過去の記録

過去の記録 ~08/17本日 08/18 | 今後の予定 08/19~

2010年03月19日(金)

講演会

11:00-12:00   数理科学研究科棟(駒場) 366号室
竹内 知哉 氏 (North Carolina State University, USA)
A Regularization Parameter for Nonsmooth Tikhonov Regularization
[ 講演概要 ]
We develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are also studied. Numerical results for several common nonsmooth functionals are presented.

2010年03月17日(水)

講演会

16:30-17:30   数理科学研究科棟(駒場) 128号室
三角 淳 氏 (東大数理)
方向依存性を持つ長距離パーコレーションの臨界曲線

2010年03月15日(月)

統計数学セミナー

15:00-16:00   数理科学研究科棟(駒場) 002号室
Cecilia Mancini 氏 (University of Florence)
BROWNIAN COVARIATION AND CO-JUMPS, GIVEN DISCRETE OBSERVATION
[ 講演概要 ]
We consider two processes driven by Brownian motions plus drift and possibly infinite activity jumps.

Given discrete observations we separately estimate the covariation between the two Brownian parts and the sum of the co-jumps. This allows to gain insight into the dependence structure of the processes and has important applications in finance.

Our estimator is based on a threshold principle allowing to isolate the jumps over a threshold.

The estimator of the continuous covariation is asymptotically Gaussian and converges at speed square root of n when the jump components have finite variation. In presence infinite variation jumps the speed is heavily influenced both by the small jumps dependence structure and by their jump activity indexes.

This talk is based on Mancini and Gobbi (2009), and Mancini (2010).
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/16.html

統計数学セミナー

14:00-15:00   数理科学研究科棟(駒場) 002号室
Alexandre Brouste 氏 (Université du Maine)
Statistical inference in the partial observation setting, in continuous time
[ 講演概要 ]
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.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/15.html

2010年03月12日(金)

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 (コモンルーム)
岡本和夫 氏 (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
[ 講演概要 ]
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 氏 (東京大学大学院数理科学研究科) 16:30-17:30
特性類と不変量を巡る旅
[ 講演概要 ]
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
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
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
俣野 博 氏 (数理科学)
空間的に非一様な場における進行波

GCOEセミナー

11:00-11:50   数理科学研究科棟(駒場) 122号室
野口 潤次郎 氏 (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セミナー

13:20-14:10   数理科学研究科棟(駒場) 122号室
儀我 美一、大塚 岳 氏 (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セミナー

14:10-14:40   数理科学研究科棟(駒場) 122号室
古場 一 氏 (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
清 智也 氏 (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
[ 講演概要 ]
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。
[ 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
津嶋 貴弘 氏 (東京大学大学院数理科学研究科)
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
阿部 知行 氏 (東京大学大学院数理科学研究科)
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
宮﨑 直 氏 (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)

博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室
長谷川 泰子 氏 (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)

博士論文発表会

09:45-11:00   数理科学研究科棟(駒場) 122号室
二木 昌宏 氏 (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)

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