限可積分系セミナー

13:30-14:30   数理科学研究科棟(駒場) 117号室
Paul Wiegmann 氏 (Chicago Univ.)
Calogero model and Quantum Benjamin-Ono Equation
[ 講演概要 ]
TBA

2007年03月09日(金)

講演会

10:30-12:00   数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
[ 講演概要 ]
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年03月08日(木)

講演会

15:30-17:00   数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演
Kazufumi Ito 氏 (North Carolina State University)
Nonsmooth Optimization and Applications in PDEs
[ 講演概要 ]
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年03月07日(水)

諸分野のための数学研究会

14:00-15:00   数理科学研究科棟(駒場) 056号室
Seung Yeal Ha 氏 (Seoul National University)
Stability theory in L^p for the space-inhomogeneous Boltzmann equation
[ 講演概要 ]
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.)
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/index.html.en

2007年02月22日(木)

講演会

10:30-12:00   数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会

※Osher先生の講演は中止になりました。

Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
[ 講演概要 ]
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.

講演会

13:00-15:00   数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ 講演概要 ]
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年02月21日(水)

講演会

10:30-12:00   数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会

※Osher先生の講演は中止になりました。

Stan Osher 氏 (UCLA)
The level set method, multivalued solutions and image science
[ 講演概要 ]
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.

講演会

13:30-15:00   数理科学研究科棟(駒場) 123号室
魅力ある大学院教育イニシアティブ特別講演会
Dietmar Hoemberg 氏 (Berlin Technical University)
Optimal control of semilinear parabolic equations and an application to laser material treatments
[ 講演概要 ]
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年02月20日(火)

講演会

10:30-17:20   数理科学研究科棟(駒場) 123号室
Erwin Bolthausen 氏 (University of Zurich) 10:30-12:00
Exit distributions for random walks in random environments
Erwin Bolthausen 氏 (University of Zurich) 14:00-15:30
Quasi one-dimensional random walks in random environments
田村要造 氏 (慶応大理工) 15:50-16:30
Large deviation principle for currents generated by stochasticline integrals
on compact Riemannian manifolds (joint work with S. Kusuoka and K. Kuwada)
長田博文 氏 (九大数理) 16:40-17:20
Interacting Brownian motions related to Ginibre random point field

解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 117号室
Patrick G¥'erard 氏 (パリ南大学)
On the dynamics of the Gross-Pitaevskii equation

2007年02月17日(土)

東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室
阿部 友紀 氏 (上智理工数学) 13:30-14:30
Finite-dimensional representations of the small quantum algebras
[ 講演概要 ]
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 氏 (Seoul National University) 15:00-16:00
Combinatorics of Young walls and crystal bases
[ 講演概要 ]
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.

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