過去の記録

2010年03月09日(火)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 123号室

Joachim Escher 氏 (Leibniz University of Hanover)
Shallow water waves with singularities
[ 講演概要 ]
The Degasperis-Procesi equation is a recently derived shallow water wave equation, which is - similar as the Camassa-Holm equation - embedded in a family of spatially periodic third order dispersive conservation laws.
The coexistence of globally in time defined classical solutions, wave breaking solutions, and spatially periodic peakons and shock waves is evidenced in the talk, and the precise blow-up scenario, including blow-up rates and blow-up sets, is discussed in detail. Finally several conditions on the initial profile are presented, which ensure the occurence of a breaking wave.

2010年02月24日(水)

講演会

15:00-16:30   数理科学研究科棟(駒場) 370号室
Robert Penner 氏 (Aarhus University / University of Southern California)
Protein Moduli Space
[ 講演概要 ]
Recent joint works with J. E. Andersen and others
provide explicit discrete and continuous models
of protein geometry. These models are inspired
by corresponding constructions in the study of moduli
spaces of flat G-connections on surfaces, in particular,
for G=PSL(2,R) and G=SO(3). These models can be used
for protein classification as well as for folding prediction,
and computer experiments towards these ends will
be discussed.

2010年02月23日(火)

講演会

14:00-15:00   数理科学研究科棟(駒場) 122号室
Bendong LOU 氏 (同済大学)
Homogenization Limit and Singular Limit of the Allen-Cahn equation
[ 講演概要 ]
We consider the Allen-Cahn equation in a cylinder with periodic undulating boundaries in the plane. Our problem involves two small parameters $\\delta$ and $\\epsilon$, where $\\delta$ appears in the equation to denote the scale of the singular limit and $\\epsilon$ appears in the boundary conditions to denote the scale of the homogenization limit. We consider the following two limiting processes:
(I): taking homogenization limit first and then taking singular limit;
(II) taking singular limit first and then taking homogenization limit.

We formally show that they both result in the same mean curvature flow equation, but with different boundary conditions.

2010年02月19日(金)

Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Orsay)
Discrete groups acting on homogeneous spaces V
[ 講演概要 ]
I will focus on recent advances on our understanding of discrete subgroups of Lie groups.
I will first survey how ideas from semisimple algebraic groups, ergodic theory and representation theory help us to understand properties of these discrete subgroups.

I will then focus on a joint work with Jean-Francois Quint studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:

We fix two integral matrices A and B of size d, of determinant 1, and such that no finite union of vector subspaces is invariant by A and B. We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.

2010年02月18日(木)

GCOEレクチャーズ

10:30-17:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
[ 講演概要 ]
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.

I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.

I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:

We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist 氏 (Paris Sud) 15:00-16:00
Discrete groups acting on homogeneous spaces IV

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
Roberto Longo 氏 (University of Rome, Tor Vergata)
Von Neumann Algebras and Boundary Quantum Field Theory

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Bendong LOU 氏 (同済大学)
Homogenization limit of a parabolic equation with nonlinear boundary conditions
[ 講演概要 ]
We consider a quasilinear parabolic equation with the following nonlinear Neumann boundary condition:
"the slope of the solution on the boundary is a function $g$ of the value of the solution". Here $g$ takes values near its supremum with the frequency of $\\epsilon$. We show that the homogenization limit of the solution, as $\\epsilon$ tends to 0, is the solution satisfying the linear Neumann boundary condition: "the slope of the solution on the boundary is the supremum of $g$".

GCOEセミナー

10:10-11:00   数理科学研究科棟(駒場) 122号室

GCOEセミナー

11:00-11:50   数理科学研究科棟(駒場) 122号室

GCOEセミナー

13:20-14:10   数理科学研究科棟(駒場) 122号室

GCOEセミナー

14:10-14:40   数理科学研究科棟(駒場) 122号室

GCOEセミナー

14:50-15:40   数理科学研究科棟(駒場) 122号室
O. Iliev 氏 (フラウンホーファー産業数学研究所、ドイツ)
Flow and material simulation for industrial purposes

2010年02月17日(水)

GCOEレクチャーズ

10:30-16:00   数理科学研究科棟(駒場) 126号室
Yves Benoist 氏 (Paris Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces I
[ 講演概要 ]
In this course I will focus on recent advances
on our understanding of discrete subgroups of Lie groups.

I will first survey how ideas from semisimple algebraic groups,
ergodic theory and representation theory help us to understand properties of these discrete subgroups.

I will then focus on a joint work with Jean-Francois Quint
studying the dynamics of these discrete subgroups on finite volume homogeneous spaces and proving the following result:

We fix two integral matrices A and B of size d, of determinant 1,
and such that no finite union of vector subspaces is invariant by A and B.
We fix also an irrational point on the d-dimensional torus. We will then prove that for n large the set of images of this point by the words in A and B of length at most n becomes equidistributed in the torus.
Yves Benoist 氏 (Paris Sud) 15:00-16:00
Discrete groups acting on homogeneous spaces II

統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/14.html

2010年02月16日(火)

トポロジー火曜セミナー

17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: 17:00 - 17:30 コモンルーム
Dieter Kotschick 氏 (Univ. M\"unchen)
Characteristic numbers of algebraic varieties
[ 講演概要 ]
The Chern numbers of n-dimensional smooth projective varieties span a vector space whose dimension is the number of partitions of n. This vector space has many natural subspaces, some of which are quite small, for example the subspace spanned by Hirzebruch--Todd numbers, the subspace of topologically invariant combinations of Chern numbers, the subspace determined by the Hodge numbers, and the subspace of Chern numbers that can be bounded in terms of Betti numbers. I shall explain the relation between these subspaces, and characterize them in several ways. This leads in particular to the solution of a long-standing open problem originally formulated by Hirzebruch in the 1950s.

2010年02月05日(金)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 118号室

ヤコビ和量指標の暴分岐部分の初等的な計算 (JAPANESE)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 118号室

Swan導手と特性サイクルの比較について (JAPANESE)

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 118号室

The structures of generalized principal series representations of SL(3,R) and related Whittaker functions (SL(3,R)の一般主系列表現の構造と関連するWhittaker関数)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室

PRINCIPAL SERIES AND GENERALIZED PRINCIPAL SERIES WHITTAKER FUNCTIONS WITH PERIPHERAL K-TYPES ON THE REAL SYMPLECTIC GROUP OF RANK 2 (実二次シンプレクティック群上の主系列表現及び一般主系列表現の周辺的K-TYPEを持つWHITTAKER 関数)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 122号室

On the generalized suspension theorem for directed Fukaya categories (有向深谷圏の懸垂定理の一般化について)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 122号室

On the Runge theorem for instantons (インスタントンに対するRungeの近似定理について)

博士論文発表会

11:00-12:15   数理科学研究科棟(駒場) 126号室

Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)

博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 126号室

Weak Amenability for a Group Acting on a Finite Dimensional CAT(0) Cube Complex (有限次元CAT(0)方体複体に作用する群の弱従順性)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室

Stone-Čech boundaries of discrete groups and measure equivalence theory (離散群のストーン-チェック境界と測度同値理論)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 128号室

CONSTRUCTION OF ISOTROPIC CELLULAR AUTOMATON AND ITS APPLICATION (等方セル・オートマトンの構成とその応用)