## Seminar information archive

Seminar information archive ～02/20｜Today's seminar 02/21 | Future seminars 02/22～

### 2011/09/20

#### Tuesday Seminar on Topology

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

Functorial semi-norms on singular homology (ENGLISH)

**Clara Loeh**(Univ. Regensburg)Functorial semi-norms on singular homology (ENGLISH)

[ Abstract ]

Functorial semi-norms on singular homology add metric information to

homology classes that is compatible with continuous maps. In particular,

functorial semi-norms give rise to degree theorems for certain classes

of manifolds; an invariant fitting into this context is Gromov's

simplicial volume. On the other hand, knowledge about mapping degrees

allows to construct functorial semi-norms with interesting properties;

for example, so-called inflexible simply connected manifolds give rise

to functorial semi-norms that are non-trivial on certain simply connected

spaces.

Functorial semi-norms on singular homology add metric information to

homology classes that is compatible with continuous maps. In particular,

functorial semi-norms give rise to degree theorems for certain classes

of manifolds; an invariant fitting into this context is Gromov's

simplicial volume. On the other hand, knowledge about mapping degrees

allows to construct functorial semi-norms with interesting properties;

for example, so-called inflexible simply connected manifolds give rise

to functorial semi-norms that are non-trivial on certain simply connected

spaces.

### 2011/08/12

#### GCOE Seminars

16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations (ENGLISH)

**Benny Hon**(Department of Mathematics City University of Hong Kong)Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations (ENGLISH)

[ Abstract ]

In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.

In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green’s functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.

### 2011/08/03

#### thesis presentations

10:00-11:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Abundance conjecture and canonical bundle formula (JAPANESE)

**Yoshinori GONGYO**(Graduate School of Mathematical Sciences the University of Tokyo)Abundance conjecture and canonical bundle formula (JAPANESE)

### 2011/07/29

#### Colloquium

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

Arc spaces and algebraic geometry (JAPANESE)

**Shihoko Ishii**(Graduate School of Mathematical Sciences, University of Tokyo)Arc spaces and algebraic geometry (JAPANESE)

### 2011/07/27

#### Number Theory Seminar

16:00-18:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Discriminants and determinant of a hypersurface of even dimension (ENGLISH)

Multiplicities of discriminants (ENGLISH)

**Takeshi Saito**(University of Tokyo) 16:00-17:00Discriminants and determinant of a hypersurface of even dimension (ENGLISH)

[ Abstract ]

The determinant of the cohomology of a smooth hypersurface

of even dimension as a quadratic character of the absolute

Galois group is computed by the discriminant of the de Rham

cohomology. They are also computed by the discriminant of a

defining polynomial. We determine the sign involved by testing

the formula for the Fermat hypersurfaces.

This is a joint work with J-P. Serre.

The determinant of the cohomology of a smooth hypersurface

of even dimension as a quadratic character of the absolute

Galois group is computed by the discriminant of the de Rham

cohomology. They are also computed by the discriminant of a

defining polynomial. We determine the sign involved by testing

the formula for the Fermat hypersurfaces.

This is a joint work with J-P. Serre.

**Dennis Eriksson**(University of Gothenburg) 17:15-18:15Multiplicities of discriminants (ENGLISH)

[ Abstract ]

The discriminant of a homogenous polynomial is another homogenous

polynomial in the coefficients of the polynomial, which is zero

if and only if the corresponding hypersurface is singular. In

case the coefficients are in a discrete valuation ring, the

order of the discriminant (if non-zero) measures the bad

reduction. We give some new results on this order, and in

particular tie it to Bloch's conjecture/the Kato-T.Saito formula

on equality of localized Chern classes and Artin conductors. We

can precisely compute all the numbers in the case of ternary

forms, giving a partial generalization of Ogg's formula for

elliptic curves.

The discriminant of a homogenous polynomial is another homogenous

polynomial in the coefficients of the polynomial, which is zero

if and only if the corresponding hypersurface is singular. In

case the coefficients are in a discrete valuation ring, the

order of the discriminant (if non-zero) measures the bad

reduction. We give some new results on this order, and in

particular tie it to Bloch's conjecture/the Kato-T.Saito formula

on equality of localized Chern classes and Artin conductors. We

can precisely compute all the numbers in the case of ternary

forms, giving a partial generalization of Ogg's formula for

elliptic curves.

### 2011/07/21

#### Operator Algebra Seminars

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

Almost completely isometric maps and applications (ENGLISH)

**Jean Roydor**(Univ. Tokyo)Almost completely isometric maps and applications (ENGLISH)

### 2011/07/14

#### Operator Algebra Seminars

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

New perspectives for the local index formula in noncommutative geometry (ENGLISH)

**Raphael Ponge**(IPMU)New perspectives for the local index formula in noncommutative geometry (ENGLISH)

### 2011/07/13

#### Seminar on Probability and Statistics

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

Statistical Inference for High-Dimension, Low-Sample-Size Data (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/02.html

**YATA, Kazuyoshi**(Institute of Mathematics, University of Tsukuba)Statistical Inference for High-Dimension, Low-Sample-Size Data (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/02.html

### 2011/07/12

#### Tuesday Seminar of Analysis

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

The inclusion relation between Sobolev and modulation spaces (JAPANESE)

**Masaharau Kobayashi**(Tokyo University of Science)The inclusion relation between Sobolev and modulation spaces (JAPANESE)

[ Abstract ]

In this talk, we consider the inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces. As an application, we give mapping properties of unimodular Fourier multiplier $e^{i|D|^\\alpha}$ between $L^p$-Sobolev spaces and modulation spaces.

Joint work with Mitsuru Sugimoto (Nagoya University).

In this talk, we consider the inclusion relations between the $L^p$-Sobolev spaces and the modulation spaces. As an application, we give mapping properties of unimodular Fourier multiplier $e^{i|D|^\\alpha}$ between $L^p$-Sobolev spaces and modulation spaces.

Joint work with Mitsuru Sugimoto (Nagoya University).

#### Tuesday Seminar on Topology

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

The self linking number and planar open book decomposition (ENGLISH)

**Keiko Kawamuro**(University of Iowa)The self linking number and planar open book decomposition (ENGLISH)

[ Abstract ]

I will show a self linking number formula, in language of

braids, for transverse knots in contact manifolds that admit planar

open book decompositions. Our formula extends the Bennequin's for

the standar contact 3-sphere.

I will show a self linking number formula, in language of

braids, for transverse knots in contact manifolds that admit planar

open book decompositions. Our formula extends the Bennequin's for

the standar contact 3-sphere.

### 2011/07/11

#### Seminar on Geometric Complex Analysis

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

Kobayashi hyperbolic imbeddings into toric varieties (JAPANESE)

**Yusaku Chiba**(University of Tokyo)Kobayashi hyperbolic imbeddings into toric varieties (JAPANESE)

### 2011/07/08

#### Classical Analysis

14:30-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)

$q$-Drinfeld-Sokolov hierarchy, $q$-Painlev¥'e equations, and $q$-hypergeometric functions (JAPANESE)

**T. Suzuki**(Osaka Prefecture University)$q$-Drinfeld-Sokolov hierarchy, $q$-Painlev¥'e equations, and $q$-hypergeometric functions (JAPANESE)

### 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.

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