過去の記録

過去の記録 ~08/18本日 08/19 | 今後の予定 08/20~

2006年08月03日(木)

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
George Elliott 氏 (University of Toronto)
The Cuntz semigroup as an invariant for $C^*$-algebras

2006年07月31日(月)

Lie群論・表現論セミナー

15:00-17:30   数理科学研究科棟(駒場) 126号室
Guster Olafsson 氏 (Louisiana State University) 15:00-16:00
The Heat equation, the Segal-Bargmann transform and generalizations - II
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html
Boris Rubin 氏 (Louisiana State University) 16:30-17:30
Radon transforms on Grassmannians and Matrix Spaces
[ 講演概要 ]
Diverse geometric problems in $R^N$ get a new flavor if a generic point $x=(x_1,...,x_N)$ is regarded as a matrix with appropriately organized entries (set, e.g., $x=(x_{i,j})_{n \\times m}$ for $N=nm$). This well known observation has led to a series of breakthrough achievements in mathematics. In integral geometry it suggests a number of the so-called ``higher-rank" problems when such traditional scalar notions as ``distance", ``angle", and ``scaling" become matrix-valued. I will be speaking about Radon transforms on Grassmann manifolds and matrix spaces and some related problems of harmonic analysis where these phenomena come into play.
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

2006年07月25日(火)

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
Boris Rubin 氏 (Louisiana State University)
Radon Transforms: Basic Concepts
[ 講演概要 ]
How can we reconstruct a function on a manifold from integrals of this function over certain submanifolds?
This is one of the central problems in integral geometry and tomography, which leads to the notion of the Radon transform.

The first talk is of introductory character.
We discuss basic ideas of the original Radon's paper (1917), then proceed to the Minkowski-Funk transform and more general totally geodesic Radon transforms on the $n$-dimensional unit sphere.
The main emphasis is an intimate connection of these transforms with the relevant harmonic analysis.
We will see that Radon transforms of this type and their inverses can be regarded as members of analytic families of suitable convolution operators and successfully studied in the framework of these families.

I also plan to discuss an open problem of small divisors on the unit sphere, which arises in studying injectivity of generalized Minkowski-Funk transforms for non-central spherical sections.
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

2006年07月24日(月)

トポロジー火曜セミナー

16:30-17:30   数理科学研究科棟(駒場) 056号室
曜日が異なります。ご注意下さい。
Boris Hasselblatt 氏 (Tufts University)
Invariant foliations in hyperbolic dynamics:
Smoothness and smooth equivalence
[ 講演概要 ]
The stable and unstable leaves of a hyperbolic dynamical system are smooth and form a continuous foliation. Smoothness of this foliation sometimes constrains the topological type of the foliation, other times restricts at least the smooth equivalence class of the dynamical system, or for geodesic flows, the type of the underlying manifold. I will present a broad introduction as well as recent work, work in progress, and open problems.
[ 講演参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/

2006年07月20日(木)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室
緒方芳子 氏 (東大数理・学振)
Linear response theory in quantum statistical mechanics

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
Guster Olafsson 氏 (Louisiana State University)
The Heat equation, the Segal-Bargmann transform and generalizations - I
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

2006年07月19日(水)

統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室
深澤 正彰 氏 (東京大学大学院数理科学研究科)
Edgeworth Expansion for Likelihood Analysis on Ergodic Diffusions with applications to Bootstrap
[ 講演概要 ]
We shall consider the maximal lilelihood estimator for the drift coefficient of a given one-dimensional diffusion. An Edgeworth expansion formula will be presented and verify a second-order correct confidence interval we shall newly propose. We are also going to mention the likelihood ratio statistic, which enjoys second-order correctness. There are Bootstrap methods closely related to the subject and introduced recently by the author. Some generalized results on those methods will be also introduced in this talk.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/06.html

2006年07月13日(木)

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室
小沢登高 氏 (東大数理)
Property (T) for universal lattices, after Y. Shalom
[ 講演概要 ]
I will talk on Shalom's recent result that
$SL_n(Z[X])$ ($n\\geq 3$) has the property (T).
The talk should be elementary.

2006年07月12日(水)

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
桜井 真 氏 (東京大学理学系研究科)
Beilinson-Drinfeld chiral algebra, geometric Langlands program and open Gromov-Witten invariants
[ 講演概要 ]
都合により、とりやめになりました。

数理ファイナンスセミナー

18:30-20:00   数理科学研究科棟(駒場) 118号室
高岡 浩一郎 氏 (一橋大)
A complete-market generalization of the Black-Scholes model

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Piotr Rybka 氏 (Warsaw University)
Analysis of a crystal growth model
[ 講演概要 ]
We are concerned with mathematical model of a single crystal growing from vapor. Mathematically this is an exterior, one-phase Stefan-type problem with Gibbs-Thomson law. We restrict our attention to an idealization of a ice crystal, i.e. our evolving free boundary is a circular cylinder. The system under consideration consists of an equation for the motion of the free boundary (the crystal surface) coupled to the quasi-steady approximation of the diffusion equation for the supersaturation of vapor. We present analysis of the system, we show well-posedness and draw the phase portrait, we use here the fact that we need just to variable to describe evolution of a cylinder.

We are mostly concerned with the shape-persitency problem of the
evolution. The problem is, the Gibbs-Thomson relation is in fact a
driven, weighted, mean, singular curvature flow and it is not obvious that the shape of the initial interface will persists throughout the evolution or even for some time. In order to solve this problem we show existence of the region in the phase plane which is a neighborhood of a unique steady state, such that in this region the shape of the cylinder is preserved. However, this set is not invariant with respect to dynamics of the problem.

It is a very interesting question what happens to surface of our crystal at the boundary of the shape-persitency (or shape stability) region. This problem in its full generality is open. However, we give some insight by studying the Gibbs-Thomson relation with a given driving, which inherits properties of the coupling to the diffusion field. We study the resulting driven weighted mean curvature flow for graphs and some special closed Lipschitz curves. We show well-posedness of the problem, but mainly we exhibit the phenomenon of bending flat parts of the curve, which grow ``too big''.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2006年07月11日(火)

トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
野田健夫 氏 (秋田大学工学資源学部)
全葉層の存在について(浅岡正幸,Emmanuel Dufraineとの共同研究)
[ 講演概要 ]
n次元多様体上のn個の余次元1葉層構造の組で、n個の葉層構造の接空間の共通部分が各点で0になるものを全葉層と呼ぶ。3次元の場合においては任意の有向閉多様体上に全葉層が存在することが Hardorpによって示されていた。3次元多様体上の全葉層をなす各々の葉層構造の接平面場は互いにホモトピックでありオイラー類が0になることが容易に分かるが、逆にオイラー類が0の平面場を与えたときそれを実現する全葉層が存在するかという問題が自然に生じる。
本講演ではこの問題に肯定的な解決をあたえる。
また、この結果の応用として双接触構造、すなわち横断的に交わる正と負の接触構造の組の存在問題にも触れたい。
[ 講演参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/

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
縫田 光司 氏 (産業技術総合研究所)
On the isomorphism problem of Coxeter groups and related topics
[ 講演概要 ]
コクセター群について、そのコクセター系としての同型類がコクセターグラフと一対一対応することは周知の事実であるが、一方で抽象群としての同型類は(ワイル群の場合に限っても)そのような対応をしていない。今回は、この同型類の決定問題について、その歴史のあらまし(特に、無限群も含めた一般の場合について、10年ほど前まで殆ど何の結果も得られていなかったことは特筆に価する)と、近年の研究の進展状況を、具体例や関連する結果を交えつつ紹介する。
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

2006年07月10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
Do Duc Thai 氏 (Hanoi教育大)
Characterization of domains in $C^n$ by their noncompact automorphism groups
[ 講演概要 ]
In this talk, the characterization of domains in $C^n$ by their noncompact automorphism groups are given. By this characterization, the Bedford-Pinchuk theorem is true for any domain (not necessary bounded) in $C^n$.

2006年07月08日(土)

保型形式の整数論月例セミナー

13:30-15:45   数理科学研究科棟(駒場) 123号室
伴 克馬 氏 (東京大学大学院数理科学研究科) 13:30-14:30
Rankin-Cohen-Ibukiyama operators for holomorphic automorphic forms on type I symmetric domains
谷口 隆 氏 (東京大学大学院数理科学研究科) 14:45-15:45
On Dirichlet series counting cubic alegebras

2006年07月07日(金)

談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:00~16:30(コモンルーム)
重定 南奈子 氏 (同志社大学)
周期的変動環境下における侵入生物の時空間パターンと伝播速度
[ 講演概要 ]
侵入生物の空間的な伝播に関する数理的研究は,Fisher (1937)の先駆的研究以来,外来植物や昆虫,伝染病などの侵入を中心に,主として一様な空間における拡散増殖モデルを用いて進められてきた.しかし,実際の自然環境は,森,林,河川,道路などの,生物にとって好適な環境と不適な環境がパッチ状に入り混じっており,決して一様な空間とはいえない.
本研究では、帯状の好適生息地と不適な生息地が交互に配列する2次元縞状 分断環境の中を、侵入生物が分布拡大する過程を拡散係数と増殖率が好適生息 地と不適生息地で異なる拡張Fisher modelを用いて記述し、それを heuristicな方法を用いて解くことにより,侵入種の分布拡大パターン,ならびに,伝播速度の数学公式を導いた.

2006年07月06日(木)

アジア数学史セミナー

17:00-18:30   数理科学研究科棟(駒場) 123号室
斎藤 憲 氏 (大阪府立大学 人間社会学部)
ユークリッドをめぐる最新の研究動向
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html

作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室
Rolf Dyre Svegstrup 氏 (東大数理)
Endomorphisms of half-sided modular inclusions

2006年07月05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
Y. H. Richard Tsai 氏 (University of Texas)
Level Set Methods and Multi-valued solutions
[ 講演概要 ]
We review the level set methods for computing multi-valued
solutions to a class of nonlinear first order partial differential
equations, including Hamilton-Jacobi equations, quasi-linear
hyperbolic equations, and conservative transport equations with
multi-valued transport speeds.
The multivalued solutions are embedded as the zeros of a set of scalar functions that solve the initial value problems of a time dependent partial differential equation in an augmented space.
We discuss the essential ideas behind the techniques, the coupling of these techniques to the projection of the interaction of zero level sets and a collection of applications including the omputation of the semiclassical limit for Schr\\"{o}dinger quations and the high frequency geometrical optics limits of linear wave equations.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年07月04日(火)

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
Alexander A. Ivanov 氏 (Imperial College (London))
Amalgams: a machinery of the modern theory of finite groups
[ 講演参考URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/

2006年07月03日(月)

複素解析幾何セミナー

14:00-15:30   数理科学研究科棟(駒場) 128号室
Jörg Winkelmann 氏 (Université Henri Poincaré Nancy)
Complex Semi-Abelian Varieties II --- Compactifications and etc.

2006年06月28日(水)

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
原下秀士 氏 (北海道大学・学振)
Configuration of the central streams in the moduli of abelian varieties

数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 118号室
楠岡 成雄 氏 (東京大)
転換社債の価格:均衡論的アプローチ

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Jian Zhai 氏 (Zhejiang University)
Uniqueness of Constant Anisotropic Mean Curvature Immersion of Sphere $S^2$ In $\\Bbb E^3$
[ 講演概要 ]
We prove that the constant anisotropic mean curvature immersion of sphere $S^2$ in $\\Bbb E^3$ is unique, provided that the energy density function $\\gamma$ satisfies some reasonable assumptions.

2006年06月27日(火)

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
Cedric Tarquini 氏 (Ecole Nomale Superieure of Lyon)
Lorentzian foliations on 3-manifolds
[ 講演概要 ]
a joint work with C. Boubel (Ecole Nomale Superieure of Lyon) and P. Mounoud (University of Bordeaux 1 sciences and technologies)

The aim of this work is to give a classification of transversely Lorentzian one dimensional foliations on compact manifolds of dimension three. There are the foliations which admit a transverse pseudo-Riemanniann metric of index one. It is the Lorentzian analogue of the better known Riemannian foliations and they still have rigid transverse geometry.

The Riemannian case was listed by Y. Carriere and we will see that the Lorentzian one is very different and much more complicated to classify. The difference comes form the fact that the completness of the transverse structure, which is automatic in the Riemannian case, is a very strong hypothesis for a transverse Lorentzian foliation.

We will give a classification of complete Lorentzian foliations and some examples which are not complete. As a natural corollary of this classification we will list the codimension one timelike geodesically complete totally geodesic foliations of Lorentzian compact three manifolds.

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