## Seminar information archive

Seminar information archive ～02/18｜Today's seminar 02/19 | Future seminars 02/20～

### 2013/06/03

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Generalized deformation theory of CR structures (JAPANESE)

**Takao Akahori**(University of Hyogo)Generalized deformation theory of CR structures (JAPANESE)

[ Abstract ]

Let $(M, {}^0 T^{''})$ be a compact strongly pseudo convex CR manifold with dimension $2n-1 \geq 5$, embedded in a complex manifold $N$ as a real hypersurface. In our former papers (T. Akahori, Invent. Math. 63 (1981); T. Akahori, P. M. Garfield, and J. M. Lee, Michigan Math. J. 50 (2002)), we constructed the versal family of CR structures. The purpose of this talk is to show that in more wide scope, our family is versal.

Let $(M, {}^0 T^{''})$ be a compact strongly pseudo convex CR manifold with dimension $2n-1 \geq 5$, embedded in a complex manifold $N$ as a real hypersurface. In our former papers (T. Akahori, Invent. Math. 63 (1981); T. Akahori, P. M. Garfield, and J. M. Lee, Michigan Math. J. 50 (2002)), we constructed the versal family of CR structures. The purpose of this talk is to show that in more wide scope, our family is versal.

### 2013/05/31

#### Colloquium

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

Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)

**Yasuhito MIYAMOTO**(Graduate School of Mathematical Sciences, The University of Tokyo)Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)

### 2013/05/30

#### FMSP Lectures

13:00-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Low-dimensional linear representations of mapping class groups (III) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups (III) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

### 2013/05/29

#### FMSP Lectures

13:00-14:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Low-dimensional linear representations of mapping class groups (II) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups (II) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

#### Number Theory Seminar

16:40-17:40 Room #002 (Graduate School of Math. Sci. Bldg.)

On logarithmic nonabelian Hodge theory of higher level in characteristic p (JAPANESE)

**Sachio Ohkawa**(University of Tokyo)On logarithmic nonabelian Hodge theory of higher level in characteristic p (JAPANESE)

[ Abstract ]

Ogus and Vologodsky studied a positive characteristic analogue of Simpson’s nonanelian Hodge theory over the complex number field. Now most part of their theory has been generalized to the case of log schemes by Schepler. In this talk, we generalize the global Cartier transform, which is one of the main theorem in nonabelian Hodge theory in positive characteristic, to the case of log schemes and of higher level. This can be regarded as a higher level version of a result of Schepler.

Ogus and Vologodsky studied a positive characteristic analogue of Simpson’s nonanelian Hodge theory over the complex number field. Now most part of their theory has been generalized to the case of log schemes by Schepler. In this talk, we generalize the global Cartier transform, which is one of the main theorem in nonabelian Hodge theory in positive characteristic, to the case of log schemes and of higher level. This can be regarded as a higher level version of a result of Schepler.

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On full group C*-algebras of discrete quantum groups (ENGLISH)

**Yuki Arano**(Univ. Tokyo)On full group C*-algebras of discrete quantum groups (ENGLISH)

### 2013/05/28

#### FMSP Lectures

17:10-18:40 Room #117 (Graduate School of Math. Sci. Bldg.)

Low-dimensional linear representations of mapping class groups (I) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

**Mustafa Korkmaz**(Middle East Technical University)Low-dimensional linear representations of mapping class groups (I) (ENGLISH)

[ Reference URL ]

http://faculty.ms.u-tokyo.ac.jp/~topology/Korkmaz.pdf

### 2013/05/27

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

2次元擬斉次特異点の接層のコホモロジーについて (JAPANESE)

**Tomohiro Okuma**(Yamagata University)2次元擬斉次特異点の接層のコホモロジーについて (JAPANESE)

[ Abstract ]

複素2次元特異点の特異点解消上の接層のコホモロジーの次元は解析的不変量である. セミナーでは, リンクが有理ホモロジー球面であるような2次元擬斉次特異点の場合にはそれが位相的不変量であり, グラフから計算できることを紹介する.

複素2次元特異点の特異点解消上の接層のコホモロジーの次元は解析的不変量である. セミナーでは, リンクが有理ホモロジー球面であるような2次元擬斉次特異点の場合にはそれが位相的不変量であり, グラフから計算できることを紹介する.

### 2013/05/25

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Multilinear fractional integral operators on weighted Morrey spaces (JAPANESE)

On factorization of divergence form elliptic operators

and its application

(JAPANESE)

**Takeshi Iida**(Fukushima National College of Technology) 13:30-15:00Multilinear fractional integral operators on weighted Morrey spaces (JAPANESE)

**Yasunori Maekawa**(Tohoku University) 15:30-17:00On factorization of divergence form elliptic operators

and its application

(JAPANESE)

### 2013/05/24

#### Lectures

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

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (JAPANESE)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (JAPANESE)

### 2013/05/21

#### Tuesday Seminar of Analysis

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

Homogenization in a Thin Layer with an Oscillating Interface and Highly Contrast Coefficients (JAPANESE)

**Masaaki Uesaka**(Graduate School of Mathematical Sciences, The University of Tokyo)Homogenization in a Thin Layer with an Oscillating Interface and Highly Contrast Coefficients (JAPANESE)

[ Abstract ]

We consider the homogenization problem of the elliptic boundary value problem in a thin domain which has a high and low conductivity zones. In our model, two media are separated by a highly oscillating interface. The asymptotic behavior is governed by the order of the thickness of the domain, oscillation period of the interface and contrast between two media. In this talk, we show that the limit problem is changed by these parameters. We also introduce the two-scale convergence result in a thin domain which is the key ingredient of the proof.

We consider the homogenization problem of the elliptic boundary value problem in a thin domain which has a high and low conductivity zones. In our model, two media are separated by a highly oscillating interface. The asymptotic behavior is governed by the order of the thickness of the domain, oscillation period of the interface and contrast between two media. In this talk, we show that the limit problem is changed by these parameters. We also introduce the two-scale convergence result in a thin domain which is the key ingredient of the proof.

#### Lectures

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

#### Tuesday Seminar on Topology

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

A Heegaard Floer homology for bipartite spatial graphs and its

properties (ENGLISH)

**Yuanyuan Bao**(The University of Tokyo)A Heegaard Floer homology for bipartite spatial graphs and its

properties (ENGLISH)

[ Abstract ]

A spatial graph is a smooth embedding of a graph into a given

3-manifold. We can regard a link as a particular spatial graph.

So it is natural to ask whether it is possible to extend the idea

of link Floer homology to define a Heegaard Floer homology for

spatial graphs. In this talk, we discuss some ideas towards this

question. In particular, we define a Heegaard Floer homology for

bipartite spatial graphs and discuss some further observations

about this construction. We remark that Harvey and O’Donnol

have announced a combinatorial Floer homology for spatial graphs by

considering grid diagrams.

A spatial graph is a smooth embedding of a graph into a given

3-manifold. We can regard a link as a particular spatial graph.

So it is natural to ask whether it is possible to extend the idea

of link Floer homology to define a Heegaard Floer homology for

spatial graphs. In this talk, we discuss some ideas towards this

question. In particular, we define a Heegaard Floer homology for

bipartite spatial graphs and discuss some further observations

about this construction. We remark that Harvey and O’Donnol

have announced a combinatorial Floer homology for spatial graphs by

considering grid diagrams.

### 2013/05/20

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

レヴィ平坦面の分類に関する最近の進展 (JAPANESE)

**Takeo Ohsawa**(Nagoya University)レヴィ平坦面の分類に関する最近の進展 (JAPANESE)

[ Abstract ]

レヴィ平坦面の分類がCP^2の場合にできていないことから、種々の興味深い問題が生じているように思われる。ここではトーラスの場合に観察されたことをホップ曲面に拡げたとき、ホップ曲面においてならレヴィ平坦面の分類が(実解析的な場合に限るが)完全にできることを報告する。

レヴィ平坦面の分類がCP^2の場合にできていないことから、種々の興味深い問題が生じているように思われる。ここではトーラスの場合に観察されたことをホップ曲面に拡げたとき、ホップ曲面においてならレヴィ平坦面の分類が(実解析的な場合に限るが)完全にできることを報告する。

### 2013/05/17

#### Seminar on Probability and Statistics

13:30-14:40 Room #052 (Graduate School of Math. Sci. Bldg.)

Computing the normalizing constant of the Bingham family by the holonomic gradient method (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/00.html

**SEI, Tomonari**(Department of Mathematics, Keio University)Computing the normalizing constant of the Bingham family by the holonomic gradient method (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/00.html

### 2013/05/16

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

A generalization of Taub-NUT deformations (JAPANESE)

**Kota Hattori**(University of Tokyo)A generalization of Taub-NUT deformations (JAPANESE)

[ Abstract ]

Taub-NUT metric on C^2 is a complete Ricci-flat Kaehler metric which is not flat. It is obtained by the Taub-NUT deformations of the Euclidean metric on C^2 using an S^1 action. Taub-NUT deformations are known to be defined for toric hyperKaehler manifolds, and deform ALE metrics to non-ALE metrics. In this talk, I explain a generalization of Taub-NUT deformations by using noncommutative Lie groups.

Taub-NUT metric on C^2 is a complete Ricci-flat Kaehler metric which is not flat. It is obtained by the Taub-NUT deformations of the Euclidean metric on C^2 using an S^1 action. Taub-NUT deformations are known to be defined for toric hyperKaehler manifolds, and deform ALE metrics to non-ALE metrics. In this talk, I explain a generalization of Taub-NUT deformations by using noncommutative Lie groups.

### 2013/05/15

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Rohlin Flows on Amalgamated Free Product Factors (ENGLISH)

**Koichi Shimada**(Univ. Tokyo)Rohlin Flows on Amalgamated Free Product Factors (ENGLISH)

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

Special values of zeta functions of singular varieties over finite fields via higher chow groups (JAPANESE)

**Hiroyasu Miyazaki**(University of Tokyo)Special values of zeta functions of singular varieties over finite fields via higher chow groups (JAPANESE)

### 2013/05/14

#### Tuesday Seminar on Topology

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

Vanishing cycles and homotopies of wrinkled fibrations (JAPANESE)

**Kenta Hayano**(Osaka University)Vanishing cycles and homotopies of wrinkled fibrations (JAPANESE)

[ Abstract ]

Wrinkled fibrations on closed 4-manifolds are stable

maps to closed surfaces with only indefinite singularities. Such

fibrations and variants of them have been studied for the past few years

to obtain new descriptions of 4-manifolds using mapping class groups.

Vanishing cycles of wrinkled fibrations play a key role in these studies.

In this talk, we will explain how homotopies of wrinkled fibrtions affect

their vanishing cycles. Part of the results in this talk is a joint work

with Stefan Behrens (Max Planck Institute for Mathematics).

Wrinkled fibrations on closed 4-manifolds are stable

maps to closed surfaces with only indefinite singularities. Such

fibrations and variants of them have been studied for the past few years

to obtain new descriptions of 4-manifolds using mapping class groups.

Vanishing cycles of wrinkled fibrations play a key role in these studies.

In this talk, we will explain how homotopies of wrinkled fibrtions affect

their vanishing cycles. Part of the results in this talk is a joint work

with Stefan Behrens (Max Planck Institute for Mathematics).

#### Lectures

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

### 2013/05/13

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Geometry and analysis of isolated essential singularities and their applications (JAPANESE)

**Yusuke Okuyama**(Kyoto Institute of Technology)Geometry and analysis of isolated essential singularities and their applications (JAPANESE)

[ Abstract ]

We establish a rescaling principle for isolated essential singularities of holomorphic curves and quasiregular mappings, and gives several applications of it in the theory of value distribution and dynamics. This is a joint work with Pekka Pankka.

We establish a rescaling principle for isolated essential singularities of holomorphic curves and quasiregular mappings, and gives several applications of it in the theory of value distribution and dynamics. This is a joint work with Pekka Pankka.

### 2013/05/11

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

Symplectic-orthogonal theta lifts and explicit formulas for archimedean Whittaker functions (JAPANESE)

Infinite product represenation of the Mumford form and its application to the values of Selberg zeta functions (JAPANESE)

**Taku Ishii**(Seikei Univeristy) 13:30-14:30Symplectic-orthogonal theta lifts and explicit formulas for archimedean Whittaker functions (JAPANESE)

**Takashi Ichikawa**(Saga University) 15:00-16:00Infinite product represenation of the Mumford form and its application to the values of Selberg zeta functions (JAPANESE)

#### Infinite Analysis Seminar Tokyo

10:30-12:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Saga of Dunkl elements (ENGLISH)

**Anatol Kirillov**(RIMS Kyoto Univ.)Saga of Dunkl elements (ENGLISH)

[ Abstract ]

The Dunkl operators has been introduced by C. Dunkl in the middle of

80's of the last century as a powerful mean in the study of orthogonal

polynomials related with finite Coxeter groups. Later it was discovered

a deep connection of the the Dunkl operators with the theory of

Integrable systems and Invariant Theory.

In my talk I introduce and study a certain class of nonhomogeneous

quadratic algebras together with the distinguish set of mutually

commuting elements inside of each, the so-called universal Dunkl elements.

The main problem I would like to discuss is : What is the algebra

generated by universal Dunkl elements in a different representations of

the quadratic algebra introduced ?

I'm planning to present partial answers on that problem related with

classical and quantum Schubert and Grothendieck Calculi as well as the

theory of elliptic series.

Also some interesting algebraic properties of the quadratic algebra(s)

in question will be described.

The Dunkl operators has been introduced by C. Dunkl in the middle of

80's of the last century as a powerful mean in the study of orthogonal

polynomials related with finite Coxeter groups. Later it was discovered

a deep connection of the the Dunkl operators with the theory of

Integrable systems and Invariant Theory.

In my talk I introduce and study a certain class of nonhomogeneous

quadratic algebras together with the distinguish set of mutually

commuting elements inside of each, the so-called universal Dunkl elements.

The main problem I would like to discuss is : What is the algebra

generated by universal Dunkl elements in a different representations of

the quadratic algebra introduced ?

I'm planning to present partial answers on that problem related with

classical and quantum Schubert and Grothendieck Calculi as well as the

theory of elliptic series.

Also some interesting algebraic properties of the quadratic algebra(s)

in question will be described.

### 2013/05/10

#### Lectures

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

**Laurent Lafforgue**(IHES)Kernels of Langlands' automorphic transfer and non-linear Poisson formulas (ENGLISH)

### 2013/05/09

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Rigidity for amalgamated free products and their envelopes (JAPANESE)

**KIDA Yoshikata**(Kyoto University)Rigidity for amalgamated free products and their envelopes (JAPANESE)

[ Abstract ]

For a discrete countable group L, we mean by an envelope of L a locally compact second countable group having a lattice isomorphic to L. In general, it is quite hard to describe all envelopes of a given L. This problem is closely related to orbit equivalence between probability-measure-preserving actions of groups, and also related to Mostow type rigidity. I explain a fundamental idea to attack this problem, and give examples of groups for which the problem is solved. The examples contain mapping class groups of surfaces and certain amalgamated free products. An outline to get an answer for the latter groups will be discussed.

For a discrete countable group L, we mean by an envelope of L a locally compact second countable group having a lattice isomorphic to L. In general, it is quite hard to describe all envelopes of a given L. This problem is closely related to orbit equivalence between probability-measure-preserving actions of groups, and also related to Mostow type rigidity. I explain a fundamental idea to attack this problem, and give examples of groups for which the problem is solved. The examples contain mapping class groups of surfaces and certain amalgamated free products. An outline to get an answer for the latter groups will be discussed.

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