## 過去の記録

### 2007年11月08日(木)

#### 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
Alexandru DIMCA 氏 (Univ Nice )
New restrictions on the fundamental groups of complex algebraic varieties
[ 講演概要 ]
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.

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
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年11月07日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室

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
[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/08.html

### 2007年11月06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

Thustion's inequality and open book foliations
[ 講演概要 ]
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群論・表現論セミナー

15:00-16:30   数理科学研究科棟(駒場) 126号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. IV
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### 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

Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年11月01日(木)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 052号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. III
[ 講演概要 ]
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.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年10月31日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 122号室

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/07.html

#### 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
Pierre Colmez 氏 (Ecole Polytechnique)
On the p-adic local Langlands correspondance for GL2(Qp)

### 2007年10月30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

On Weyl groups for parabolic subalgebras
[ 講演概要 ]
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.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### Lie群論・表現論セミナー

15:00-16:30   数理科学研究科棟(駒場) 126号室
Michaël Pevzner 氏 (Université de Reims and University of Tokyo)
Quantization of symmetric spaces and representation. II
[ 講演概要 ]
Back to Mathematics. Two methods of quantization.

-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.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### 代数幾何学セミナー

10:00-12:00   数理科学研究科棟(駒場) 128号室

Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homological methods in Non-commutative Geometry

#### 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

$L_{\\infty}$ action on Lagrangian filtered $A_{\\infty}$ algebras.
[ 講演概要 ]
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年10月29日(月)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Hiroshige Kajiura 氏 (RIMS, Kyoto University)
Some examples of triangulated and/or $A_\\infty$-categories
related to homological mirror symmetry

[ 講演概要 ]
In this talk, I would like to discuss on some examples of
triangulated and/or $A_\\infty$-categories associated to
(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年10月25日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 410号室

An introduction to expander graphs

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

Michael Pevzner 氏 (Universite de Reims and University of Tokyo)
Quantization of symmetric spaces and representations. I
[ 講演概要 ]
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.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2007年10月24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

l進層のSwan導手とunit-root
overconvergent F-isocrystalの特性サイクルについて
[ 講演概要 ]

### 2007年10月23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) 002号室
Tea: 16:00 - 16:30 コモンルーム
Jun O'Hara 氏 (首都大学東京)
Spaces of subspheres and their applications
[ 講演概要 ]
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.

#### 解析学火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 128号室
いつもと30分ずれていますのでお間違いなく.
Fr\'{e}d\'{e}ric Klopp 氏 (パリ北大学)
Localization for random quantum graphs (joint with K. Pankrashkin)

### 2007年10月22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

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年10月18日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Mikael Pichot 氏 (学振・東大数理)
On the classification of Bruhat-Tits buildings

### 2007年10月17日(水)

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 470号室
J. Fritz 氏 (TU Budapest)
The method of compensated compactness for
microscopic systems

### 2007年10月16日(火)

#### 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

Toric Sasaki-Einstein manifolds
[ 講演概要 ]
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.

#### 代数幾何学セミナー

10:00-12:00   数理科学研究科棟(駒場) 128号室
10月16日開始, 毎週火曜10時から12時の連続講演です. 10月23日と12月4日は休講です.
Dmitry KALEDIN 氏 (Steklov研究所, 東大数理)
Homogical methods in Non-commutative Geometry
[ 講演概要 ]
Of all the approaches to non-commutative geometry, probably the most promising is the homological one, developed by Keller, Kontsevich, Toen and others, where non-commutative eometry is understood as "geometry of triangulated categories". Examples of "geometric" triangulated categories come from representation theory, symplectic geometry (Fukaya category) and algebraic geometry (the derived category of coherent sheaves on an algebraic variety and
various generalizations). Non-commutative point of view is expected to be helpful even in traditional questions of algebraic geometry such as the termination of flips.

We plan to give an introduction to the subject, with emphasis on homological methods (such as e.g. Hodge theory which, as it turns out, can be mostly formulated in the non-commutative setting).

No knowledge of non-commutative geometry whatsoever is assumed. However, familiarity with basic homological algebra and algebraic geometry will be helpful.

### 2007年10月15日(月)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Shinobu Hosono 氏 (The University of Tokyo)
Topics on string theory, mirror symmetry, and Gromov-Witten invariants
[ 講演概要 ]
Recently, some technical developments in solving BCOV
(Bershadsky-Cecotti-Ooguri-Vafa) holomorphic anomaly equation has been
made and it has become possible to predict higher genus Gromov-Witten
invariants for some class of Calabi-Yau 3 folds.

With a brief introduction to BCOV equation, I will present some
predictions for Gromov-Witten invariants of certain Calabi-Yau 3 folds,
which are not birational but derived equivalent. (This is based on
a work with Y. Konishi which appeared in mathAG/0704.2928.)

Before coming to this specific topic, I will review some recent
topics of the homological mirror symmetry focusing on
its connection to the `classical' mirror symmetry, where the
variation theory of Hodge structures (VHS) plays a central role.
The BCOV equation and its open string generalization have their grounds
on the VHS.