## 過去の記録

### 2006年09月04日(月)

#### 数理ファイナンスセミナー

17:00-18:30   数理科学研究科棟(駒場) 117号室
9月4日～6日までの3日間の日程です。講演は英語で行われます。
Freddy Delbaen 氏 (ETH)
Dynamic Risk Measures and Backward Stochastic Differential Equation

#### 数理ファイナンスセミナー

15:45-16:45   数理科学研究科棟(駒場) 117号室
9月4日～6日の3日間の日程です。

リスク尺度入門及び概説

### 2006年08月25日(金)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 128号室
いつもと曜日・部屋ともに違います
A. Marmora 氏 (パリ北大・東大/学振)
p-adic local constants

### 2006年08月22日(火)

#### 統計数学セミナー

15:30-16:40   数理科学研究科棟(駒場) 128号室
Jeannette H.C. WOERNER 氏 (University of Gottingen)
A unifying approach to inference in semimartingale and long-memory models
[ 講演概要 ]
Over the recent years classical stochastic volatility models based on Brownian motion have been generalized in different ways, either replacing the Brownian motion by a pure jump Levy process, which leads to a pure jump model, or by a fractional Brownian motion, which makes it possible to model both long memory or turbulent behaviour. We consider robust and easily computable estimators for the inte- grated volatility, providing insight in the level of volatility, as needed for risk measurement and pricing of variance and volatility swaps. We discuss consistency and distributional results for the power and multi- power variation estimates based on high frequency data. Furthermore, we consider robustness against additive components and compare the results for the different classes of semimartingale and fractional Brow- nian motion models.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/07.html

#### 統計数学セミナー

16:50-18:00   数理科学研究科棟(駒場) 128号室
Delphine DAVID 氏 (Departement de Mathematiques, Universite de La Rochelle)
A computation of Theta in a jump diffusion model by integration by parts
[ 講演概要 ]
Using Malliavin weights in a jump-diffusion model we obtain an expression for Theta (the sensitivity of an option price with respect to the time remaining until exercise), with application to non-smooth payoff functions. Optimal weights are computed by minimization of variance and numerical simulations are presented for digital and European options. Some results are also presented for Asian options. Our representation formula for Theta differs in general from the one obtained from the Black-Scholes PDE in terms of Delta and Gamma.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/08.html

### 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

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

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

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

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

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

#### 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''.
[ 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

[ 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。
[ 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

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

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
[ 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/