## Seminar information archive

### 2006/07/20

#### Operator Algebra Seminars

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)

Linear response theory in quantum statistical mechanics

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Guster Olafsson (Louisiana State University)
The Heat equation, the Segal-Bargmann transform and generalizations - I
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2006/07/19

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

Edgeworth Expansion for Likelihood Analysis on Ergodic Diffusions with applications to Bootstrap
[ Abstract ]
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.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/06.html

### 2006/07/13

#### Operator Algebra Seminars

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)

Property (T) for universal lattices, after Y. Shalom
[ Abstract ]
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.

### 2006/07/12

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Beilinson-Drinfeld chiral algebra, geometric Langlands program and open Gromov-Witten invariants
[ Abstract ]

#### Mathematical Finance

18:30-20:00   Room #118 (Graduate School of Math. Sci. Bldg.)

A complete-market generalization of the Black-Scholes model

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Piotr Rybka (Warsaw University)
Analysis of a crystal growth model
[ Abstract ]
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''.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

### 2006/07/11

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
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。
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

On the isomorphism problem of Coxeter groups and related topics
[ Abstract ]
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。
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2006/07/10

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Do Duc Thai (Hanoi教育大)
Characterization of domains in $C^n$ by their noncompact automorphism groups
[ Abstract ]
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 $C^n$.

### 2006/07/08

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-15:45   Room #123 (Graduate School of Math. Sci. Bldg.)

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

On Dirichlet series counting cubic alegebras

### 2006/07/07

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

### 2006/07/06

#### Seminar for Mathematical Past of Asia

17:00-18:30   Room #123 (Graduate School of Math. Sci. Bldg.)

ユークリッドをめぐる最新の研究動向
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html

#### Operator Algebra Seminars

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)
Rolf Dyre Svegstrup (東大数理)
Endomorphisms of half-sided modular inclusions

### 2006/07/05

#### Seminar on Mathematics for various disciplines

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Y. H. Richard Tsai (University of Texas)
Level Set Methods and Multi-valued solutions
[ Abstract ]
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.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/07/04

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Alexander A. Ivanov (Imperial College (London))
Amalgams: a machinery of the modern theory of finite groups
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/

### 2006/07/03

#### Seminar on Geometric Complex Analysis

14:00-15:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Jörg Winkelmann (Université Henri Poincaré Nancy)
Complex Semi-Abelian Varieties II --- Compactifications and etc.

### 2006/06/28

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Configuration of the central streams in the moduli of abelian varieties

#### Mathematical Finance

17:30-19:00   Room #118 (Graduate School of Math. Sci. Bldg.)

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Jian Zhai (Zhejiang University)
Uniqueness of Constant Anisotropic Mean Curvature Immersion of Sphere $S^2$ In $\\Bbb E^3$
[ Abstract ]
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.

### 2006/06/27

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Cedric Tarquini (Ecole Nomale Superieure of Lyon)
Lorentzian foliations on 3-manifolds
[ Abstract ]
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.

### 2006/06/26

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Toward construction of Green current for modular cycles in modular varieties

### 2006/06/23

#### Colloquium

17:00-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Robert Gompf (University of Texas at Austin)
25 years of exotic $\\mathbb{R}^4s$
[ Abstract ]
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.

### 2006/06/22

#### Operator Algebra Seminars

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)
Detlev Buchholz (Univ. Göttingen)
Integrable models and operator algebras
[ Abstract ]
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.

### 2006/06/21

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

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