Seminar information archive

Seminar information archive ~05/28Today's seminar 05/29 | Future seminars 05/30~

2007/11/12

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
野口 潤次郎 (東京大学)
蕭の有理型接続と関連する話題 (Siu's meromorphic connection and related topics)

2007/11/09

Colloquium

16:40-17:40   Room #123 (Graduate School of Math. Sci. Bldg.)
吉川謙一 (東京大学数理科学)
解析的捩率と保型形式
[ Abstract ]
70年代にRayとSingerは位相幾何学におけるReidemeister捩率の解析的類似を考察し,解析的捩率と呼ばれるスペクトル不変量を導入した. de Rham複体とDolbeault複体に対応して, 解析的捩率には実解析的捩率と正則解析的捩率の二種類の理論があり,80年代から現在に至るBismutの研究により両理論は長足の発展を遂げた.
一般論が整備された後で講演者が興味を持ったのは,解析的捩率を具体的に計算するという問題であった.既にRayとSingerは正則解析的捩率を導入した論文の中で楕円曲線の正則解析的捩率を計算し,それが楕円曲線の判別式のノルムで与えられることを示していた. この講演では「楕円曲線の解析的捩率はモジュライ空間上の保型形式で与えられる」というRay-Singerの主張がどのように高次元化されるのかを対合付きK3曲面とEnriques曲面の場合を中心に概観したい. 時間が許せば, その他の場合(三次元Calabi-Yau多様体やAbel多様体等)についても言及したい.

2007/11/08

Algebraic Geometry Seminar

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Alexandru DIMCA (Univ Nice )
New restrictions on the fundamental groups of complex algebraic varieties
[ Abstract ]
My talk will be based on joint work with S. Papadima (Bucarest, Romania) and A. Suciu (Boston, USA). First I will recall the basic facts on characteristic varieties $V_k(M)$ associated to rank one local systems on a complex algebraic variety $M$ which are due to Beauville, Simpson and Arapura. Then I will introduce the resonance varities $R_k(M)$, which may be related to the Isotropic Subspace Theorems by Catanese and Bauer. One of the main new results is that for a class of algebraic varieties (the 1-formal ones), the two types of varieties $V_k(M)$ and $R_k(M)$ are strongly related. Applications to right angle Artin groups, Bestvina-Brady groups and to a conjecture by Kollar will be discussed in the end.

Applied Analysis

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
倉田 和浩 (首都大学東京・理工学研究科・数理情報科学専攻)
弱い飽和効果をもったGierer-Meinhardt systemにおける軸対称領域上での多重ピーク解の構成と漸近挙動について
[ Abstract ]
This talk is based on the joint work with Kotaro Morimoto (Tokyo Metropolitan University).

We are concerned with stationary solutions to the following reaction diffusion system which is called the Gierer-Meinhardt system with saturation.
$A_t=\\epsilon^2 \\Delta A-A+A^2/(H(1+kA^2), A>0,$
$\\tau H_t=D\\Delta H-H+A2, H>0,$
where $\\epsilon >0$, $\\tau \\geq 0$, $k>0$.
The unknowns $A$ and $H$ represent the concentrations of the activator and the inhibitor. Here $\\Omega$ is a bounded smooth domain in $R^N$ and we consider homogeneous Neumann boundary conditions. When $\\Omega$ is an $x_N$-axially symmetric domain and $2\\leq N\\leq 5$, for sufficiently small $\\epsilon>0$ and large $D>0$, we construct a multi-peak stationary solution peaked at arbitrarily chosen intersections of $x^N$-axis and $\\partial \\Omega$, under the condition that $k\\epsilon^{-2N}$ converges to some $k_0\\in[0,\\infty)$ as $\\epsilon \\to 0$.

In my talk, I will explain related results comparing the differences between the case $k=0$ and $k>0$, the basic strategy of the proof of our results with some details, and open questions.

2007/11/07

Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
鎌谷 研吾 (東京大学大学院数理科学研究科)
ハプロタイプ関連解析:EMアルゴリズムによるアプローチ
[ Abstract ]
最尤推定量の計算法である, EMアルゴリズムについて考察する. EMアルゴリズムのグローバルな観点の収束を示すことは容易でない事が多い. 一方で局所的な収束は容易に示すことができて, 一次漸近有効な推定量を 構成できる. その構成法とハプロタイプ関連解析への応用を考える. 時間があれば, ベイズ推定量の近似である, MCMCによる統計量の漸近有効性にも触れる.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/08.html

2007/11/06

Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
児玉 大樹 (東京大学大学院数理科学研究科)
Thustion's inequality and open book foliations
[ Abstract ]
We will study codimension 1 foliations on 3-manifolds.
Thurston's inequality, which implies convexity of the foliation in
some sense, folds for Reebless foliations [Th]. We will discuss
whether the inequality holds or not for open book foliations.
[Th] W. Thurston: Norm on the homology of 3-manifolds, Memoirs of the
AMS, 339 (1986), 99--130.

Lie Groups and Representation Theory

15:00-16:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Michaël Pevzner (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. IV
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
森脇政泰 (広島大学)
Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2007/11/01

Lie Groups and Representation Theory

16:30-18:00   Room #052 (Graduate School of Math. Sci. Bldg.)
Michaël Pevzner (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. III
[ Abstract ]
Kontsevich's formality theorem and applications in Representation theory.

We shall first give an explicit construction of an associative star-product on an arbitrary smooth finite-dimensional Poisson manifold.

As application, we will consider in details the crucial example of the dual of a finite-dimensional Lie algebra and will sketch a generalization of the Duflo isomorphism describing the set of infinitesimal characters of irreducible unitary representations of the corresponding Lie group.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2007/10/31

Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)
深澤 正彰 (東京大学大学院数理科学研究科)
最尤推定量の漸近展開とその応用:とくに拡散過程の場合について
[ Abstract ]
最尤推定量とそのスチューデント化統計量の漸近展開公式について、 スキューネス修正の観点から考察し、AR過程や、あるクラスの拡散過程モデルへの応用について述べる。 一般の対称拡散過程モデルにおける最尤推定量のバイアス推定量、 スキューネス推定量も提案する。
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/07.html

Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Pierre Colmez (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)

2007/10/30

Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
松本久義 (東京大学大学院数理科学研究科)
On Weyl groups for parabolic subalgebras
[ Abstract ]
Let ${\\mathfrak g}$ be a complex semisimple Lie algebra.
We call a parabolic subalgebra ${\\mathfrak p}$ of ${\\mathfrak g}$
normal, if any parabolic subalgebra which has a common Levi part with ${\\mathfrak p}$
is conjugate to ${\\mathfrak p}$ under an inner automorphism of ${\\mathfrak g}$.
For a normal parabolic subalgebra, we have a good notion of the restricted root system
or the little Weyl group. We have a comparison result on the Bruhat order on the Weyl group for
${\\mathfrak g}$ and the little Weyl group.
We also apply this result to the existence problem of the homomorphisms between scalar generalized Verma modules.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

Lie Groups and Representation Theory

15:00-16:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Michaël Pevzner (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. II
[ Abstract ]
Back to Mathematics. Two methods of quantization.

We will start with a discussion on

-Weyl symbolic calculus on a symplectic vector space
and its asymptotic behavior.


In the second part, as a consequence of previous considerations, we will define the notion of deformation quantization.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

Algebraic Geometry Seminar

10:00-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Dmitry KALEDIN (Steklov研究所, 東大数理)
Homological methods in Non-commutative Geometry

Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
太田 啓史 (名大多元数理)
$L_{\\infty}$ action on Lagrangian filtered $A_{\\infty}$ algebras.
[ Abstract ]
I will discuss $L_{\\infty}$ actions on Lagrangian filtered
$A_{\\infty}$ algebras by cycles of the ambient symplectic
manifold. In the course of the construction,
I like to remark that the stable map compactification is not
sufficient in some case when we consider ones from genus zero
bordered Riemann surface. Also, if I have time, I like to discuss
some relation to (absolute) Gromov-Witten invariant and other
applications.
(This talk is based on my joint work with K.Fukaya, Y-G Oh and K. Ono.)

2007/10/29

Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Hiroshige Kajiura (RIMS, Kyoto University)
Some examples of triangulated and/or $A_\\infty$-categories
related to homological mirror symmetry

[ Abstract ]
In this talk, I would like to discuss on some examples of
triangulated and/or $A_\\infty$-categories associated to
manifolds with additional structures
(symplectic structure, complex structure, ...)
which can appear in the homological mirror symmetry (HMS) set-up
proposed by Kontsevich'94.

The strongest form of the HMS may be to show the equivalence
of Fukaya category on a symplectic manifold with the category
of coherent sheaves on the mirror dual complex manifold
at the level of $A_\\infty$-categories.
On the other hand, for a given $A_\\infty$-category,
there is a canonical way (due to Bondal-Kapranov, Kontsevich)
to construct an enlarged $A_\\infty$-category
whose restriction to the zero-th cohomology forms a triangulated category.

I plan to talk about the triangulated structure of categories
associated to regular systems of weights
(joint work with Kyoji Saito and Atsushi Takahashi),
and also give a realization of higher $A_\\infty$-products in
Fukaya categories from the mirror dual complex manifold
via HMS in some easy examples.

2007/10/25

Operator Algebra Seminars

16:30-18:00   Room #410 (Graduate School of Math. Sci. Bldg.)
見村万佐人 (東大数理)
An introduction to expander graphs

Lie Groups and Representation Theory

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Michael Pevzner (Universite de Reims and University of Tokyo)
Quantization of symmetric spaces and representations. I
[ Abstract ]
The first and introductory lecture of a series of four will be devoted to the discussion of fundamental principles of the Quantum mechanics and their mathematical formulation. This part is not essential for the rest of the course but it might give a global vision of the subject to be considered.

We shall introduce the Weyl symbolic calculus, that relates classical and quantum observables, and will explain its relationship with the so-called deformation quantization of symplectic manifolds.

Afterwards, we will pay attention to a more algebraic question of formal deformation of an arbitrary smooth Poisson manifold and will define the Kontsevich star-product.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

2007/10/24

Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
阿部知行 (東京大学大学院数理科学研究科)
l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて
[ Abstract ]
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。

2007/10/23

Tuesday Seminar on Topology

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Jun O'Hara (首都大学東京)
Spaces of subspheres and their applications
[ Abstract ]
The set of q-dimensional subspheres in S^n is a Grassmann manifold which has natural pseudo-Riemannian structure, and in some cases, symplectic structure as well. Both of them are conformally invariant.
I will explain some examples of their applications to geometric aspects of knots and links.

Tuesday Seminar of Analysis

17:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Fr\'{e}d\'{e}ric Klopp (パリ北大学)
Localization for random quantum graphs (joint with K. Pankrashkin)

2007/10/22

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
志賀弘典 (千葉大学)
ガウス算術幾何平均定理の多変数化とその保型形式的解釈(小池健二氏との共同研究)

2007/10/18

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (学振・東大数理)
On the classification of Bruhat-Tits buildings

2007/10/17

Lectures

16:00-17:00   Room #470 (Graduate School of Math. Sci. Bldg.)
J. Fritz (TU Budapest)
The method of compensated compactness for
microscopic systems

2007/10/16

Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
二木 昭人 (東京工業大学大学院理工学研究科)
Toric Sasaki-Einstein manifolds
[ Abstract ]
A compact toric Sasaki manifold admits a Sasaki-Einstein metric if and only if it is obtained by the Delzant construction from a toric diagram of a constant height. As an application we see that the canonical line bundle of a toric Fano manifold admits a complete Ricci-flat K\\"ahler metric.

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