## Seminar information archive

Seminar information archive ～02/21｜Today's seminar 02/22 | Future seminars 02/23～

#### Infinite Analysis Seminar Tokyo

13:00-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Dynamical r-matrices coupled with dual Poisson Lie group

Yang-Baxter Equation and Quantum Geometry

**Gleb Novichkov**(Keio Univ.) 13:00-14:30Dynamical r-matrices coupled with dual Poisson Lie group

[ Abstract ]

The notion dynamical r-matrix coupled with Poisson manifold

is a natural generalization of the notion of the classical

dynamical r-matrix. We will consider special case when

Poisson manifold is a dual Poisson Lie group. We discuss

necessary conditions for the existence dynamical r-matrices

coupled with dual Poisson Lie groups and provide

some examples. We will also discuss some open questions

and possible relations to other subjects.

The notion dynamical r-matrix coupled with Poisson manifold

is a natural generalization of the notion of the classical

dynamical r-matrix. We will consider special case when

Poisson manifold is a dual Poisson Lie group. We discuss

necessary conditions for the existence dynamical r-matrices

coupled with dual Poisson Lie groups and provide

some examples. We will also discuss some open questions

and possible relations to other subjects.

**Vladimir V. Bazhanov**(Australian National Univ.) 15:00-16:30Yang-Baxter Equation and Quantum Geometry

[ Abstract ]

We demonstrate that certain integrable models

of statistical mechanics and quantum field theory

can be interpreted as quantization's of objects

of classical discrete geometry.

The fluctuating variables in these models take continuous

values. The classical geometry corresponds to stationary

configurations in the quasi-classical (or zero-temperature)

limit of the quantum system.

Our main example is the Faddeev-Volkov model which describes

the quantization of the circle patterns and associated with

the Thurston's discrete analogue of the Riemann mapping theorem

(discrete conformal transformations of the 2D plane).

Other examples will be also considered.

Finally we will discuss the geometric origins of integrability

which stem from from the classical results of Lam\\'e,

Darboux and Bianchi in differential geometry.

We demonstrate that certain integrable models

of statistical mechanics and quantum field theory

can be interpreted as quantization's of objects

of classical discrete geometry.

The fluctuating variables in these models take continuous

values. The classical geometry corresponds to stationary

configurations in the quasi-classical (or zero-temperature)

limit of the quantum system.

Our main example is the Faddeev-Volkov model which describes

the quantization of the circle patterns and associated with

the Thurston's discrete analogue of the Riemann mapping theorem

(discrete conformal transformations of the 2D plane).

Other examples will be also considered.

Finally we will discuss the geometric origins of integrability

which stem from from the classical results of Lam\\'e,

Darboux and Bianchi in differential geometry.

### 2007/11/15

#### Operator Algebra Seminars

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Generators of II$_1$ factors (Dykema-Sinclair-Smith-White)の紹介

**水田有一**(東大数理)Generators of II$_1$ factors (Dykema-Sinclair-Smith-White)の紹介

### 2007/11/14

#### Seminar on Probability and Statistics

16:20-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Estimation of Distortion Risk Measures

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/09.html

**塚原 英敦**(成城大学経済学部)Estimation of Distortion Risk Measures

[ Abstract ]

By Kusuoka's representation theorem, the class of distortion risk measures with convex distortions coincides with the set of coherent risk measures that are law invariant and comonotonically additive. The class includes the renowned expected shortfall which has many nice features and is of frequent use in practice. To implement the risk management/regulatory procedure using risk measures, it is necessary to estimate the values of such risk measures. For a distortion risk measure, its form suggests a natural estimator which is a simple form of $L$-statistics. We have seen in our previous work that it has nice asymptotic properties with i.i.d.\\ data. After reviewing these results briefly, we investigate the large sample properties of the estimator based on dependent data, especially GARCH sequences, which are often used for modelling financial time series data. Related issues such as semiparametric estimation with the extreme value theory and backtesting are briefly addressed.

[ Reference URL ]By Kusuoka's representation theorem, the class of distortion risk measures with convex distortions coincides with the set of coherent risk measures that are law invariant and comonotonically additive. The class includes the renowned expected shortfall which has many nice features and is of frequent use in practice. To implement the risk management/regulatory procedure using risk measures, it is necessary to estimate the values of such risk measures. For a distortion risk measure, its form suggests a natural estimator which is a simple form of $L$-statistics. We have seen in our previous work that it has nice asymptotic properties with i.i.d.\\ data. After reviewing these results briefly, we investigate the large sample properties of the estimator based on dependent data, especially GARCH sequences, which are often used for modelling financial time series data. Related issues such as semiparametric estimation with the extreme value theory and backtesting are briefly addressed.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/09.html

### 2007/11/13

#### Lectures

16:00-17:30 Room #052 (Graduate School of Math. Sci. Bldg.)

Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb

**Jens Starke**(Technical University of Denmark)Modelling the olfactory system: From receptor neuron dynamics over axonal pathfinding and sorting to spatio-temporal activities in the bulb

[ Abstract ]

The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.

(1) Nonlinear dynamics in receptor neurons:

A mathematical model for Ca oscillations in the cilia of olfactory

sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.

(2) Sorting by self-organization:

A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.

(3) Spatio-temporal pattern formation in the olfactory bulb:

Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.

This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.

The olfactory system of e.g. mice serves as important model case for other brain regions. The odor signals are processed from receptor neurons over the glomeruli level to a neural network of mitral and granular cells while various types of nonlinear behaviour can be observed.

(1) Nonlinear dynamics in receptor neurons:

A mathematical model for Ca oscillations in the cilia of olfactory

sensory neurons is suggested and analyzed. The existence of an oscillatory regime based on a Hopf bifurcation is proven using stoichiometric network analysis where the knowledge of exact parameters is not required. Predictions of the model are in quantitative agreement with experiment, both with respect to oscillations and to fast adaptation.

(2) Sorting by self-organization:

A many particle model with attracting and repulsive interactions is proposed which is able to reproduce the experimental findings of sorting and convergence during axonal pathfinding in the olfactory system. Many axon species, each represented by a huge number of axons, are spatially disordered at the beginning of their growth at the receptor neurons and converge by a self-organized process to a sorted state, i.e. axons of the same receptor type converge to a common position. Under certain model assumptions, it can be proved that the interacting many-particle system of different particle types converges to a sorted state.

(3) Spatio-temporal pattern formation in the olfactory bulb:

Odors evoke a variety of stimulus specific spatio-temporal patterns on the levels of glomeruli and neural network of mitral and granular cells in the olfactory bulb which can be measured in vivo using Ca and voltage sensitive dyes for optical imaging. A spatial independent component analysis of this high-resolution imaging data was used to identify and separate different neuronal populations based on their stimulus specific spatio-temporal activation. Equation-free techniques were used to obtain bifurcation diagramms for the network activity. First, contrast enhancement between several spatially close activations depending on the network topology and second, hysteres effects in recognition of differences between similar odorants depending on the concentration ratios of odorant mixtures.

This is in parts joint work with P. Borowski, M. Eiswirth, C. Ellsaesser, A. Grinvald, N. Hummel, S. Kokkendorff, D. Omer, J. Reidl, H. Spors, J. Strotmann, M. Zapotocky.

### 2007/11/12

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

蕭の有理型接続と関連する話題 (Siu's meromorphic connection and related topics)

**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.)

解析的捩率と保型形式

**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.

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.)

New restrictions on the fundamental groups of complex algebraic varieties

**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.

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.)

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

**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.

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.)

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

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/08.html

**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 ]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.

http://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.)

Thustion's inequality and open book foliations

**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.

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.)

Quantization of symmetric spaces and representation. IV

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Michaël Pevzner**(Université de Reims and University of Tokyo)Quantization of symmetric spaces and representation. IV

[ Reference URL ]

http://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.)

Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**森脇政泰**(広島大学)Multiplicity-free decompositions of the minimal representation of the indefinite orthogonal group

[ Reference URL ]

http://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.)

Quantization of symmetric spaces and representation. III

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**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 ]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.

http://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.)

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

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/07.html

**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 ]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。

http://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.)

On the p-adic local Langlands correspondance for GL2(Qp)

**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.)

On Weyl groups for parabolic subalgebras

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**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 ]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.

http://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.)

Quantization of symmetric spaces and representation. II

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**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 ]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.

http://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.)

Homological methods in Non-commutative Geometry

**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.)

$L_{\\infty}$ action on Lagrangian filtered $A_{\\infty}$ algebras.

**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.)

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.)

Some examples of triangulated and/or $A_\\infty$-categories

related to homological mirror symmetry

**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.

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.)

An introduction to expander graphs

**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.)

Quantization of symmetric spaces and representations. I

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**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 ]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.

http://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.)

l進層のSwan導手とunit-root

overconvergent F-isocrystalの特性サイクルについて

**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。

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.)

Spaces of subspheres and their applications

**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.

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.)

Localization for random quantum graphs (joint with K. Pankrashkin)

**Fr\'{e}d\'{e}ric Klopp**(パリ北大学)Localization for random quantum graphs (joint with K. Pankrashkin)

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