過去の記録

過去の記録 ~11/11本日 11/12 | 今後の予定 11/13~

東京幾何セミナー

14:45-18:00   数理科学研究科棟(駒場) 056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��

近藤剛史 (Kondo Takefumi) 氏 (神戸大学大学院理学研究科) 14:45-16:15
Fixed point theorems for non-positively curved spaces and random groups
[ 講演概要 ]
It is not easy to construct a finitely generated group with a fixed point property for non-positively curved spaces. However, if we randomly choose relators, then we can get examples of such groups. To show this, we need a criterion for deducing a fixed point property from a local property of a group. In this talk, we will introduce one such criterion, and our approach is via a scaling limit argument.
赤穂まなぶ (Akaho Manabu) 氏 (首都大学東京大学院理工学研究科) 16:30-18:00
Lagrangian mean curvature flow and symplectic area
[ 講演概要 ]
In this talk, we consider symplectic area of smooth maps from a Riemann surface with boundary on embedded Lagrangian mean curvature flow in Kahler-Einstein manifolds. As an application, we observe a relation between embedded Lagrangian mean curvature flow and Floer theory of monotone Lagrangian submanifolds in Kahler-Einstein manifolds; in this case non-trivial holomorphic discs turn out to be an obstruction to the existence of long time solution of the flow.

GCOEセミナー

16:30-17:30   数理科学研究科棟(駒場) 370号室
O. Emanouilov 氏 (Colorado State University)
Partial Cauchy data for general second order elliptic operators in two dimensions
[ 講演概要 ]
We consider the problem of determining the coefficients of a first-order perturbation of the Laplacian in two dimensions by measuring the corresponding Cauchy data on an arbitrary open subset of the boundary. From this information we obtained a coupled PDE system of first order which the coefficients satisfy. As a corollary we show for the magnetic Schr"odinger equation that the magnetic field and the electric potential are uniquely determined by measuring the partial Cauchy data on an arbitrary part of the boundary. We also show that the coefficients of any real vector field perturbation of the Laplacian, the convection terms, are uniquely determined by their partial Cauchy data.

2009年10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
笹平 裕史 氏 (東京大学大学院数理科学研究科)
Instanton Floer homology for lens spaces
[ 講演概要 ]
Let Y be an oriented closed 3-manifold and P be an SU(2)-bundle on Y. Under a certain condition, instanton Floer homology for Y can be defined as the Morse homology of the Chern-Simons functional. The condition is that all flat connections on P are irreducible. When there is a reducible flat connection on P, instanton Floer homology is not defined in general.
Since the fundamental group of a lens sapce is commutative, all flat connections on the lens space are reducible. In this talk I will introduce instanton Floer homology for lens spaces. I also show calculations for some lens spaces.

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
小寺諒介 氏 (東京大学)
Extensions between finite-dimensional simple modules over a generalized current Lie algebra

[ 講演概要 ]
$\\mathfrak{g}$を$\\mathbb{C}$上の有限次元半単純Lie代数,$A$を有限生成可換$\\mathbb {C}$代数とする.
テンソル積$A \\otimes \\mathfrak{g}$に自然にLie代数の構造を与えたものを一般化されたカレントLie代数と呼ぶ.
一般化されたカレントLie代数の任意の2つの有限次元既約表現に対して,その1次のExt群を完全に決定することができたので,その結果について発表する.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2009年10月09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) 117号室
岡本龍明 氏 (NTT 情報流通プラットフォーム研究所 岡本特別研究室長)
暗号の実践編

GCOEレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 128号室
Duflo氏による講義 2講目
Michel Duflo 氏 (Paris 7)
Associated varieties for Representations of classical Lie
super-algebras
[ 講演概要 ]
In this lecture, I'll discuss the notion of "Associated
varieties for Representations of classical Lie super-algebras (joint work with Vera Serganova)" and the relation with the degree of atypicality. This is related to a conjecture of Kac and Wakimoto.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2009年10月07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
北海道大学のHPには、第1回(2004年9月29日)~第38回(2008年10月15日)までの情報が掲載されております。
劉和平(Liu Heping) 氏 (Beijing University)
Wiener measure and Feynman-Kac formula on the Heisenberg group
[ 講演概要 ]
It is well known that the Feynman-Kac formula on the Euclidean space gives the solution of Schrodinger equation by the Wiener integral. We will discuss the Wiener measure and Feynman-Kac formula on the Heisenberg group. The results hold on the H-type groups.

GCOEレクチャーズ

16:30-17:30   数理科学研究科棟(駒場) 128号室
Duflo氏による一講目
Michel Duflo 氏 (Paris 7)
Representations of classical Lie super-algebras

[ 講演概要 ]
In this lecture, I'll survey classical topics on finite dimensional representations of classical Lie super-algebras, in particular the notion of the degree of atypicality.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

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
Ahmed Abbes 氏 (Université de Rennes 1)
On GAGA theorems for the rigide-étale topology
[ 講演概要 ]
Last year, I finished my course in Todai on "Rigide Geometry following M. Raynaud" by stating a GAGA theorem for the rigide-étale topology, due to Gabber and Fujiwara. I will give a new proof of this theorem, inspired by another theorem of Gabber, namely the Affine analog of the proper base change theorem.

2009年10月05日(月)

GCOEレクチャーズ

15:30-17:00   数理科学研究科棟(駒場) 128号室
Claudio Landim 氏 (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅲ

GCOEレクチャーズ

13:30-15:00   数理科学研究科棟(駒場) 128号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Mini course on the gradient models, I: Effective gradient models, definitions and examples
[ 講演概要 ]
We describe a phase separation in $R^{d+1}$ by an effective interface model with basis in $Z^d$ and height in $R$. We assume that the interaction potential depends only on the discrete gradient and that the a priori measure is the product Lebesgue measure. Note that this is an unbounded massless model with continuous symmetry and this implies that the interface is delocalized for the infinite model in lower lattice dimensions $d=1,2$. Instead of looking at the distribution of the height of the interface itself, we consider the measure on the height differences the so called gradient Gibbs measure, which exists in any dimensions. The gradient field must satisfy the loop condition, that is the sum of the gradient along any closed loop is zero, this implies a long range interaction with a slow decay of the correlations. We are interested in characterizing the ergodic components of this gradient field, in the decay of correlations, large deviations and continuous scaling limits. As an example we consider the harmonic or discrete gaussian free field with quadratic interactions.

代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
伊藤 敦 氏 (東大数理)
代数曲面上の随伴束の基底点集合について
[ 講演概要 ]
偏極付き代数多様体上(X,L)は、Lに数値的な条件を付け加えると
その随伴束が自由になったり、基底点集合が具体的にかけることがある。しかし
、曲線の場合は簡単であるが高次元の場合は難しい。今回の講演では主に代数曲
面の場合について解説する。

2009年10月02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) 117号室
岡本龍明 氏 (NTT 情報流通プラットフォーム研究所 岡本特別研究室長)
暗号の基礎編

2009年09月30日(水)

GCOEレクチャーズ

15:30-17:00   数理科学研究科棟(駒場) 123号室
Claudio Landim 氏 (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, Ⅱ

統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室
矢田 和善 氏 (筑波大学大学院数理物質科学研究科)
HDLSSデータにおけるPCAについて
[ 講演概要 ]
マイクロアレイデータなどに見られるように,データの次元数dが標本数nよりも遥かに大きな高次元小標本(HDLSS)データが,解析対象になる場面が増えてきている.

HDLSSデータに対して従来の統計手法を用いると,次元の呪いによって解析が上手くいかない.解決策の一つとして次元縮約法があり, その一つにPCAがある.高次元における従来型のPCAの漸近的性質は,正規性もしくは同等な仮定のもとで,先行研究が多数存在する. しかしながら,これら仮定は,HDLSSを研究する上で,厳しい制約にもなっている. Yata and Aoshimaの一連の研究は,この制約条件の枠を外すことから始まった.HDLSSにおける従来型PCAの限界は何か?推測が一致性をもつための標本数nと 次元数dの関係が,オーダー条件として明らかにされる.従来型PCAの限界を超える手法は何か?一つの実用的な方法として,クロス行列と呼ばれるデータの変換行列が導入され, この行列の特異値分解に基づいた新しいPCAが提案される.

当日は,マイクロアレイデータによる実例と,シミュレーション結果も交えながら,お話します.本研究は,筑波大学数理物質科学研究科の青嶋誠先生との共同研究です.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/05.html

2009年09月29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
Sergei Duzhin 氏 (Steklov Mathematical Institute, Petersburg Division)
Symbol of the Conway polynomial and Drinfeld associator
[ 講演概要 ]
The Magnus expansion is a universal finite type invariant of pure braids
with values in the space of horizontal chord diagrams. The Conway polynomial
composed with the short circuit map from braids to knots gives rise to a
series of finite type invariants of pure braids and thus factors through
the Magnus map. We describe explicitly the resulting mapping from horizontal
chord diagrams on 3 strands to univariante polynomials and evaluate it on
the Drinfeld associator obtaining a beautiful generating function whose
coefficients are integer combinations of multple zeta values.

2009年09月28日(月)

GCOEレクチャーズ

15:30-17:00   数理科学研究科棟(駒場) 123号室
Claudio Landim 氏 (IMPA, Brazil)
Macroscopic fluctuation theory for nonequilibrium stationary states, I
[ 講演概要 ]
We present a review of recent work on the statistical mechanics of nonequilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and can be studied rigorously providing a source of challenging mathematical problems. In this way, some principles of wide validity have been obtained leading to interesting physical consequences.

2009年09月17日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Norayr MATEVOSYAN 氏 (ケンブリッジ大学・数理)
On a parabolic free boundary problem modelling price formation
[ 講演概要 ]
We will discuss existence and uniqueness of solutions for a one dimensional parabolic evolution equation with a free boundary. This problem was introduced by J.-M. Lasry and P.-L. Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in time-extension of the local solution which is intimately connected to the regularity of the free boundary.
We also present numerical results.

2009年09月15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
打越 敬祐 氏 (防衛大学校数学教育室)
渦層の超局所解析
[ 講演概要 ]
渦層とは,2次元流体が界面を境に2層に分かれて流れる状態で,今井功氏は「佐藤超関数は渦層である」と言っている.この考え方を用いると,
界面の時間変化を記述するBirkoff-Rott方程式を,擬微分方程式に書き直して解けることを説明する.

2009年09月14日(月)

代数学コロキウム

11:00-12:00   数理科学研究科棟(駒場) 123号室
いつもと、曜日、時間、教室が違います。
午後からは、織田先生還暦記念の研究集会がはじまります。

Dinakar Ramakrishnan 氏 (カリフォルニア工科大学)
Modular forms and Calabi-Yau varieties

2009年09月10日(木)

応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Henrik SHAHGHOLIAN 氏 (王立工科大学・ストックホルム)
A two phase free boundary problem with applications in potential theory
[ 講演概要 ]
In this talk I will present some recent directions, still to be developed, in potential theory, that are connected to a two-phase free boundary problems. The potential theoretic topic that I will discuss is the so called Quadrature Domains.

The most simple free boundary/potential problem that we can present is the following. Given constants $a_\\pm, \\lambda_\\pm >0$ and two points $x^\\pm$ in ${\\bf R}^n$. Find a function $u$ such that
$$\\Delta u = \\left( \\lambda_+ \\chi_{\\{u>0 \\}} - a_+\\delta_{x^+}\\right) - \\left( \\lambda_- \\chi_{\\{u<0 \\}} - a_-\\delta_{x^-}\\right),$$
where $\\delta$ is the Dirac mass.

In general this problem is solvable for two Dirac masses. The requirement, somehow implicit in the above equation, is that the support of the measures (in this case the Dirac masses) is to be in included in the positivity and the negativity set (respectively).

In general this problem does not have a solution, and there some strong restrictions on the measures, in order to have some partial results.

2009年09月08日(火)

GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 123号室
H.R.Thieme 氏 (Arizona State University)
Global compact attractors and their tripartition under persistence (ENGLISH)
[ 講演概要 ]
The study of the dynamics of a semiflow (inertial manifolds, persistence) is largely facilitated if there is a global compact attractor, i.e. a compact invariant subset which attracts a sufficiently broad class of subsets of the state space.
Unfortunately, there in no uniform use of the concept of a global compact attractor in the literature: it has been used for a compact attractor of points, compact attractor of neighborhoods of compact sets, and compact attractor of bounded sets.
Persistence theory allows to discuss the long-term survival of populations in a dynamical systems framework. There is a two-way interaction between persistence and global compact attractors. On the one hand, the existence of a compact attractor of points helps to establish the persistence of the semiflow. On the other hand, the global attractor of a uniformly persistent semiflow divides into three invariant parts: an extinction attractor, a persistence attractor, and a set of orbits that connect the extinction to the persistence attractor. The persistence attractor has further interesting properties like local stability and connectedness. Examples are presented where the persistence attractor can be used to prove the global stability of the persistence equilibrium. (joint work with Hal L. Smith)

GCOEセミナー

16:15-17:15   数理科学研究科棟(駒場) 123号室
Glenn Webb 氏 (Vanderbilt University)
Analysis of a Model for Transfer Phenomena in Biological Populations (ENGLISH)
[ 講演概要 ]
We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernel corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.

2009年09月07日(月)

作用素環セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Marek Bozejko 氏 (University of Wroclaw)
Generalized Gaussian field, theta function of Jacobi and functor of second quantization

2009年09月01日(火)

代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室
部屋・曜日にご注意ください。
Matthias Schuett 氏 (Leibniz University Hannover)
Arithmetic of K3 surfaces
[ 講演概要 ]
This talk aims to review recent developments in the arithmetic of K3 surfaces, with emphasis on singular K3 surfaces.
We will consider in particular modularity, Galois action on Neron-Severi groups and behaviour in families.

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