## Seminar information archive

Seminar information archive ～02/15｜Today's seminar 02/16 | Future seminars 02/17～

#### Kavli IPMU Komaba Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

The correspondence between Frobenius algebra of Hurwitz numbers

and matrix models (JAPANESE)

**Akishi Ikeda**(The University of Tokyo)The correspondence between Frobenius algebra of Hurwitz numbers

and matrix models (JAPANESE)

[ Abstract ]

The number of branched coverings of closed surfaces are called Hurwitz

numbers. They constitute a Frobenius algebra structure, or

two dimensional topological field theory. On the other hand, correlation

functions of matrix models are expressed in term of ribbon graphs

(graphs embedded in closed surfaces).

In this talk, I explain how the Frobenius algebra structure of Hurwitz

numbers are described in terms of matrix models. We use the

correspondence between ribbon graphs and covering of S^2 ramified at

three points, both of which have natural symmetric group actions.

As an application I use Frobenius algebra structure to compute Hermitian

matrix models, multi-variable matrix models, and their large N

expansions. The generating function of Hurwitz numbers is also expressed

in terms of matrix models. The relation to integrable hierarchies and

random partitions is briefly discussed.

The number of branched coverings of closed surfaces are called Hurwitz

numbers. They constitute a Frobenius algebra structure, or

two dimensional topological field theory. On the other hand, correlation

functions of matrix models are expressed in term of ribbon graphs

(graphs embedded in closed surfaces).

In this talk, I explain how the Frobenius algebra structure of Hurwitz

numbers are described in terms of matrix models. We use the

correspondence between ribbon graphs and covering of S^2 ramified at

three points, both of which have natural symmetric group actions.

As an application I use Frobenius algebra structure to compute Hermitian

matrix models, multi-variable matrix models, and their large N

expansions. The generating function of Hurwitz numbers is also expressed

in terms of matrix models. The relation to integrable hierarchies and

random partitions is briefly discussed.

#### Seminar on Geometric Complex Analysis

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

Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

**Yoshihiro AIHARA**(Fukushima Univ.)Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

### 2010/04/23

#### Colloquium

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

疑似乱数発生に用いられる数学:メルセンヌ・ツイスターを例に (JAPANESE)

http://www.ms.u-tokyo.ac.jp/~matumoto/PRESENTATION/tokyo-univ2010-4-23.pdf

**松本 眞**(東京大学大学院数理科学研究科)疑似乱数発生に用いられる数学:メルセンヌ・ツイスターを例に (JAPANESE)

[ Abstract ]

疑似乱数生成法とは、あたかも乱数であるかのようにふるまう数列を、計算機内で高速に、再現性があるように生成する方法の総称です。確率的事象を含む現象の計算機シミュレーションには、疑似乱数は欠かせません。たとえば、核物理シミュレーション、株価に関する商品の評価、DNA塩基配列からのたんぱく質の立体構造推定など、広い範囲で疑似乱数は利用されています。講演者と西村拓士氏が97年に開発したメルセン・ツイスタ―生成法は、生成が高速なうえ周期が$2^19937-1$で623次元空間に均等分布することが証明されており、ISO規格にも取り入れられるなど広く利用が進んでいます。ここでは、メルセンヌ・ツイスターとその後の発展において、(初等的・古典的な)純粋数学(有限体、線形代数、多項式、べき級数環、格子など)がどのように使われたかを、非専門家向けに解説します。学部1年生を含め、他学部・他専攻の方の参加を期待して講演を準備します。

[ Reference URL ]疑似乱数生成法とは、あたかも乱数であるかのようにふるまう数列を、計算機内で高速に、再現性があるように生成する方法の総称です。確率的事象を含む現象の計算機シミュレーションには、疑似乱数は欠かせません。たとえば、核物理シミュレーション、株価に関する商品の評価、DNA塩基配列からのたんぱく質の立体構造推定など、広い範囲で疑似乱数は利用されています。講演者と西村拓士氏が97年に開発したメルセン・ツイスタ―生成法は、生成が高速なうえ周期が$2^19937-1$で623次元空間に均等分布することが証明されており、ISO規格にも取り入れられるなど広く利用が進んでいます。ここでは、メルセンヌ・ツイスターとその後の発展において、(初等的・古典的な)純粋数学(有限体、線形代数、多項式、べき級数環、格子など)がどのように使われたかを、非専門家向けに解説します。学部1年生を含め、他学部・他専攻の方の参加を期待して講演を準備します。

http://www.ms.u-tokyo.ac.jp/~matumoto/PRESENTATION/tokyo-univ2010-4-23.pdf

### 2010/04/22

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The Baum-Connes Conjecture and Group Representations (ENGLISH)

**Nigel Higson**(Pennsylvania State Univ.)The Baum-Connes Conjecture and Group Representations (ENGLISH)

[ Abstract ]

The Baum-Connes conjecture asserts a sort of duality between the reduced unitary dual of a group and (a variant of) the classifying space of the group. The conjectured duality occurs at the level of K-theory. For example, for free abelian groups it amounts to a K-theoretic form of Fourier-Mukai duality. The conjecture has well-known applications in topology and geometry, but it also resonates in various ways with Lie groups and representation theory. I'll try to indicate how this comes about, and then focus on a fairly new aspect of the relationship that develops some early ideas of Mackey.

The Baum-Connes conjecture asserts a sort of duality between the reduced unitary dual of a group and (a variant of) the classifying space of the group. The conjectured duality occurs at the level of K-theory. For example, for free abelian groups it amounts to a K-theoretic form of Fourier-Mukai duality. The conjecture has well-known applications in topology and geometry, but it also resonates in various ways with Lie groups and representation theory. I'll try to indicate how this comes about, and then focus on a fairly new aspect of the relationship that develops some early ideas of Mackey.

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Deterministic and stochastic modelling of catalytic surface processes (ENGLISH)

**Jens Starke**(Technical University of Denmark)Deterministic and stochastic modelling of catalytic surface processes (ENGLISH)

[ Abstract ]

Three levels of modelling, the microscopic, the mesoscopic and the macroscopic level are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. The macroscopic description can be derived rigorously for low pressure conditions as limit of the stochastic many particle model for large particle numbers. This is in correspondence with the successful description of experiments under low pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The introduced models include a new approach for the platinum phase transition which allows for a unification of existing models for Pt(100) and Pt(110).

The rich nonlinear dynamical behaviour of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, so-called raindrop patterns which are not captured by earlier models, can be reproduced and are shown in simulations.

This is joint work with M. Eiswirth, H. Rotermund, G. Ertl,

Frith Haber Institut, Berlin, K. Oelschlaeger, University of

Heidelberg and C. Reichert, INSA, Lyon.

Three levels of modelling, the microscopic, the mesoscopic and the macroscopic level are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. The macroscopic description can be derived rigorously for low pressure conditions as limit of the stochastic many particle model for large particle numbers. This is in correspondence with the successful description of experiments under low pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The introduced models include a new approach for the platinum phase transition which allows for a unification of existing models for Pt(100) and Pt(110).

The rich nonlinear dynamical behaviour of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, so-called raindrop patterns which are not captured by earlier models, can be reproduced and are shown in simulations.

This is joint work with M. Eiswirth, H. Rotermund, G. Ertl,

Frith Haber Institut, Berlin, K. Oelschlaeger, University of

Heidelberg and C. Reichert, INSA, Lyon.

### 2010/04/21

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Direct observation of elementary processes of crystal growth by advanced optical microscopy (JAPANESE)

**Gen Sazaki**(Hokkaido University)Direct observation of elementary processes of crystal growth by advanced optical microscopy (JAPANESE)

[ Abstract ]

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

On the interpolation constant over triangular and rectangular elements (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Kenta Kobayashi**(Kanazawa University)On the interpolation constant over triangular and rectangular elements (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

### 2010/04/20

#### Tuesday Seminar on Topology

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

Homotopy of foliations in dimension 3. (ENGLISH)

**Helene Eynard-Bontemps**(東京大学大学院数理科学研究科, JSPS)Homotopy of foliations in dimension 3. (ENGLISH)

[ Abstract ]

We are interested in the connectedness of the space of

codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved

the fundamental result:

Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a

foliation.

W. R. gave a new proof of (and generalized) this result in 1973 using

local constructions. It is then natural to wonder if two foliations with

homotopic tangent plane fields can be linked by a continuous path of

foliations.

A. Larcanch\\'e gave a positive answer in the particular case of

"sufficiently close" taut foliations. We use the key construction of her

proof (among other tools) to show that this is actually always true,

provided one is not too picky about the regularity of the foliations of

the path:

Theorem: Two C^\\infty foliations with homotopic tangent plane fields can

be linked by a path of C^1 foliations.

We are interested in the connectedness of the space of

codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved

the fundamental result:

Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a

foliation.

W. R. gave a new proof of (and generalized) this result in 1973 using

local constructions. It is then natural to wonder if two foliations with

homotopic tangent plane fields can be linked by a continuous path of

foliations.

A. Larcanch\\'e gave a positive answer in the particular case of

"sufficiently close" taut foliations. We use the key construction of her

proof (among other tools) to show that this is actually always true,

provided one is not too picky about the regularity of the foliations of

the path:

Theorem: Two C^\\infty foliations with homotopic tangent plane fields can

be linked by a path of C^1 foliations.

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Proper actions of SL(2,R) on semisimple symmetric spaces (JAPANESE)

**Takayuki Okuda**(the University of Tokyo)Proper actions of SL(2,R) on semisimple symmetric spaces (JAPANESE)

[ Abstract ]

Complex irreducible symmetric spaces which admit proper SL(2,R)-actions were classified by Katsuki Teduka.

In this talk, we generalize Teduka's method and classify semisimple symmetric spaces which admit proper SL(2,R)-actions.

Complex irreducible symmetric spaces which admit proper SL(2,R)-actions were classified by Katsuki Teduka.

In this talk, we generalize Teduka's method and classify semisimple symmetric spaces which admit proper SL(2,R)-actions.

### 2010/04/19

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

制限型体積と因子的ザリスキー分解

**松村 慎一**(東大数理)制限型体積と因子的ザリスキー分解

[ Abstract ]

豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.

(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,

多くの状況で出現する重要な概念である.

様々な部分多様体に沿った制限型体積の振る舞いと

巨大な因子のザリスキー分解可能性の関係について考察したい.

また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に

ついても触れたい.

豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.

(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,

多くの状況で出現する重要な概念である.

様々な部分多様体に沿った制限型体積の振る舞いと

巨大な因子のザリスキー分解可能性の関係について考察したい.

また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に

ついても触れたい.

#### Lectures

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

**Cyrill Muratov**(New Jersey Institute of Technology)Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

[ Abstract ]

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

#### Seminar on Geometric Complex Analysis

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

Loewner's theory on complex manifolds (ENGLISH)

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**Filippo Bracci**(Universita di Roma, ``Tor Vergata'')Loewner's theory on complex manifolds (ENGLISH)

[ Abstract ]

Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

[ Reference URL ]Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

#### Mathematical Biology Seminar

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

骨髄増殖性疾患の起源細胞に関する数理的研究 (JAPANESE)

**Horoshi HAENO**(Memorial Sloan-Kettering Cancer Center)骨髄増殖性疾患の起源細胞に関する数理的研究 (JAPANESE)

### 2010/04/17

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Principal series Whittaker functions on $Sp(2,C)$ (JAPANESE)

A paving of the Siegel 10-fold of positive characteristic (JAPANESE)

**MIYAZAKI Tadashi**(Tokyo Univ. of agr. and indus.) 13:30-14:30Principal series Whittaker functions on $Sp(2,C)$ (JAPANESE)

[ Abstract ]

Not given here.

Not given here.

**HARASHITA Shushi**(Yokohama National Univ.) 15:00-16:00A paving of the Siegel 10-fold of positive characteristic (JAPANESE)

[ Abstract ]

Not given here.

Not given here.

### 2010/04/15

#### Lie Groups and Representation Theory

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

Generalized hypergeometric systems (ENGLISH)

**Uuganbayar Zunderiya**(Nagoya University)Generalized hypergeometric systems (ENGLISH)

[ Abstract ]

A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\\times l$ matrices of derivations with respect to certain variables.

In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.

A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\\times l$ matrices of derivations with respect to certain variables.

In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Long-time behaviour of solutions of a forward-backward parabolic equation

**Alberto Tesei**(University of Rome 1)Long-time behaviour of solutions of a forward-backward parabolic equation

[ Abstract ]

We discuss some recent results concerning the asymptotic behaviour of entropy measure-valued solutions for a class of ill-posed forward-backward parabolic equations, which arise in the theory of phase transitions.

We discuss some recent results concerning the asymptotic behaviour of entropy measure-valued solutions for a class of ill-posed forward-backward parabolic equations, which arise in the theory of phase transitions.

#### Classical Analysis

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

The Galois group of projectively isomonodromic deformations (ENGLISH)

**Claude Mitschi**(Univ. de Strasbourg)The Galois group of projectively isomonodromic deformations (ENGLISH)

[ Abstract ]

Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.

Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.

### 2010/04/14

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The cohomological weighted fundamental lemma

**Gerard Laumon**(CNRS, Universite Paris XI - Orsay)The cohomological weighted fundamental lemma

[ Abstract ]

Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station

--basal plane growth rate and dendritic growth velocity

(JAPANESE)

**Etsuro Yokoyama**(Gakushuin University)Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station

--basal plane growth rate and dendritic growth velocity

(JAPANESE)

### 2010/04/13

#### Tuesday Seminar on Topology

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

Torsors in non-commutative geometry (ENGLISH)

**Christian Kassel**(CNRS, Univ. de Strasbourg)Torsors in non-commutative geometry (ENGLISH)

[ Abstract ]

G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.

G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Strichartz estimates and the Isozaki-Kitada parametrix

on asymptotically hyperbolic manifolds (ENGLISH)

**Jean-Marc Bouclet**(Toulouse University, France)Strichartz estimates and the Isozaki-Kitada parametrix

on asymptotically hyperbolic manifolds (ENGLISH)

### 2010/04/12

#### Seminar on Geometric Complex Analysis

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

Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**千葉 優作**(東大数理)Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

### 2010/04/06

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On the characters of tempered modules of affine Hecke

algebras of classical type

**加藤周**(京都大学)On the characters of tempered modules of affine Hecke

algebras of classical type

[ Abstract ]

We present an inductive algorithm to compute the characters

of tempered modules of an affine Hecke algebras of classical

types, based on a new class of representations which we call

"tempered delimits". They have some geometric origin in the

eDL correspondence.

Our new algorithm has some advantage to the Lusztig-Shoji

algorithm (which also describes the characters of tempered

modules via generalized Green functions) in the sense it

enables us to tell how the characters of tempered modules

changes as the parameters vary.

This is a joint work with Dan Ciubotaru at Utah.

We present an inductive algorithm to compute the characters

of tempered modules of an affine Hecke algebras of classical

types, based on a new class of representations which we call

"tempered delimits". They have some geometric origin in the

eDL correspondence.

Our new algorithm has some advantage to the Lusztig-Shoji

algorithm (which also describes the characters of tempered

modules via generalized Green functions) in the sense it

enables us to tell how the characters of tempered modules

changes as the parameters vary.

This is a joint work with Dan Ciubotaru at Utah.

### 2010/04/05

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

From Lang's Conjecture to finiteness properties of Torelli groups

**Alexandru Dimca**(Université Nice-Sophia Antipolis)From Lang's Conjecture to finiteness properties of Torelli groups

[ Abstract ]

First we recall one of Lang's conjectures in diophantine geometry

on the interplay between subvarieties and translated subgroups in a

commutative algebraic group

(proved by M. Laurent in the case of affine tori in 1984).

Then we present the technique of resonance and characteristic varieties,

a powerful tool in the study of fundamental groups of algebraic varieties.

Finally, using the two ingredients above, we show that the Torelli

groups $T_g$

have some surprising finiteness properties for $g>3$.

In particular, we show that for any subgroup $N$ in $T_g$ containing

the Johnson kernel $K_g$, the complex vector space $N_{ab} \\otimes C$

is finite dimensional.

All the details are available in our joint preprint with S. Papadima

arXiv:1002.0673.

First we recall one of Lang's conjectures in diophantine geometry

on the interplay between subvarieties and translated subgroups in a

commutative algebraic group

(proved by M. Laurent in the case of affine tori in 1984).

Then we present the technique of resonance and characteristic varieties,

a powerful tool in the study of fundamental groups of algebraic varieties.

Finally, using the two ingredients above, we show that the Torelli

groups $T_g$

have some surprising finiteness properties for $g>3$.

In particular, we show that for any subgroup $N$ in $T_g$ containing

the Johnson kernel $K_g$, the complex vector space $N_{ab} \\otimes C$

is finite dimensional.

All the details are available in our joint preprint with S. Papadima

arXiv:1002.0673.

### 2010/03/30

#### GCOE Seminars

10:00-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)

産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)

量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)

Semismooth Newton法の理論、及び応用 (JAPANESE)

TBA (JAPANESE)

**Masahiro Yamamoto**(University of Tokyo) 10:00-10:50産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)

**Shu Nakamura**(University of Tokyo) 11:00-11:50量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)

**Kazufumi Ito**(University of Tokyo, North Carolina State University) 13:20-14:10Semismooth Newton法の理論、及び応用 (JAPANESE)

**Georg Weiss**(University of Tokyo) 14:10-15:00TBA (JAPANESE)

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