過去の記録

過去の記録 ~05/25本日 05/26 | 今後の予定 05/27~

統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室
Stefano Maria Iacus 氏 (Universita degli Studi di Milano, Italy)
Divergences Test Statistics for Discretely Observed Diffusion Processes
[ 講演概要 ]
In this paper we propose the use of $\\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process dXt = b(Xt, theta)dt + sigma(Xt, theta) dWt, from discrete observations at times ti = i*Dn, i=0, 1, ..., n, under the asymptotic scheme Dn - 0, n*Dn - +oo and n*Dn^2 - 0. The class of phi-divergences is wide and includes several special members like Kullback-Leibler, Renyi, power and alpha-divergences. We derive the asymptotic distribution of the test statistics based on phi- divergences. The limiting law takes different forms depending on the regularity of phi. These convergence differ from the classical results for independent and identically distributed random variables. Numerical analysis is used to show the small sample properties of the test statistics in terms of estimated level and power of the test.

joint work with A. De Gregorio
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/10.html

統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 002号室
Nicolas Privault 氏 (City University of Hong Kong)
Stein estimation of Poisson process intensities
[ 講演概要 ]
In this talk we will construct superefficient estimators of Stein type for the intensity parameter lambda > 0 of a Poisson process, using integration by parts and superharmonic functionals on the Poisson space.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/11.html

2008年12月12日(金)

GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 128号室
吉野 伸 氏 (東京電力)
ガスタービン翼の伝熱について

2008年12月11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
佐藤康彦 氏 (北大理)
Certain aperiodic automorphisms of unital simple projectionless $C^*$-algebras

2008年12月10日(水)

東京幾何セミナー

14:45-18:00   数理科学研究科棟(駒場) 122号室
場所は東大数理(駒場)、東京工業大学(大岡山)のいずれかで行います。
詳細については、上記セミナーURLよりご確認下さい。
「今後の予定」欄には、東工大で行われるセミナーは表��

吉田 尚彦 氏 (明治大学大学院理工学研究科) 14:45-16:15
Acyclic polarizations and localization of Riemann-Roch numbers
[ 講演概要 ]
前量子化可能な閉シンプレクティック多様体が(特異)Lagrange ファイバー空間の構造を持つ場合,Riemann-Roch 数が Bohr-Sommerfeld ファイバーの個数と一致することがトーリック多様体,ユニタリー群の Gelfand-Cetlin 系や Riemann 面上の平坦 SU(2) 束のモジュライなどの例で,双方を別々に計算し比較することにより,確かめられている.本講演では,spin^c Dirac 作用素の指数に対する Witten 流の局所化を用いることによって,Riemann-Roch 数が非特異 Bohr-Sommerfeld ファイバー及び特異ファイバーに局所化することを示す.(古田幹雄氏(東大数理),藤田玄氏(学習院大学)との共同研究.論文:arXiv:0804.3258)
Megumi Harada 氏 (McMaster University) 16:30-18:00
The topology of symplectic and hyperkahler quotients
[ 講演概要 ]
Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a Hamiltonian G-action for a Lie group G, i.e. an action with an associated moment map -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as Hamiltonian quotients. In the first part of the talk, I will give a bird's-eye, motivating overview of this subject, and in particular will introduce one of the main technical tools of the field, which is the Morse theory associated to the moment map. In the second part, I will give a more detailed account of recent joint work with Graeme Wilkin, which deals with Nakajima quiver varieties, a special case of hyperkahler Hamiltonian quotients. In particular, we develop a Morse theory for the hyperkahler moment map analogous to the case of the moduli space of Higgs bundles. In particular, we show that the Harder-Narasimhan stratification of spaces of representations of quivers coincide with the Morse-theoretic stratification associated to the norm-square of the real moment map. Our approach also provides insight into the topology of specific examples of small-rank quiver varieties, including hyperpolygon spaces and some ADHM quivers.

2008年12月09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
Bertrand Deroin 氏 (CNRS, Orsay, Universit\'e Paris-Sud 11)
Tits alternative in $Diff^1(S^1)$
[ 講演概要 ]
The following form of Tits alternative for subgroups of
homeomorphisms of the circle has been proved by Margulis: or the group
preserve a probability measure on the circle, or it contains a free
subgroup on two generators. We will prove that if the group acts by diffeomorphisms of
class $C^1$ and does not preserve a probability measure on the circle, then
in fact it contains a subgroup topologically conjugated to a Schottky group.
This is a joint work with V. Kleptsyn and A. Navas.

2008年12月08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
上田 哲生 氏 (京大理)
Critically finite holomorphic maps on projective spaces

2008年12月05日(金)

GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 128号室
池森 俊文 氏 (みずほ第一フィナンシャルテクノロジー)
金融リスク管理と数理Ⅰ(基礎編)

2008年12月04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
戸松玲治 氏 (東大数理)
カッツ環の作用の分類

Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
いつもと開始時刻および場所が違いますのでご注意ください
Genkai Zhang 氏 (Chalmers and Gothenburg University)
Realization of quanternionic discrete series as spaces of H-holomorphic
functions
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2008年12月03日(水)

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) 122号室
Freddy Delaben 氏 (ETH)
The structure of dynamic utility functions in a Brownian Filtration

[ 講演概要 ]
The penalty function for monetary dynamic utility functions
has a special form. They can be seen as potentials. In the Brownian Filtration Rao's theorem permits to give a complete description.

代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室
鈴木正俊 氏 (東京大学大学院数理科学研究科)
Mean-periodicity and analytic properties of zeta-functions
[ 講演概要 ]
Mean-periodicityというのは周期性の概念のひとつの一般化である。最近、I. Fesenko, G. Ricottaとの共同研究により、数論的スキームのゼータ関数を含むある複素関数のクラスと、mean-periodicityとの関連性が新しく見出された。
これはHecke-Weilによる, 解析接続と関数等式を持つDirichlet級数と保型形式との対応の一つの拡張ともみなせる. この背景には, I. Fesenkoの高次元アデール上のゼータ積分の理論があり、数論的スキームのHasseゼータ関数の解析接続を高次元アデール上の調和解析から導こうというプログラムの一環となっている。
この講演ではそのような背景にも若干触れた上、ゼータ関数の解析的性質とmean-periodicityの関連、特に解析接続と関数等式との関連について解説する。

2008年12月02日(火)

Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同で開催します. またいつもと開催時刻および開催場所が違います。
金井雅彦 氏 (名古屋大学)
消滅と剛性
[ 講演概要 ]
The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other.

The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム (Lie群論・表現論セミナーと合同で開催)
金井 雅彦 氏 (名古屋大学多元数理科学研究科)
Vanishing and Rigidity
[ 講演概要 ]
The aim of my talk is to reveal an unforeseen link between
the classical vanishing theorems of Matsushima and Weil, on the one hand,
andrigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank
noncompact Lie group, on the other. The connection is established via
"transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the
orbit foliation of the Weyl chamber flow that is tangentially closed
(and satisfies a certain mild additional condition) can be extended to a closed 1- form on the
whole space in a canonical manner. In particular, infinitesimal
rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.

2008年12月01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
川上 裕 氏 (九大数理/大阪市立大)
双曲的Gauss写像の値分布

Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Kentaro Hori 氏 (University of Toronto / IPMU)
A pair of non-birational but derived equivalent Calabi-Yau
manifolds from non-Abelian gauge theories
[ 講演概要 ]
We construct a family of (2,2) supersymmetric gauge theories
in 2-dimensions that flows to a family of (2,2) superconformal fields theories with \\hat{c}=3. The family has two limits and three singular points. The two limits correspond to two Calabi-Yau manifolds which are not birationally equivalent. The two are, however, derived equivalent
by general principle of supersymmetric quantum field theory.

2008年11月28日(金)

GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 128号室
中川 淳一 氏 (新日本製鐵先端技術研究所)
製鐵プロセスの数学Ⅱ

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)
川又雄二郎 氏 (東京大学大学院数理科学研究科)
曲線の錐体と因子の錐体
[ 講演概要 ]
代数多様体上に載っている曲線と因子の交点数を使うと、互いに双対な有限次元実ベクトル空間内の、互いに双対な閉凸錐体 -- 曲線の錐体と因子の錐体が定義される。極小モデル理論では、曲線の錐体の端射線から収縮写像が構成されるが、双有理同値な代数多様体をたくさん同時に考えるためには、因子の錐体のほうが便利である。標準環の有限生成定理は、因子の錐体の集まりの間の壁越えの様子を詳しく調べることによって証明された。一般の代数多様体に対する極小モデルの存在は未解決問題であるが、そのためには因子の錐体についてのより深い理解が必要と思われる。この講演ではそのあたりの事情を解説する。
[ 講演参考URL ]
[開催日にご注意下さい]

GCOEレクチャーズ

14:40-16:10   数理科学研究科棟(駒場) 002号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Circle-valued Morse theory
, Lecture 2

2008年11月26日(水)

代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Piotr Pragacz
(Banach Institute)
Diagonal subschemes and vector bundles

GCOEレクチャーズ

14:40-16:10   数理科学研究科棟(駒場) 002号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Circle-valued Morse theory, Lecture 1
[ 講演概要 ]
Morse theory of circle-valued functions, initiated by S. P. Novikov in 1980-1982 is now a rapidly developing domain with applications and connections to many other fields of geometry and topology such as dynamical systems, Lagrangian intersections,
knots and links in three-dimensional sphere.

We will start with the basics of the theory, discuss the construction of the Novikov complex, relations with the dynamical zeta functions, and the knot theory. We will conclude with a list of the open problems of the theory.

代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室
平田典子 氏 (日本大学理工学部)
Lang's Observation in Diophantine Problems
[ 講演概要 ]
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\\varphi$ be a rational function on $E$. Then, for every point $P\\in E(K)$ where $\\varphi$ does not vanish at $P$, the logarithms of a norm of $\\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.

2008年11月25日(火)

解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Ovidiu Calin 氏 (Eastern Michigan University)
Heat kernels for subelliptic operators
[ 講演概要 ]
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.

代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Xavier Roulleau 氏 (東大)
Cotangent maps of surfaces of general type
[ 講演概要 ]
Surfaces are usualy studied and classified via the properties of the pluricanonical maps. For surfaces of general type whose cotangent sheaf is generated by global sections, we propose to study an other map, called the cotangent map, in order to obtain geometric informations on the surface. In this way, we obtain informations on the ampleness of the cotangent sheaf of such a surface. We will illustate this talk with the example of the Fano surface of lines of cubic threefolds.

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
吉野太郎 氏 (東工大)
$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
[ 講演概要 ]
Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:

"Does the quotient topology admits a manifold structure?"

Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.

If Lipsman's conjecture were true, all of the answer should be affirmative.

But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.

As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

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