## Seminar information archive

Seminar information archive ～10/22｜Today's seminar 10/23 | Future seminars 10/24～

### 2011/10/19

#### Number Theory Seminar

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

K_2 of the biquaternion algebra (ENGLISH)

[ Reference URL ]

http://www.ihes.fr/~abbes/SGA/suslin.pdf

**Andrei Suslin**(Northwestern University)K_2 of the biquaternion algebra (ENGLISH)

[ Reference URL ]

http://www.ihes.fr/~abbes/SGA/suslin.pdf

### 2011/10/17

#### Seminar on Geometric Complex Analysis

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

Compact locally homogeneous Kähler manifolds $\Gamma\backslash G/K$ (JAPANESE)

**Yoshinobu Kamishima**(Tokyo Metropolitan University)Compact locally homogeneous Kähler manifolds $\Gamma\backslash G/K$ (JAPANESE)

### 2011/10/12

#### Seminar on Probability and Statistics

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html

**SUZUKI, Taiji**(University of Tokyo)On Convergence Rate of Multiple Kernel Learning with Various Regularization Types (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2011/03.html

### 2011/10/11

#### Tuesday Seminar on Topology

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

Making foliations of codimension one,

thirty years after Thurston's works

(ENGLISH)

**Gael Meigniez**(Univ. de Bretagne-Sud, Chuo Univ.)Making foliations of codimension one,

thirty years after Thurston's works

(ENGLISH)

[ Abstract ]

In 1976 Thurston proved that every closed manifold M whose

Euler characteristic is null carries a smooth foliation F of codimension

one. He actually established a h-principle allowing the regularization of

Haefliger structures through homotopy. I shall give some accounts of a new,

simpler proof of Thurston's result, not using Mather's homology equivalence; and also show that this proof allows to make F have dense leaves if dim M is at least 4. The emphasis will be put on the high dimensions.

In 1976 Thurston proved that every closed manifold M whose

Euler characteristic is null carries a smooth foliation F of codimension

one. He actually established a h-principle allowing the regularization of

Haefliger structures through homotopy. I shall give some accounts of a new,

simpler proof of Thurston's result, not using Mather's homology equivalence; and also show that this proof allows to make F have dense leaves if dim M is at least 4. The emphasis will be put on the high dimensions.

#### Tuesday Seminar of Analysis

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

On the best constant of the weighted Trudinger-Moser

type inequality (JAPANESE)

**Hidemitsu Wadade**(Waseda University (JSPS-PD))On the best constant of the weighted Trudinger-Moser

type inequality (JAPANESE)

### 2011/10/07

#### Operator Algebra Seminars

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

Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)

**Takeshi Katsura**(Keio University)Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)

### 2011/10/05

#### Seminar on Mathematics for various disciplines

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

Energetic Variational Approaches for Ionic Fluids (ENGLISH)

**Chun Liu**(University of Tokyo / Pennsylvania State University)Energetic Variational Approaches for Ionic Fluids (ENGLISH)

[ Abstract ]

In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.

In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.

### 2011/10/04

#### Tuesday Seminar on Topology

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

Relatively quasiconvex subgroups of relatively hyperbolic groups (JAPANESE)

**Yoshifumi Matsuda**(The University of Tokyo)Relatively quasiconvex subgroups of relatively hyperbolic groups (JAPANESE)

[ Abstract ]

Relative hyperbolicity of groups was introduced by Gromov as a

generalization of word hyperbolicity. Motivating examples of relatively

hyperbolic groups are fundamental groups of noncompact complete

hyperbolic manifolds of finite volume. The class of relatively

quasiconvex subgroups of a realtively hyperbolic group is defined as a

genaralization of that of quasicovex subgroups of a word hyperbolic

group. The notion of hyperbolically embedded subgroups of a relatively

hyperbolic group was introduced by Osin and such groups are

characterized as relatively quasiconvex subgroups with additional

algebraic properties. In this talk I will present an introduction to

relatively quasiconvex subgroups and discuss recent joint work with Shin

-ichi Oguni and Saeko Yamagata on hyperbolically embedded subgroups.

Relative hyperbolicity of groups was introduced by Gromov as a

generalization of word hyperbolicity. Motivating examples of relatively

hyperbolic groups are fundamental groups of noncompact complete

hyperbolic manifolds of finite volume. The class of relatively

quasiconvex subgroups of a realtively hyperbolic group is defined as a

genaralization of that of quasicovex subgroups of a word hyperbolic

group. The notion of hyperbolically embedded subgroups of a relatively

hyperbolic group was introduced by Osin and such groups are

characterized as relatively quasiconvex subgroups with additional

algebraic properties. In this talk I will present an introduction to

relatively quasiconvex subgroups and discuss recent joint work with Shin

-ichi Oguni and Saeko Yamagata on hyperbolically embedded subgroups.

### 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)

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