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Seminar information archive
Seminar information archive ～07/02｜Today's seminar 07/03 | Future seminars 07/04～
Seminar on Probability and Statistics
14:00-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Alexandre Brouste (Université du Maine)
Statistical inference in the partial observation setting, in continuous time
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html
Alexandre Brouste (Université du Maine)
Statistical inference in the partial observation setting, in continuous time
[ Abstract ]
In various fields, the {\\it signal} process, whose law depends on an unknown parameter $ artheta \\in \\Theta \\subset \\R^p$, can not be observed directly but only through an {\\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\\left( Y_t, t \\geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \\label{mod:modelgeneral} Y_t = Y_0 + \\int_0^t h(X_s, artheta) ds + \\sigma W^H_t\\,, \\quad t > 0 \\end{equation} where the function $ h: \\, \\R imes \\Theta \\longrightarrow \\R$ and the constant $\\sigma>0$ are known and the noise $\\left( W^H_t\\,, t\\geq 0 ight)$ is a fractional Brownian motion valued in $\\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $ artheta \\in \\Theta$ given the observation of the continuous sample path $Y^T=\\left( Y_t , 0 \\leq t \\leq T ight)$, $T>0$, naturally arises.
[ Reference URL ]In various fields, the {\\it signal} process, whose law depends on an unknown parameter $ artheta \\in \\Theta \\subset \\R^p$, can not be observed directly but only through an {\\it observation} process. We will talk about the so called fractional partial observation setting, where the observation process $Y=\\left( Y_t, t \\geq 0 ight)$ is given by a stochastic differential equation: egin{equation} \\label{mod:modelgeneral} Y_t = Y_0 + \\int_0^t h(X_s, artheta) ds + \\sigma W^H_t\\,, \\quad t > 0 \\end{equation} where the function $ h: \\, \\R imes \\Theta \\longrightarrow \\R$ and the constant $\\sigma>0$ are known and the noise $\\left( W^H_t\\,, t\\geq 0 ight)$ is a fractional Brownian motion valued in $\\R$ independent of the signal process $X$ and the initial condition $Y_0$. In this setting, the estimation of the unknown parameter $ artheta \\in \\Theta$ given the observation of the continuous sample path $Y^T=\\left( Y_t , 0 \\leq t \\leq T ight)$, $T>0$, naturally arises.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html
2010/03/12
Colloquium
15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
岡本和夫 (東京大学大学院数理科学研究科) 15:00-16:00
ガルニエ系の数理
特性類と不変量を巡る旅
岡本和夫 (東京大学大学院数理科学研究科) 15:00-16:00
ガルニエ系の数理
[ Abstract ]
ガルニエ系は,パンルヴェ方程式の拡張であり,完全積分可能な多時間ハミルトン系として与えられる。これは2階線型常微分方程式のホロノミック変形を与える非線型完全積分可能な偏微分方程式系であり,講演の対象である2次元系では,8つのタイプの基本形がある。ガルニエ系の研究は,初期値空間やソリトン方程式系の相似簡約などの立場から行われているが,材料が揃ってくれば,一般リーマン・ヒルベルト対応を経由して考察することが自然であるし,数学的であるだろう。パンルヴェ方程式の場合もそのような方向に進んでいる。一方,パンルヴェ方程式については,そのハミルトニアンの満足する非線型常微分方程式が,アフィンワイル群の対称性など数学的な材料を与える上で一定の役割を果たした。ガルニエ系についても,そのハミルトニアンについての非線型偏微分方程式系を具体的に書き下すことは,意味のあることと信じているが,未完である。この話題について,部分的な結果を紹介する。
森田茂之 (東京大学大学院数理科学研究科) 16:30-17:30ガルニエ系は,パンルヴェ方程式の拡張であり,完全積分可能な多時間ハミルトン系として与えられる。これは2階線型常微分方程式のホロノミック変形を与える非線型完全積分可能な偏微分方程式系であり,講演の対象である2次元系では,8つのタイプの基本形がある。ガルニエ系の研究は,初期値空間やソリトン方程式系の相似簡約などの立場から行われているが,材料が揃ってくれば,一般リーマン・ヒルベルト対応を経由して考察することが自然であるし,数学的であるだろう。パンルヴェ方程式の場合もそのような方向に進んでいる。一方,パンルヴェ方程式については,そのハミルトニアンの満足する非線型常微分方程式が,アフィンワイル群の対称性など数学的な材料を与える上で一定の役割を果たした。ガルニエ系についても,そのハミルトニアンについての非線型偏微分方程式系を具体的に書き下すことは,意味のあることと信じているが,未完である。この話題について,部分的な結果を紹介する。
特性類と不変量を巡る旅
[ Abstract ]
40年近くの間,さまざまな幾何構造に関する特性類と不変量の研究を続けてきた.葉層構造やリーマン面のモジュライ空間の特性類,そして3次元多様体の位相不変量等である.これらについて振り返りつつ,これからの目標をいくつかの予想を交えてお話ししたい.
40年近くの間,さまざまな幾何構造に関する特性類と不変量の研究を続けてきた.葉層構造やリーマン面のモジュライ空間の特性類,そして3次元多様体の位相不変量等である.これらについて振り返りつつ,これからの目標をいくつかの予想を交えてお話ししたい.
2010/03/09
PDE Real Analysis Seminar
10:30-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Joachim Escher (Leibniz University of Hanover)
Shallow water waves with singularities
Joachim Escher (Leibniz University of Hanover)
Shallow water waves with singularities
[ Abstract ]
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.
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.
2010/02/24
Lectures
15:00-16:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Robert Penner (Aarhus University / University of Southern California)
Protein Moduli Space
Robert Penner (Aarhus University / University of Southern California)
Protein Moduli Space
[ Abstract ]
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.
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.
2010/02/23
Lectures
14:00-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Bendong LOU (同済大学)
Homogenization Limit and Singular Limit of the Allen-Cahn equation
Bendong LOU (同済大学)
Homogenization Limit and Singular Limit of the Allen-Cahn equation
[ Abstract ]
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.
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.
2010/02/19
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (Orsay)
Discrete groups acting on homogeneous spaces V
Yves Benoist (Orsay)
Discrete groups acting on homogeneous spaces V
[ Abstract ]
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.
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.
2010/02/18
GCOE lecture series
10:30-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
Discrete groups acting on homogeneous spaces IV
Yves Benoist (Pars Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces III
[ Abstract ]
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 (Paris Sud) 15:00-16:00In 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.
Discrete groups acting on homogeneous spaces IV
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Roberto Longo (University of Rome, Tor Vergata)
Von Neumann Algebras and Boundary Quantum Field Theory
Roberto Longo (University of Rome, Tor Vergata)
Von Neumann Algebras and Boundary Quantum Field Theory
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Bendong LOU (同済大学)
Homogenization limit of a parabolic equation with nonlinear boundary conditions
Bendong LOU (同済大学)
Homogenization limit of a parabolic equation with nonlinear boundary conditions
[ Abstract ]
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 $g$".
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 Seminars
10:10-11:00 Room #122 (Graduate School of Math. Sci. Bldg.)
俣野 博 (数理科学)
空間的に非一様な場における進行波
俣野 博 (数理科学)
空間的に非一様な場における進行波
GCOE Seminars
11:00-11:50 Room #122 (Graduate School of Math. Sci. Bldg.)
野口 潤次郎 (数理科学)
岡の連接定理から一致の定理(点分布から分かるもの)まで
野口 潤次郎 (数理科学)
岡の連接定理から一致の定理(点分布から分かるもの)まで
GCOE Seminars
13:20-14:10 Room #122 (Graduate School of Math. Sci. Bldg.)
儀我 美一、大塚 岳 (数理科学、明治大学先端数理科学インスティチュート)
結晶界面の成長と偏微分方程式
儀我 美一、大塚 岳 (数理科学、明治大学先端数理科学インスティチュート)
結晶界面の成長と偏微分方程式
GCOE Seminars
14:10-14:40 Room #122 (Graduate School of Math. Sci. Bldg.)
古場 一 (数理科学)
成層の影響を考えたエクマン層の安定性について
古場 一 (数理科学)
成層の影響を考えたエクマン層の安定性について
GCOE Seminars
14:50-15:40 Room #122 (Graduate School of Math. Sci. Bldg.)
O. Iliev (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
O. Iliev (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
2010/02/17
GCOE lecture series
10:30-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yves Benoist (Paris Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces I
Discrete groups acting on homogeneous spaces II
Yves Benoist (Paris Sud) 10:30-11:30
Discrete groups acting on homogeneous spaces I
[ Abstract ]
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 (Paris Sud) 15:00-16:00In 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.
Discrete groups acting on homogeneous spaces II
Seminar on Probability and Statistics
15:00-16:10 Room #128 (Graduate School of Math. Sci. Bldg.)
清 智也 (東京大学 情報理工学系研究科)
勾配写像で表される球面上の確率分布族
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/14.html
清 智也 (東京大学 情報理工学系研究科)
勾配写像で表される球面上の確率分布族
[ Abstract ]
球面上の確率分布族は、方向統計学において重要である。本講演では、コスト凸関数 (c-凸関数)と呼ばれる関数とその勾配写像を用いて、球面上の分布族を構成する。 コスト凸関数とは、最適輸送理論の分野で導入された概念であり、ユークリッド空間 における凸関数をリーマン多様体の場合へ拡張させたものである。提案する分布族の 性質をいくつか示し、簡単な方向データの解析例を示す。
[ Reference URL ]球面上の確率分布族は、方向統計学において重要である。本講演では、コスト凸関数 (c-凸関数)と呼ばれる関数とその勾配写像を用いて、球面上の分布族を構成する。 コスト凸関数とは、最適輸送理論の分野で導入された概念であり、ユークリッド空間 における凸関数をリーマン多様体の場合へ拡張させたものである。提案する分布族の 性質をいくつか示し、簡単な方向データの解析例を示す。
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/14.html
2010/02/16
Tuesday Seminar on Topology
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Dieter Kotschick (Univ. M\"unchen)
Characteristic numbers of algebraic varieties
Dieter Kotschick (Univ. M\"unchen)
Characteristic numbers of algebraic varieties
[ Abstract ]
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.
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.
2010/02/05
thesis presentations
09:45-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Takahiro Tsushima (University of Tokyo)
Elementary computation of ramified components of Jacobi sum Hecke characters (JAPANESE)
Takahiro Tsushima (University of Tokyo)
Elementary computation of ramified components of Jacobi sum Hecke characters (JAPANESE)
thesis presentations
11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Abe (University of Tokyo)
Comparison between Swan conductors and characteristic cycles (JAPANESE)
Tomoyuki Abe (University of Tokyo)
Comparison between Swan conductors and characteristic cycles (JAPANESE)
thesis presentations
13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
宮﨑 直 (東京大学大学院数理科学研究科)
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)
宮﨑 直 (東京大学大学院数理科学研究科)
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)
thesis presentations
14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)
長谷川 泰子 (東京大学大学院数理科学研究科)
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)
長谷川 泰子 (東京大学大学院数理科学研究科)
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)
thesis presentations
09:45-11:00 Room #122 (Graduate School of Math. Sci. Bldg.)
二木 昌宏 (東京大学大学院数理科学研究科)
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)
二木 昌宏 (東京大学大学院数理科学研究科)
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)
thesis presentations
11:00-12:15 Room #122 (Graduate School of Math. Sci. Bldg.)
松尾 信一郎 (東京大学大学院数理科学研究科)
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)
松尾 信一郎 (東京大学大学院数理科学研究科)
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)
thesis presentations
11:00-12:15 Room #126 (Graduate School of Math. Sci. Bldg.)
西岡 斉治 (東京大学大学院数理科学研究科)
Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)
西岡 斉治 (東京大学大学院数理科学研究科)
Solvability and irreducibility of difference equations (差分方程式の可解性と既約性)
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
水田 有一 (東京大学大学院数理科学研究科)
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)
水田 有一 (東京大学大学院数理科学研究科)
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)
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