過去の記録

過去の記録 ~02/17本日 02/18 | 今後の予定 02/19~

2006年10月10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
Elmar Vogt 氏 (Frie Universitat Berlin)
Estimating Lusternik-Schnirelmann Category for Foliations:A Survey of Available Techniques
[ 講演概要 ]
The Lusternik-Schnirelmann category of a space $X$ is the smallest number $r$ such that $X$ can be covered by $r + 1$ open sets which are contractible in $X$.For foliated manifolds there are several notions generalizing this concept, all of them due
to Helen Colman. We are mostly concerned with the concept of tangential Lusternik-Schnirelmann category (tangential LS-category). Here one requires a covering by open sets $U$ with the following property. There is a leafwise homotopy starting with the inclusion of $U$ and ending in a map that throws for each leaf $F$ of the foliation each component of $U \\cap F$ onto a single point. A leafwise homotopy is a homotopy moving points only inside leaves. Rather than presenting the still very few results obtained about the LS category of foliations, we survey techniques, mostly quite elementary, to estimate the tangential LS-category from below and above.

2006年10月06日(金)

数理人口学・数理生物学セミナー

16:30-17:30   数理科学研究科棟(駒場) 123号室
石井 太 氏 (国立社会保障・人口問題研究所)
人口指標の精度について
[ 講演概要 ]
近年の急速な少子化の進行に伴い、出生率の動向への関心が高まっている。しかしながら、その指標が注目され、様々に論じられる中に、指標の持つ精度を度外視した議論なども見受けられる。人口統計は人口分析の中心となるデータソースであり、人口指標の精度は重要な問題であるが、わが国においてはこれまで比較的精度の高い人口統計が取得されてきたこともあり、それほど重視せず、確定的なものと捉えがちな傾向があったように思われる。一方では、近年、統計調査環境の悪化などもあり、各々の人口指標についてどこまで詳細な議論が可能なのか、指標の精度について理論的・実務的な観点からより深い認識を持つことが必要となってきている。
本報告では、出生率での具体例を中心に、さまざまな誤差の発生要因に応じた人口指標の評価について提示することとしたい。

2006年10月05日(木)

諸分野のための数学研究会

16:30-17:30   数理科学研究科棟(駒場) 123号室
成田誠 氏 (Department of Mathematics, National Taiwan University)
Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field
[ 講演概要 ]
We study global properties of Gowdy symmetric (the existence of a symmetry group with two-dimensional spacelike orbits) spacetimes with nonlinear scalar field, which naturally arises in modern cosmology based on superstring theory.
The system of the Einstein and scalar field equations becomes a system consisting of wave map and nonlinear wave equations in one space dimension. We prove a global existence theorem for this system. Also, asymptotic energy decay will be discussed.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年09月27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
Professor Vakhtang Kokilashvili 氏 (A. Razmadze Mathematical Institute, Georgian Academy of Science)
Integral operators in the weighted Lebesgue spaces with a variable exponent
[ 講演概要 ]
We present a boundedness criteria of the maximal functions and the singular integral operators defined on Carleson curves in the weighted Lebesgue spaces with a variable exponent. There are also given the weighted estimates for the generalized singular integrals raised in the theory of generalized analytic functions of I.N.Vekua and the weighted Sobolev theorems for potentials on Carleson curves. The weight functions may be of power function type as well as oscillating type. The certain version of a Muckenhoupt-type condition for a variable exponent will be considered.

We also expect to treat two-weight problems for the classical integral operators in the variable Lebesgue spaces and to give some applications of the obtained results to the summability problems of Fourier series in two-weighted setting.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html

数理人口学・数理生物学セミナー

16:30-17:30   数理科学研究科棟(駒場) 123号室
中丸麻由子 氏 (東京工業大学)
The coevolution of altruism and punishment:role of the selfish punisher
[ 講演概要 ]
Punishment is an important mechanism promoting the evolution of altruism among nonrelatives. We investigate the coevolution of altruism and punitive behavior, considering four strategies: a cooperator who punishes defectors (AP), a pure cooperator (AN), a defector who punishes defectors (selfish punisher or SP), and a pure defector (SN). We especially focus on the effects of SP on the coevolution of altruism and punishment, studying both the score-dependent viability model (whereby the game's score affects survivorship only) and the score-dependent fertility model (whereby the score affects fertility only). In the viability model of a completely mixed population, SP helps cooperators to evolve, but SP does not in the fertility model. In both models of a lattice-structured population, SP promotes the spread of AP, but AN discourages it. These results indicate that punishment is a form of spite behavior and that different models give different magnitude of advantage to spite behavior.

2006年09月25日(月)

統計数学セミナー

13:00-14:10   数理科学研究科棟(駒場) 128号室
西山 陽一 氏 (統計数理研究所)
Nonparametric testing time-homogeneity for L'evy processes
[ 講演概要 ]
First, a review about uniform central limit theorems for martingales is given. The main part of the talk is concerned with a change point problem for L'evy processes. The null hypothesis is that the L'evy process is time-homogeneous, and the alternative is that the L'evy measure changes at a certain time point of the observation period. We propose an empirical process type statistics, and derive its asymptotic behaviour under the null and the alternative hypotheses. The limiting distribution under the null hypothesis is a functional of the standard Brownian motion.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/09.html

2006年09月13日(水)

関数解析セミナー

13:00-16:45   数理科学研究科棟(駒場) 123号室
Nicolas Burq氏は9月7日から13日まで、Andre Martinez氏とVania Sordoni氏は、9月11日から22日まで、東京大学数理科学研究科に滞在の予定です。
Andre' Martinez 氏 (Bologna University) 13:00-14:00
On the determination of non-analytic resonances
(joint work with T.Ramond and J. Sjostrand)
Nicolas Burq 氏 (Université de Paris Sud) 14:15-15:15
Global existence for energy critical waves in 3-d domains
(joint work with G. Lebeau and F. Planchon)
[ 講演概要 ]
I will present some recent results obtained recently with G. Lebeau and F. Planchon. We prove that the energy critical (quintic) non linear wave equation in 3-d domains with Dirichlet boundary conditions is globally well posed for any initial data (with finite energy). I will give some hints about the proof of this result which is based on some recent results by Smith and Sogge on $L^p$ estimates for spectral projectors and a carefull study of the boundary value problem.
Vania Sordoni 氏 (Bologna University) 15:45-16:45
On the Born-Oppenheimer approximation of wave-operators

2006年09月11日(月)

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
Claude-Alain Pillet 氏 (Univ. de Toulon et du Var)
Operator-algebraic techniques in nonequilibrium statistical mechanics

2006年09月06日(水)

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
代数幾何セミナーと共催です
Bas Edixhoven 氏 (Univ. of Leiden)
Computation of the mod l Galois representations associated to Delta

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。
楠岡成雄氏・梅澤祐二 氏 (東京大)
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
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

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