過去の記録

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

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''.
[ 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

[ 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。

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。
[ 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

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。
[ 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

Rankin-Cohen-Ibukiyama operators for holomorphic automorphic forms on type I symmetric domains

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)

[ 講演概要 ]

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

ユークリッドをめぐる最新の研究動向
[ 参考URL ]
https://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.
[ 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
[ 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

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

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.

2006年06月26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

Toward construction of Green current for modular cycles in modular varieties

2006年06月23日(金)

談話会・数理科学講演会

17:00-18:00   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:30～17:00(コモンルーム)
Robert Gompf 氏 (University of Texas at Austin)
25 years of exotic $\\mathbb{R}^4s$
[ 講演概要 ]
A quarter century ago, 4-manifold theory was revolutionized by the Fields-Medal winning breakthroughs of Freedman and Donaldson, with Freedman showing that topological 4-manifolds behave like their higher dimensional counterparts, but Donaldson showing that smooth 4-manifolds behave in a completely different way. The interplay between these theories produces results unique to dimension 4: A fixed topological 4-manifold often admits infinitely many distinct smooth structures, for which no classification scheme is yet available. The quintessential example is that in contrast with other dimensions, Euclidean 4-space admits exotic smooth structures. That is, there are "exotic R^4s" homeomorphic to R4 but not diffeomorphic to it. We will survey what has been learned about these strange creatures in the last quarter century, and exhibit an explicit example.

2006年06月22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
Detlev Buchholz 氏 (Univ. Göttingen)
Integrable models and operator algebras
[ 講演概要 ]
Recently, it has been possible to establish rigorously the existence of an abundance of 1+1-dimensional local nets of von Neumann algebras describing an interacting massive particle with factorizing scattering matrix. This novel approach is based on structural results in algebraic quantum field theory concerning the modular structure of such theories. It is thus complementary to the older methods of constructive quantum field theory and settles some longstanding questions in the context of integrable models (form-factor program). In this talk, a survey is given on basic ideas, results and perspectives of this promising new approach.

2006年06月21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

Malliavin calculus applied to mathematical finance and a new formulation of the intgration-by-parts
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/05.html

2006年06月19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

Deformations and smoothing of (generalized) holomorphic symplectic structures

2006年06月15日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 056号室
6月15日は,集中講義と重なるため,開始時間を遅らせます.
Mark Bowen 氏 (東京大学大学院数理科学研究科/日本学術振興会)
Spreading and draining in thin fluid films
[ 講演概要 ]
The surface tension driven flow of a thin fluid film arises in a number of contexts. In this talk, we will begin with an overview of thin film theory and present a number of examples from the natural sciences and industrial process engineering. Similarity solutions play an important role in understanding the dynamics of general thin film motion and we shall use them to investigate the dynamics of an archetypal (degenerate high-order parabolic) thin film equation. In this context, we will encounter self-similarity of the first and second kind, undertake an investigation of a four-dimensional phase space and discover a surprisingly rich set of stable sign-changing solutions for the intermediate asymptotics of a generalised problem.

2006年06月14日(水)

PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Qing-Ming Cheng 氏 (Saga University)
Bounds on eigenvalues of Dirichlet aplacian
[ 講演概要 ]
In this talk, I shall consider the eigenvalue problem of the Dirichlet Laplacian. I shall mention the Weyl asymptotic formula,
Polya conjecture and its partial solution. Furthermore, I shall talk about Bochner-Kac problem.
For universal inequalities for eigenvalues, I shall consider
conjectures of Payne, Polya and Weinberger and their development. In the final, I shall talk the universal bounds for eigenvalues as main part of my talk, which is my recent joint work with rofessor Yang.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

2006年06月13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

A note on C1-moves
[ 講演概要 ]

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

[ 講演概要 ]

(1) 各λに対する $M_Θ(λ)$ の最小多項式の明示公式
(2) $M_Θ(λ)= M(λ)/I_Θ(λ)M(λ)$ が成り立つためのλの 必要十分条件

が得られた(これらは大島により g = gln の場合には既に得られている).セミナーでは(2)を示すための q(F) の各成分の Harish-Chandra 準同型像の計算法を主に説明する.