## Seminar information archive

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

### 2011/07/06

#### PDE Real Analysis Seminar

10:00-11:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Trace inequality and Morrey spaces (JAPANESE)

**Hitoshi Tanaka**(University of Tokyo)Trace inequality and Morrey spaces (JAPANESE)

### 2011/07/05

#### Numerical Analysis Seminar

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

High-accuracy computation of Goursat-Hardy's integral--- Computation example of unbounded infinite integral---

(JAPANESE)

[ Reference URL ]

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

**Takuya Ooura**(RIMS, Kyoto University)High-accuracy computation of Goursat-Hardy's integral--- Computation example of unbounded infinite integral---

(JAPANESE)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

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

The C*-algebra of codimension one foliations which

are almost without holonomy (ENGLISH)

**Catherine Oikonomides**(The University of Tokyo, JSPS)The C*-algebra of codimension one foliations which

are almost without holonomy (ENGLISH)

[ Abstract ]

Foliation C*-algebras have been defined abstractly by Alain Connes,

in the 1980s, as part of the theory of Noncommutative Geometry.

However, very few concrete examples of foliation C*-algebras

have been studied until now.

In this talk, we want to explain how to compute

the K-theory of the C*-algebra of codimension

one foliations which are "almost without holonomy",

meaning that the holonomy of all the noncompact leaves

of the foliation is trivial. Such foliations have a fairly

simple geometrical structure, which is well known thanks

to theorems by Imanishi, Hector and others. We will give some

concrete examples on 3-manifolds, in particular the 3-sphere

with the Reeb foliation, and also some slighty more

complicated examples.

Foliation C*-algebras have been defined abstractly by Alain Connes,

in the 1980s, as part of the theory of Noncommutative Geometry.

However, very few concrete examples of foliation C*-algebras

have been studied until now.

In this talk, we want to explain how to compute

the K-theory of the C*-algebra of codimension

one foliations which are "almost without holonomy",

meaning that the holonomy of all the noncompact leaves

of the foliation is trivial. Such foliations have a fairly

simple geometrical structure, which is well known thanks

to theorems by Imanishi, Hector and others. We will give some

concrete examples on 3-manifolds, in particular the 3-sphere

with the Reeb foliation, and also some slighty more

complicated examples.

### 2011/07/04

#### Algebraic Geometry Seminar

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

Birational Geometry of O'Grady's six dimensional example over the Donaldson-Uhlenbeck compactification (JAPANESE)

**Yasunari Nagai**(Waseda University)Birational Geometry of O'Grady's six dimensional example over the Donaldson-Uhlenbeck compactification (JAPANESE)

[ Abstract ]

O'Grady constructed two sporadic examples of compact irreducible symplectic Kaehler manifold, by resolving singular moduli spaces of sheaves on a K3 surface or an abelian surface. We will give a full description of the birational geometry of O'Grady's six dimensional example over the corresponding Donaldson-Uhlenbeck compactification, using an explicit calculation of certain kind of GIT quotients.

If time permits, we will also discuss an involution of the example induced by a Fourier-Mukai transformation.

O'Grady constructed two sporadic examples of compact irreducible symplectic Kaehler manifold, by resolving singular moduli spaces of sheaves on a K3 surface or an abelian surface. We will give a full description of the birational geometry of O'Grady's six dimensional example over the corresponding Donaldson-Uhlenbeck compactification, using an explicit calculation of certain kind of GIT quotients.

If time permits, we will also discuss an involution of the example induced by a Fourier-Mukai transformation.

#### Seminar on Geometric Complex Analysis

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

Toward a Hirzebruch-Riemann-Roch formula in CR geometry (ENGLISH)

**Raphael Ponge**(University of Tokyo)Toward a Hirzebruch-Riemann-Roch formula in CR geometry (ENGLISH)

### 2011/06/30

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

On the macroscopic models for type-II superconductivity in 3D (JAPANESE)

**Yohei Kashima**(Graduate School of Mathematical Sciences, The University of Tokyo)On the macroscopic models for type-II superconductivity in 3D (JAPANESE)

### 2011/06/29

#### Seminar on Mathematics for various disciplines

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

Computational understanding of diverse structures in human anatomy by landmark detection in medical images (JAPANESE)

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

**Yoshitaka Masutani**(University of Tokyo)Computational understanding of diverse structures in human anatomy by landmark detection in medical images (JAPANESE)

[ Abstract ]

Robust recognition of anatomical structures in medical images is indispensable for clinical support of diagnosis and therapy. In this lecture, the diverse system of human anatomy is shortly introduced first. Then, the overview of detection techniques for such structures in medical images is shown. Finally, our approach of anatomical structure recognition is presented and is discussed, which is realized by a unified framework of landmark detection based on appearance model matching and MAP estimation on inter-landmark distance probabilities.

[ Reference URL ]Robust recognition of anatomical structures in medical images is indispensable for clinical support of diagnosis and therapy. In this lecture, the diverse system of human anatomy is shortly introduced first. Then, the overview of detection techniques for such structures in medical images is shown. Finally, our approach of anatomical structure recognition is presented and is discussed, which is realized by a unified framework of landmark detection based on appearance model matching and MAP estimation on inter-landmark distance probabilities.

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

#### Seminar on Probability and Statistics

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Statistics in genetic association studies (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/01.html

**OKADA, Yukinori**(Laboratory for Statistical Analysis, Center for Genomic Medicine, RIKEN)Statistics in genetic association studies (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/01.html

### 2011/06/28

#### Tuesday Seminar on Topology

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

On a Sebastiani-Thom theorem for directed Fukaya categories (JAPANESE)

**Masahiro Futaki**(The University of Tokyo)On a Sebastiani-Thom theorem for directed Fukaya categories (JAPANESE)

[ Abstract ]

The directed Fukaya category defined by Seidel is a "

categorification" of the Milnor lattice of hypersurface singularities.

Sebastiani-Thom showed that the Milnor lattice and its monodromy behave

as tensor product for the sum of singularities. A directed Fukaya

category version of this theorem was conjectured by Auroux-Katzarkov-

Orlov (and checked for the Landau-Ginzburg mirror of P^1 \\times P^1). In

this talk I introduce the directed Fukaya category and show that a

Sebastiani-Thom type splitting holds in the case that one of the

potential is of complex dimension 1.

The directed Fukaya category defined by Seidel is a "

categorification" of the Milnor lattice of hypersurface singularities.

Sebastiani-Thom showed that the Milnor lattice and its monodromy behave

as tensor product for the sum of singularities. A directed Fukaya

category version of this theorem was conjectured by Auroux-Katzarkov-

Orlov (and checked for the Landau-Ginzburg mirror of P^1 \\times P^1). In

this talk I introduce the directed Fukaya category and show that a

Sebastiani-Thom type splitting holds in the case that one of the

potential is of complex dimension 1.

### 2011/06/27

#### Seminar on Geometric Complex Analysis

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

Vanishing cycles for the entire functions of type $A_{1/2\infty}$ and $D_{1/2\infty}$ (JAPANESE)

**Kyoji Saito**(IPMU, University of Tokyo)Vanishing cycles for the entire functions of type $A_{1/2\infty}$ and $D_{1/2\infty}$ (JAPANESE)

[ Abstract ]

We introduce two elementary transcendental functions $f_{A_{1/2\infty}}$ and $f_{D_{1/2\infty}}$ of two variables. They have countably infinitely many critical points. Then, the vanishing cycles associated with the critical points form Dynkin diagrams of type $A_{1/2\infty}$ and $D_{1/2\infty}$. We calculate the spectral decomposition of the monodromy transformation by embedding the lattice of vanishing cycles into a Hilbert space. All these stories are connected with a new understanding of KP and KdV integral hierarchy. But the relationship is not yet clear.

We introduce two elementary transcendental functions $f_{A_{1/2\infty}}$ and $f_{D_{1/2\infty}}$ of two variables. They have countably infinitely many critical points. Then, the vanishing cycles associated with the critical points form Dynkin diagrams of type $A_{1/2\infty}$ and $D_{1/2\infty}$. We calculate the spectral decomposition of the monodromy transformation by embedding the lattice of vanishing cycles into a Hilbert space. All these stories are connected with a new understanding of KP and KdV integral hierarchy. But the relationship is not yet clear.

#### Algebraic Geometry Seminar

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

MMP revisited, II (ENGLISH)

**Vladimir Lazić**(Imperial College London)MMP revisited, II (ENGLISH)

[ Abstract ]

I will talk about how finite generation of certain adjoint rings implies everything we currently know about the MMP. This is joint work with A. Corti.

I will talk about how finite generation of certain adjoint rings implies everything we currently know about the MMP. This is joint work with A. Corti.

### 2011/06/24

#### thesis presentations

13:15-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Spatial-temporal Modeling and Simulation of Transcription (JAPANESE)

**Yoshihiro OTA**(Graduate School of Mathematical Sciences University of Tokyo)Spatial-temporal Modeling and Simulation of Transcription (JAPANESE)

#### Classical Analysis

15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)

A Schwarz map of Appell's $F_2$ whose monodromy group is

related to the reflection group of type $D_4$ (JAPANESE)

**J. Sekiguchi**(Tokyo University of Agriculture and Technology)A Schwarz map of Appell's $F_2$ whose monodromy group is

related to the reflection group of type $D_4$ (JAPANESE)

[ Abstract ]

The system of differential equations for Appell's hypergeometric function $F_2(a,b,b',c,c';x,y)$ has four fundamental solutions.

Let $u_1,u_2,u_3,u_4$ be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map $U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y))$

is a hypersurface $S$ of the 3-dimensional projective space ${\\bf P}^3$. Then $S$ is defined by $P(u_1,u_2,u_3,u_4)=0$ for a polynomial $P(t_1,t_2,t_3,t_4)$.

It is M. Kato (Univ. Ryukyus) who determined the parameter

$a,b,b',c,c'$ such that the monodromy group of the system for $F_2(a,b,b',c,c';x,y)$ is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group $G$ of rank four by an abelian group.

In this talk, we treat the system for $F_2(a,b,b',c,c';x,y)$ with

$(a,b,b',c,c')=(1/2,1/6,-1/6,1/3,2/3$. In this case, the monodromy group is the semidirect group of $G$ by $Z/3Z$, where $G$ is the reflection group of type $D_4$. The polynomial $P(t_1,t_2,t_3,t_4)$ in this case is of degree four. There are 16 ordinary singular points in the hypersurface $S$.

In the rest of my talk, I explain the background of the study.

The system of differential equations for Appell's hypergeometric function $F_2(a,b,b',c,c';x,y)$ has four fundamental solutions.

Let $u_1,u_2,u_3,u_4$ be such solutions. If the monodromy group of the system is finite, the closure of the image of the Schwarz map $U(x,y)=(u_1(x,y),u_2(x,y),u_3(x,y),u_4(x,y))$

is a hypersurface $S$ of the 3-dimensional projective space ${\\bf P}^3$. Then $S$ is defined by $P(u_1,u_2,u_3,u_4)=0$ for a polynomial $P(t_1,t_2,t_3,t_4)$.

It is M. Kato (Univ. Ryukyus) who determined the parameter

$a,b,b',c,c'$ such that the monodromy group of the system for $F_2(a,b,b',c,c';x,y)$ is finite. It follows from his result that such a group is the semidirect product of an irreducible finite reflection group $G$ of rank four by an abelian group.

In this talk, we treat the system for $F_2(a,b,b',c,c';x,y)$ with

$(a,b,b',c,c')=(1/2,1/6,-1/6,1/3,2/3$. In this case, the monodromy group is the semidirect group of $G$ by $Z/3Z$, where $G$ is the reflection group of type $D_4$. The polynomial $P(t_1,t_2,t_3,t_4)$ in this case is of degree four. There are 16 ordinary singular points in the hypersurface $S$.

In the rest of my talk, I explain the background of the study.

#### Colloquium

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

On logarithmic extension of p-adic differential equations (JAPANESE)

**Jun SHIHO**(Graduate School of Mathematical Sciences, University of Tokyo)On logarithmic extension of p-adic differential equations (JAPANESE)

### 2011/06/22

#### Seminar on Probability and Statistics

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

計算機代数を用いた統計的漸近論 (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/00.html

**KOBAYASHI, Kei**(The Institute of Statistical Mathematics)計算機代数を用いた統計的漸近論 (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/00.html

### 2011/06/21

#### Numerical Analysis Seminar

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

Research on CFD (Computational Fluid Dynamics) and Its Application to Development of Spacecraft and Rockets

(JAPANESE)

[ Reference URL ]

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

**Keiichi Kitamura**(Japan Aerospace Exploration Agency (JAXA))Research on CFD (Computational Fluid Dynamics) and Its Application to Development of Spacecraft and Rockets

(JAPANESE)

[ Reference URL ]

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

### 2011/06/20

#### Seminar on Geometric Complex Analysis

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

Domains which satisfy the Oka-Grauert principle in a Stein space (JAPANESE)

**Makoto Abe**(Hiroshima University)Domains which satisfy the Oka-Grauert principle in a Stein space (JAPANESE)

### 2011/06/16

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Introduction to rigidity theory of von Neumann algebras (JAPANESE)

**Yusuke Isono**(Univ. Tokyo)Introduction to rigidity theory of von Neumann algebras (JAPANESE)

### 2011/06/15

#### Number Theory Seminar

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

Product formula for $p$-adic epsilon factors (ENGLISH)

**Tomoyuki Abe**(IPMU)Product formula for $p$-adic epsilon factors (ENGLISH)

[ Abstract ]

I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.

I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.

### 2011/06/14

#### Tuesday Seminar on Topology

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Donaldson-Tian-Yau's Conjecture (JAPANESE)

**Toshiki Mabuchi**(Osaka University)Donaldson-Tian-Yau's Conjecture (JAPANESE)

[ Abstract ]

For polarized algebraic manifolds, the concept of K-stability

introduced by Tian and Donaldson is conjecturally strongly correlated

to the existence of constant scalar curvature metrics (or more

generally extremal K\\"ahler metrics) in the polarization class. This is

known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable

progress has been made by many authors toward its solution. In this

talk, I'll discuss the topic mainly with emphasis on the existence

part of the conjecture.

For polarized algebraic manifolds, the concept of K-stability

introduced by Tian and Donaldson is conjecturally strongly correlated

to the existence of constant scalar curvature metrics (or more

generally extremal K\\"ahler metrics) in the polarization class. This is

known as Donaldson-Tian-Yau's conjecture. Recently, a remarkable

progress has been made by many authors toward its solution. In this

talk, I'll discuss the topic mainly with emphasis on the existence

part of the conjecture.

### 2011/06/13

#### Seminar on Geometric Complex Analysis

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

On the complement of effective divisors with semipositive normal bundle (JAPANESE)

**Takeo Ohsawa**(Nagoya Univeristy)On the complement of effective divisors with semipositive normal bundle (JAPANESE)

#### Lectures

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)

**CHEN Hua**(Wuhan University)Regularity of Solutions for a Class of Degenerate Equations (ENGLISH)

[ Abstract ]

In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including

(1) generalized Kolmogorov equations,

(2) Fokker-Planck equations,

(3) Landau equations and

(4) sub-elliptic Monge-Ampere equations.

In this talk, I would report some recent joint results on the Gevrey (or analytic) regularities of solutions for some degenerate partial differential equations, which including

(1) generalized Kolmogorov equations,

(2) Fokker-Planck equations,

(3) Landau equations and

(4) sub-elliptic Monge-Ampere equations.

### 2011/06/09

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)

**Hiroaki Yoshida**(Ochanomizu Univ.)On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)

#### Applied Analysis

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

Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)

**Kiyoshi Mochizuki**(Tokyo Metropolitan University, Emeritus Professor)Spectral representations and scattering for Schr\\"odinger operators on star graphs (JAPANESE)

[ Abstract ]

We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.

We consider Schr\\"odinger operators defined on star graphs with Kirchhoff boundary conditions. Under suitable decay conditions on the potential, we construct a complete set of eigenfunctions to obtain spectral representations of the operator. The results are applied to give a time dependent formulation of the scattering theory. Also we use the spectral representation to determine an integral equation of Marchenko which is fundamental to enter into the inverse scattering problems.

### 2011/06/08

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Congruences of modular forms and the Iwasawa λ-invariants (JAPANESE)

**Yuichi Hirano**(University of Tokyo)Congruences of modular forms and the Iwasawa λ-invariants (JAPANESE)

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