過去の記録

過去の記録 ~11/11本日 11/12 | 今後の予定 11/13~

2009年03月17日(火)

GCOEレクチャーズ

10:00-17:30   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 11:00-12:00
Dirac Cohomology
Salah Mehdi 氏 (Metz University) 13:30-14:30
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz
(Max Planck Institute) 15:00-16:00
Harish-Chandra modules
Peter Trapa 氏 (Utah) 16:30-17:30
Special unipotent representations of real reductive groups

2009年03月16日(月)

GCOEレクチャーズ

10:00-16:20   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Bernhard Krötz
(Max Planck Institute) 10:00-11:00
Harish-Chandra modules
[ 講演概要 ]
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:

1.Topological representation theory on various types of locally convex vector spaces.

2.Basic algebraic theory of Harish-Chandra modules

3. Unique globalization versus lower bounds for matrix coefficients

4. Dirac type sequences for representations

5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#kroetz
Peter Trapa 氏 (Utah) 11:15-12:15
Special unipotent representations of real reductive groups
[ 講演概要 ]
These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:

1.Algebraic definition of special unipotent representations and examples.

2.Localization and duality for Harish-Chandra modules.

3. Geometric definition of special unipotent representations.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#trapa
Roger Zierau 氏 (Oklahoma State University) 13:30-14:30
Dirac Cohomology
[ 講演概要 ]
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\\mathfrak g = \\mathfrak h + \\mathfrak q$. Let S\\mathfrak q be the restriction of the spin representation of SO(\\mathfrak q) to H ⊂ SO(\\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q, where V is an $\\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\\mathfrak n$-cohomology. The lectures will roughly contain the following.

1.Construction of the spin representations of \\widetilde{SO}(n).

2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.

3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.

4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.

5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.

The lectures will be fairly elementary.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#zierau
Salah Mehdi 氏 (Metz University) 15:20-16:20
Enright-Varadarajan modules and harmonic spinors
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory.
Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/index.files/springschooltokyo200903.html#mehdi

2009年03月14日(土)

GCOEレクチャーズ

09:00-14:00   数理科学研究科棟(駒場) 123号室
Roger Zierau 氏 (Oklahoma State University) 09:00-10:00
Dirac cohomology
Salah Mehdi 氏 (Metz University) 10:15-11:15
Enright-Varadarajan modules and harmonic spinors
Bernhard Krötz 氏 (Max Planck Institute) 11:45-12:45
Harish-Chandra modules
Peter Trapa 氏 (Utah University) 13:00-14:00
Special unipotent representations of real reductive groups

2009年03月13日(金)

GCOEレクチャーズ

09:30-16:30   数理科学研究科棟(駒場) 123号室
Salah Mehdi 氏 (Metz) 09:30-10:30
Enright-Varadarajan modules and harmonic spinors
[ 講演概要 ]
The aim of these lectures is twofold. First we would like to describe the construction of the Enright-Varadarajan modules which provide a nice algebraic characterization of discrete series representations. This construction uses several important tools of representations theory. Then we shall use the Enright-Varadarajan modules to define a product for harmonic spinors on homogeneous spaces.
Peter Trapa 氏 (Utah) 11:00-12:00
Special unipotent representations of real reductive groups
Bernhard Krötz
(Max Planck Institute) 13:30-14:30
Harish-Chandra modules
Roger Zierau 氏 (Oklahoma State University) 15:00-16:00
Dirac Cohomology

2009年03月12日(木)

談話会・数理科学講演会

15:00-17:30   数理科学研究科棟(駒場) 050号室
お茶&Coffee&お菓子: 16:00~16:30
菊地文雄 氏 (東京大学大学院数理科学研究科) 15:00-16:00
数値解析:得られた成果と残された課題
[ 講演概要 ]
有限要素法を中心とする偏微分方程式の数値計算と数値解析に従事して長い歳月を経た。その間に偏微分方程式としては、Poisson方程式、弾性論のCauchy-Navierの方程式、非圧縮流体のStokes方程式、平板の曲げに対する重調和方程式やReissner-Mindlinの方程式、電磁気学のMaxwell方程式、プラズマ平衡のGrad-Shafranov方程式などを扱ってきたが、得られた成果もかなりある反面、残された課題も多いと思う。定年退職にあたり、少々整理と総括をしておきたい。
桂 利行 氏 (東京大学大学院数理科学研究科) 16:30-17:30
正標数の世界に40年
[ 講演概要 ]
正標数における代数幾何学には、標数0の場合とは異なる特有の現象がある。1950年代には、これらは病理的現象として捉えられ、研究している人の数も少なかった。現在では、特有の現象を扱うための手段がかなり整備され、正標数の様々な対象に対して興味ある現象が解析されている。代数多様体の単有理性、野性的ファイバーの問題、正標数特有のサイクルの構造等、これまで正標数の世界で行ってきた研究を中心に思い出を交えてお話ししたい。

GCOEレクチャーズ

09:30-14:30   数理科学研究科棟(駒場) 123号室
GCOE Spring School on Representation Theory
Roger Zierau 氏 (Oklahoma State University) 09:30-10:30
Dirac Cohomology
[ 講演概要 ]
Dirac operators have played an important role in representation theory. An early example is the construction of discrete series representations as spaces of L2 harmonic spinors on symmetric spaces G/K. More recently a very natural Dirac operator has been discovered by Kostant; it is referred to as the cubic Dirac operator. There are algebraic and geometric versions. Suppose G/H is a reductive homogeneous space and $\\mathfrak g = \\mathfrak h + \\mathfrak q$. Let S\\mathfrak q be the restriction of the spin representation of SO(\\mathfrak q) to H ⊂ SO(\\mathfrak q). The algebraic cubic Dirac operator is an H-homomorphism \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q, where V is an $\\mathfrak g$-module. The geometric geometric version is a differential operator acting on smooth sections of vector bundles of spinors on G/H. The algebraic cubic Dirac operator leads to a notion of Dirac cohomology, generalizing $\\mathfrak n$-cohomology. The lectures will roughly contain the following.

1.Construction of the spin representations of \\widetilde{SO}(n).

2.The algebraic cubic Dirac operator \\mathcal D: V \\otimes S\\mathfrak q → V \\otimes S\\mathfrak q will be defined and some properties, including a formula for the square, will be given.

3. Of special interest is the case when H=K, a maximal compact subgroup of G and V is a unitarizable $(\\mathfrak g,K)$-module. This case will be discussed.

4.The Dirac cohomology of a finite dimensional representation will be computed. We will see how this is related to $\\mathfrak n$-cohomology of V.

5. The relationship between the algebraic and geometric cubic Dirac operators will be described. A couple of open questions will then be discussed.

The lectures will be fairly elementary.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html
Bernhard Krötz 氏 (Max Planck) 11:00-12:00
Harish-Chandra modules
[ 講演概要 ]
We plan to give a course on the various types of topological globalizations of Harish-Chandra modules. It is intended to cover the following topics:

1.Topological representation theory on various types of locally convex vector spaces.

2.Basic algebraic theory of Harish-Chandra modules

3. Unique globalization versus lower bounds for matrix coefficients

4. Dirac type sequences for representations

5. Deformation theory of Harish-Chandra modules
The new material presented was obtained in collaboration with Joseph Bernstein and Henrik Schlichtkrull. A first reference is the recent preprint "Smooth Frechet Globalizations of Harish-Chandra Modules" by J. Bernstein and myself, downloadable at arXiv:0812.1684v1.
Peter Trapa 氏 (Utah大学) 13:30-14:30
Special unipotent representations of real reductive groups
[ 講演概要 ]
These lectures are aimed at beginning graduate students interested in the representation theory of real Lie groups. A familiarity with the theory of compact Lie groups and the basics of Harish-Chandra modules will be assumed. The goal of the lecture series is to give an exposition (with many examples) of the algebraic and geometric theory of special unipotent representations. These representations are of considerable interest; in particular, they are predicted to be the building blocks of all representation which can contribute to spaces of automorphic forms. They admit many beautiful characterizations, but their construction and unitarizability still remain mysterious.
The following topics are planned:

1.Algebraic definition of special unipotent representations and examples.

2.Localization and duality for Harish-Chandra modules.
3. Geometric definition of special unipotent representations.

2009年03月05日(木)

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
いつもと曜日が異なります. Tea: 16:00 - 16:30 コモンルーム
Shicheng Wang 氏 (Peking University)
Extending surface automorphisms over 4-space
[ 講演概要 ]
Let $e: M^p\\to R^{p+2}$ be a co-dimensional 2 smooth embedding
from a closed orientable manifold to the Euclidean space and $E_e$ be the subgroup of ${\\cal M}_M$, the mapping class group
of $M$, whose elements extend over $R^{p+2}$ as self-diffeomorphisms. Then there is a spin structure
on $M$ derived from the embedding which is preserved by each $\\tau \\in E_e$.

Some applications: (1) the index $[{\\cal M}_{F_g}:E_e]\\geq 2^{2g-1}+2^{g-1}$ for any embedding $e:F_g\\to R^4$, where $F_g$
is the surface of genus $g$. (2) $[{\\cal M}_{T^p}:E_e]\\geq 2^p-1$ for any unknotted embedding
$e:T^p\\to R^{p+2}$, where $T^p$ is the $p$-dimensional torus. Those two lower bounds are known to be sharp.

This is a joint work of Ding-Liu-Wang-Yao.

GCOEセミナー

10:15-11:15   数理科学研究科棟(駒場) 270号室
V. Isakov 氏 (Wichita State Univ.)
Carleman type estimates with two large parameters and applications to elasticity theory woth residual stress
[ 講演概要 ]
We give Carleman estimates with two large parameters for general second order partial differential operators with real-valued coefficients.
We outline proofs based on differential quadratic forms and Fourier analysis. As an application, we give Carleman estimates for (anisotropic)elasticity system with residual stress and discuss applications to control theory and inverse problems.

GCOEセミナー

11:15-12:15   数理科学研究科棟(駒場) 270号室
J. Ralston 氏 (UCLA)
Determining moving boundaries from Cauchy data on remote surfaces
[ 講演概要 ]
We consider wave equations in domains with time-dependent boundaries (moving obstacles) contained in a fixed cylinder for all time. We give sufficient conditions for the determination of the moving boundary from the Cauchy data on part of the boundary of the cylinder. We also study the related problem of reachability of the moving boundary by time-like curves from the boundary of the cylinder.

2009年03月04日(水)

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室
P. Gaitan (with H. Isozaki and O. Poisson) 氏 (Univ. Marseille)
Probing for inclusions for the heat equation with complex
spherical waves

GCOEセミナー

16:15-17:15   数理科学研究科棟(駒場) 270号室
M. Cristofol 氏 (Univ. Marseille)
Coefficient reconstruction from partial measurements in a heterogeneous
equation of FKPP type
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/abstractTokyo.pdf

2009年03月03日(火)

GCOEセミナー

16:15-17:15   数理科学研究科棟(駒場) 270号室
O. Poisson 氏 (Univ. Marseille)
Carleman estimates for the heat equation with discontinuous diffusion coefficients and applications
[ 講演概要 ]
We consider a heat equation in a bounded domain. We assume that the coefficient depends on the spatial variable and admits a discontinuity across an interface. We prove a Carleman estimate for the solution of the above heat equation without assumptions on signs of the jump of the coefficient.

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室
Y. Dermenjian 氏 (Univ. Marseille)
Controllability of the heat equation in a stratified media : a consequence of its spectral structure.

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/DermenjianTokyo2009.pdf

2009年03月02日(月)

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 270号室
Bernd Hofmann 氏 (Chemnitz University of Technology)
Convergence rates for nonlinear ill-posed problems based on variational inequalities expressing source conditions
[ 講演概要 ]
Twenty years ago Engl, Kunisch and Neubauer presented the fundamentals of a systematic theory for convergence rates in Tikhonov regularization
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/activity/documents/hofmann.pdf

2009年02月26日(木)

講演会

17:00-18:30   数理科学研究科棟(駒場) 270号室
Freddy DELBAEN 氏 (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 470号室
時間が15:00~16:00に変わりましたのでご注意ください。
Jijun Liu 氏 (Southeast University, P.R.China)
Reconstruction of biological tissue conductivity by MREIT technique
[ 講演概要 ]
Magnetic resonance electrical impedance tomography (MREIT) is a new technique in medical imaging, which aims to provide electrical conductivity images of biological tissue. Compared with the traditional electrical impedance tomography (EIT)model, MREIT reconstructs the interior conductivity from the deduced magnetic field information inside the tissue. Since the late 1990s, MREIT imaging techniques have made significant progress experimentally and numerically. However, the theoretical analysis on the MREIT algorithms is still at the initial stage. In this talk, we will give a state of the art of the MREIT technique and to concern the convergence property as well as the numerical implementation of harmonic B_z algorithm and nonlinear integral equation algorithm. We present some late advances in the convergence issues of MREIT algorithm. Some open problems related to the noisy effects and the numerical implementations are also given.

2009年02月24日(火)

談話会・数理科学講演会

16:00-17:00   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 15:30~16:00 (コモンルーム)
次回談話会は,3月12日(木) 15:00--17:30.
講演者は,桂 利行氏(東京大学大学院数理科学研究科),
菊地文雄氏(東京大学大学院数理科学研究科)�

神保道夫 氏 (東京大学大学院数理科学研究科)
相関関数の構成要素
[ 講演概要 ]
2次元の可積分な格子模型や、それと等価な1次元量子スピンチェインは、ベーテ、オンサーガー以来多くの研究が重ねられ、詳細に調べられている。ハミルトニアンのスペクトルと並ぶ重要な物理量に相関関数がある。イジング模型や共形場理論では相関関数自身が微分方程式で特徴づけられるがこのような簡明な結果はそれ以外の場合には知られていない。イジング模型を超える代表的な例として1次元のXXZ模型がある。相関関数は多重積分であらわされ、その長距離漸近挙動の研究が近年フランスのグループにより大きく進展している。
講演の前半では、相関関数に焦点をあててこれまでの研究の歴史を概観する。結合定数や温度などのパラメータの関数として見た場合、相関関数は2つの要素的超越関数から原理的には有理的に決まっていることがわかる。後半ではこの話題を紹介したい。

2009年02月23日(月)

講演会

13:30-14:30   数理科学研究科棟(駒場) 123号室
長田 博文 氏 (九大数理)
TBA

講演会

14:40-16:10   数理科学研究科棟(駒場) 123号室
Herbert Spohn 氏 (ミュンヘン工科大学)
Some problems from Statistical Mechanics linked to matrix-valued
Brownian motion

講演会

16:20-17:50   数理科学研究科棟(駒場) 123号室
Stefano Olla 氏 (パリ第9大学)
Macroscopic energy transport: a weak coupling approach

2009年02月19日(木)

講演会

17:00-18:30   数理科学研究科棟(駒場) 056号室
Freddy DELBAEN 氏 (チューリッヒ工科大学名誉教授)
Introduction to Coherent Risk Measure

代数幾何学セミナー

15:50-18:00   数理科学研究科棟(駒場) 128号室
O. F. Pasarescu 氏 (Romanian Academy)
・Linear Systems on Rational Surfaces; Applications (15:50--16: 50)

・Some Applications of Model Theory in Algebraic Geometry (17:00 --18:00)

2009年02月18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
野原勉 氏 (武蔵工業大学)
Non-existence theorem of periodic solutions except out-of-phase
and in-phase solutions in the coupled van der Pol equation system
[ 講演概要 ]
We consider the periodic solutions of the coupled van der Pol equation system $\\Sigma$, which is quite different from the ordinary van der Pol equation. We show the necessary and sufficient condition for the periodic solutions of $\\Sigma$. Non-existence theorem of periodic solutions except out-of-phase and in-phase solutions in $\\Sigma$ is presented.

博士論文発表会

17:00-18:10   数理科学研究科棟(駒場) 122号室
清野和彦 氏 (東京大学大学院数理科学研究科)
Finite group actions on spin 4-manifolds(四次元スピン多様体への有限群作用)

2009年02月14日(土)

東京無限可積分系セミナー

10:30-14:00   数理科学研究科棟(駒場) 117号室
藤健太 氏 (神戸理) 10:30-11:30
野海・山田系におけるタウ関数の関係式
[ 講演概要 ]
野海・山田系は, A型のドリンフェルト・ソコロフ階層の相似簡約から得られる高階
の常微分方程式系である.
本講演では, ドリンフェルト・ソコロフ階層を波動作用素を用いて考察することによっ
て, 野海・山田系のタウ関数の双線形方程式を求める.
鈴木貴雄 氏 (神戸理) 13:00-14:00
ワイル群の regular な共役類に付随するドリンフェルト・ソコロフ階層とパンルヴェ型微分方程式
[ 講演概要 ]
ドリンフェルト・ソコロフ階層はKdV階層のアフィン・リー代数への一般化で, ワイ
ル群の共役類(またはハイゼンベルグ部分代数)によって特徴付けられる可積分系で
ある.
本講演では, ワイル群の共役類のうち特に regular と呼ばれるものに注目し, それ
に対応するドリンフェルト・ソコロフ階層の定式化について, F.Kroode-J.Leur, Kik
uchi-Ikeda-Kakei 等の仕事を紹介しつつ解説する.
また, パンルヴェ型微分方程式との関連についても述べる.

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