## Seminar information archive

Seminar information archive ～02/19｜Today's seminar 02/20 | Future seminars 02/21～

### 2014/05/02

#### Colloquium

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

From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)

**A.P. Veselov**(Loughborough, UK and Tokyo, Japan)From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)

[ Abstract ]

Gaudin subalgebras are abelian Lie subalgebras of maximal

dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,

associated to A-type hyperplane arrangement.

It turns out that Gaudin subalgebras form a smooth algebraic variety

isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of

stable genus zero curves with n+1 marked points.

A real version of this result allows to describe the

moduli space of integrable n-dimensional tops and

separation coordinates on the unit sphere

in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.

Schoebel.

Gaudin subalgebras are abelian Lie subalgebras of maximal

dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,

associated to A-type hyperplane arrangement.

It turns out that Gaudin subalgebras form a smooth algebraic variety

isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of

stable genus zero curves with n+1 marked points.

A real version of this result allows to describe the

moduli space of integrable n-dimensional tops and

separation coordinates on the unit sphere

in terms of the geometry of Stasheff polytope.

The talk is based on joint works with L. Aguirre and G. Felder and with K.

Schoebel.

### 2014/04/30

#### Number Theory Seminar

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

An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)

**Takuya Maruyama**(University of Tokyo)An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)

#### Operator Algebra Seminars

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

Noncommutative real algebraic geometry of Kazhdan's property (T) (ENGLISH)

**Narutaka Ozawa**(RIMS, Kyoto University)Noncommutative real algebraic geometry of Kazhdan's property (T) (ENGLISH)

### 2014/04/28

#### Seminar on Geometric Complex Analysis

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

On the existence problem of Kähler-Ricci solitons (JAPANESE)

**Sunsuke Saito**(The University of Tokyo)On the existence problem of Kähler-Ricci solitons (JAPANESE)

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Syzygies of jacobian ideals and Torelli properties (ENGLISH)

**Alexandru Dimca**(Institut Universitaire de France )Syzygies of jacobian ideals and Torelli properties (ENGLISH)

[ Abstract ]

Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.

Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.

### 2014/04/26

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)

Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)

**Ryutarou Okazaki**(Doushisha Univ. until March, 2014) 13:30-14:30The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)

**Ryutarou Okazaki**(Doushisha Univ. until March, 2014) 15:00-16:00Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)

### 2014/04/24

#### Geometry Colloquium

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

On rigidity of Lie foliations (JAPANESE)

**Hiraku Nozawa**(Ritsumeikan University)On rigidity of Lie foliations (JAPANESE)

[ Abstract ]

If the leaves of a Lie foliation are isometric to a symmetric space of noncompact type of higher rank, then, by a theorem of Zimmer, the holonomy group of the Lie foliation has rigidity similar to that of lattices of semisimple Lie groups of higher rank. The main result of this talk is a generalization of Zimmer's theorem including the case of real rank one based on an application of a variant of Mostow rigidity. (This talk is based on a joint work with Ga¥"el Meigniez.)

If the leaves of a Lie foliation are isometric to a symmetric space of noncompact type of higher rank, then, by a theorem of Zimmer, the holonomy group of the Lie foliation has rigidity similar to that of lattices of semisimple Lie groups of higher rank. The main result of this talk is a generalization of Zimmer's theorem including the case of real rank one based on an application of a variant of Mostow rigidity. (This talk is based on a joint work with Ga¥"el Meigniez.)

### 2014/04/23

#### Operator Algebra Seminars

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

Bost-Connes system for local fields of characteristic zero (ENGLISH)

**Takuya Takeishi**(Univ. Tokyo)Bost-Connes system for local fields of characteristic zero (ENGLISH)

#### Number Theory Seminar

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

Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)

**Yoichi Mieda**(University of Tokyo)Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)

#### Mathematical Biology Seminar

14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Age-structured epidemic model with infection during transportation (JAPANESE)

**Yukihiko Nakata**(Graduate School of Mathematical Sciences, University of Tokyo)Age-structured epidemic model with infection during transportation (JAPANESE)

### 2014/04/22

#### Tuesday Seminar of Analysis

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

Bounded small solutions to a chemotaxis system with

non-diffusive chemical (JAPANESE)

**Yohei Tsutsui**(The University of Tokyo)Bounded small solutions to a chemotaxis system with

non-diffusive chemical (JAPANESE)

[ Abstract ]

We consider a chemotaxis system with a logarithmic

sensitivity and a non-diffusive chemical substance. For some chemotactic

sensitivity constants, Ahn and Kang proved the existence of bounded

global solutions to the system. An entropy functional was used in their

argument to control the cell density by the density of the chemical

substance. Our purpose is to show the existence of bounded global

solutions for all the chemotactic sensitivity constants. Assuming the

smallness on the initial data in some sense, we can get uniform

estimates for time. These estimates are used to extend local solutions.

This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu

Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).

We consider a chemotaxis system with a logarithmic

sensitivity and a non-diffusive chemical substance. For some chemotactic

sensitivity constants, Ahn and Kang proved the existence of bounded

global solutions to the system. An entropy functional was used in their

argument to control the cell density by the density of the chemical

substance. Our purpose is to show the existence of bounded global

solutions for all the chemotactic sensitivity constants. Assuming the

smallness on the initial data in some sense, we can get uniform

estimates for time. These estimates are used to extend local solutions.

This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu

Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).

### 2014/04/21

#### Numerical Analysis Seminar

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

Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)

[ Reference URL ]

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

**Takashi Nakazawa**(Tohoku University)Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)

[ Reference URL ]

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

#### Seminar on Geometric Complex Analysis

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

Lagrangian mean curvature flows and some examples (JAPANESE)

**Hikaru Yamamoto**(The University of Tokyo)Lagrangian mean curvature flows and some examples (JAPANESE)

### 2014/04/19

#### Harmonic Analysis Komaba Seminar

13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Strichartz estimates for incompressible rotating fluids (JAPANESE)

On the interpolation of functions for scattered data on random infinite points with a sharp error estimate (JAPANESE)

**Ryo Takada**(Tohoku University) 13:30-15:00Strichartz estimates for incompressible rotating fluids (JAPANESE)

**Masami Okada**(Tokyo Metropolitan Unversity) 15:30-16:30On the interpolation of functions for scattered data on random infinite points with a sharp error estimate (JAPANESE)

### 2014/04/16

#### Number Theory Seminar

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

On the cycle class map for zero-cycles over local fields (ENGLISH)

**Olivier Wittenberg**(ENS and CNRS)On the cycle class map for zero-cycles over local fields (ENGLISH)

[ Abstract ]

The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.

The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.

### 2014/04/15

#### Tuesday Seminar on Topology

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

On the rational string operations of classifying spaces and the

Hochschild cohomology (JAPANESE)

**Takahito Naito**(The University of Tokyo)On the rational string operations of classifying spaces and the

Hochschild cohomology (JAPANESE)

[ Abstract ]

Chataur and Menichi initiated the theory of string topology of

classifying spaces.

In particular, the cohomology of the free loop space of a classifying

space is endowed with a product

called the dual loop coproduct. In this talk, I will discuss the

algebraic structure and relate the rational dual loop coproduct to the

cup product on the Hochschild cohomology via the Van den Bergh isomorphism.

Chataur and Menichi initiated the theory of string topology of

classifying spaces.

In particular, the cohomology of the free loop space of a classifying

space is endowed with a product

called the dual loop coproduct. In this talk, I will discuss the

algebraic structure and relate the rational dual loop coproduct to the

cup product on the Hochschild cohomology via the Van den Bergh isomorphism.

#### PDE Real Analysis Seminar

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

An application of weighted Hardy spaces to the Navier-Stokes equations (JAPANESE)

**Yohei Tsutsui**(The University of Tokyo)An application of weighted Hardy spaces to the Navier-Stokes equations (JAPANESE)

[ Abstract ]

The purpose of this talk is to investigate decay orders of the L^2 energy of solutions to the incompressible homogeneous Navier-Stokes equations on the whole spaces by the aid of the theory of weighted Hardy spaces. The main estimates are two weighted inequalities for heat semigroup on weighted Hardy spaces and a weighted version of the div-curl lemma due to Coifman-Lions-Meyer-Semmes. It turns out that because of the use of weighted Hardy spaces, our decay orders of the energy can be close to the critical one of Wiegner.

The purpose of this talk is to investigate decay orders of the L^2 energy of solutions to the incompressible homogeneous Navier-Stokes equations on the whole spaces by the aid of the theory of weighted Hardy spaces. The main estimates are two weighted inequalities for heat semigroup on weighted Hardy spaces and a weighted version of the div-curl lemma due to Coifman-Lions-Meyer-Semmes. It turns out that because of the use of weighted Hardy spaces, our decay orders of the energy can be close to the critical one of Wiegner.

#### Lie Groups and Representation Theory

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

Toward the graded Cartan invariants of the symmetric groups (JAPANESE)

**Shunsuke Tsuchioka**(the University of Tokyo)Toward the graded Cartan invariants of the symmetric groups (JAPANESE)

[ Abstract ]

We propose a graded analog of Hill's conjecture which is equivalent to K\\"ulshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups.

We give justifications for it and discuss implications between the variants.

Some materials are based on the joint work with Anton Evseev.

We propose a graded analog of Hill's conjecture which is equivalent to K\\"ulshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups.

We give justifications for it and discuss implications between the variants.

Some materials are based on the joint work with Anton Evseev.

### 2014/04/14

#### Seminar on Geometric Complex Analysis

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

Alternative proof of the geometric vrsion of Lemma on logarithmic derivatives (JAPANESE)

**Katsutoshi Yamanoi**(Tokyo Institute of Technology)Alternative proof of the geometric vrsion of Lemma on logarithmic derivatives (JAPANESE)

### 2014/04/10

#### Geometry Colloquium

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

Deformations of homogeneous Cayley cone submanifolds (JAPANESE)

**Kotaro Kawai**( University of Tokyo)Deformations of homogeneous Cayley cone submanifolds (JAPANESE)

[ Abstract ]

A Cayley submanifold is a minimal submanifold in a Spin(7)-manifold, and is a special class of calibrated submanifolds introduced by Harvey and Lawson. The deformation of calibrated submanifolds is first studied by Mclean. He studied the compact case, and many people try to generalize it to noncompact cases (conical case, asymptotically conical case etc.). In general, the moduli space of deformations of a Cayley cone is known not to be smooth. In this talk, we focus on the homogeneous Cayley cones in R^8, and study their deformation spaces explicitly.

A Cayley submanifold is a minimal submanifold in a Spin(7)-manifold, and is a special class of calibrated submanifolds introduced by Harvey and Lawson. The deformation of calibrated submanifolds is first studied by Mclean. He studied the compact case, and many people try to generalize it to noncompact cases (conical case, asymptotically conical case etc.). In general, the moduli space of deformations of a Cayley cone is known not to be smooth. In this talk, we focus on the homogeneous Cayley cones in R^8, and study their deformation spaces explicitly.

### 2014/04/09

#### Operator Algebra Seminars

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

Index and determnant of n-tuples of commuting operators (ENGLISH)

**Ryszard Nest**(Univ. Copenhagen)Index and determnant of n-tuples of commuting operators (ENGLISH)

### 2014/04/08

#### Tuesday Seminar on Topology

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

On the number of commensurable fibrations on a hyperbolic 3-manifold. (JAPANESE)

**Hidetoshi Masai**(The University of Tokyo)On the number of commensurable fibrations on a hyperbolic 3-manifold. (JAPANESE)

[ Abstract ]

By work of Thurston, it is known that if a hyperbolic fibred

$3$-manifold $M$ has Betti number greater than 1, then

$M$ admits infinitely many distinct fibrations.

For any fibration $\\omega$ on a hyperbolic $3$-manifold $M$,

the number of fibrations on $M$ that are commensurable in the sense of

Calegari-Sun-Wang to $\\omega$ is known to be finite.

In this talk, we prove that the number can be arbitrarily large.

By work of Thurston, it is known that if a hyperbolic fibred

$3$-manifold $M$ has Betti number greater than 1, then

$M$ admits infinitely many distinct fibrations.

For any fibration $\\omega$ on a hyperbolic $3$-manifold $M$,

the number of fibrations on $M$ that are commensurable in the sense of

Calegari-Sun-Wang to $\\omega$ is known to be finite.

In this talk, we prove that the number can be arbitrarily large.

#### Seminar on Probability and Statistics

13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)

Parametric estimation in fractional Ornstein-Uhlenbeck process (ENGLISH)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/00.html

**Alexandre Brouste**(Universite du Maine, France)Parametric estimation in fractional Ornstein-Uhlenbeck process (ENGLISH)

[ Abstract ]

Several statistical models that imply the fractional Ornstein-Uhlenbeck (fOU) process will be presented: direct observations of the process or partial observations in an additive independent noise, continuous observations or discrete observations. In this different settings, we exhibit large sample (or high-frequency) asymptotic properties of the estimators (maximum likelihood estimator, quadratic variation based estimator, moment estimator, …) for all parameters of interest of the fOU. We also illustrate our results with the R package yuima.

[ Reference URL ]Several statistical models that imply the fractional Ornstein-Uhlenbeck (fOU) process will be presented: direct observations of the process or partial observations in an additive independent noise, continuous observations or discrete observations. In this different settings, we exhibit large sample (or high-frequency) asymptotic properties of the estimators (maximum likelihood estimator, quadratic variation based estimator, moment estimator, …) for all parameters of interest of the fOU. We also illustrate our results with the R package yuima.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/00.html

### 2014/03/19

#### Classical Analysis

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

Discrete Schlesinger Equations and Difference Painlevé Equations (ENGLISH)

**Anton Dzhamay**(University of Northern Colorado)Discrete Schlesinger Equations and Difference Painlevé Equations (ENGLISH)

[ Abstract ]

The theory of Schlesinger equations describing isomonodromic

dynamic on the space of matrix coefficients of a Fuchsian system

w.r.t.~continuous deformations is well-know. In this talk we consider

a discrete version of this theory. Discrete analogues of Schlesinger

deformations are Schlesinger transformations that shift the eigenvalues

of the coefficient matrices by integers. By discrete Schlesinger equations

we mean the evolution equations on the matrix coefficients describing

such transformations. We derive these equations, show how they can be

split into the evolution equations on the space of eigenvectors of the

coefficient matrices, and explain how to write the latter equations in

the discrete Hamiltonian form. We also consider some reductions of those

equations to the difference Painlevé equations, again in complete parallel

to the differential case.

This is a joint work with H. Sakai (the University of Tokyo) and

T.Takenawa (Tokyo Institute of Marine Science and Technology).

The theory of Schlesinger equations describing isomonodromic

dynamic on the space of matrix coefficients of a Fuchsian system

w.r.t.~continuous deformations is well-know. In this talk we consider

a discrete version of this theory. Discrete analogues of Schlesinger

deformations are Schlesinger transformations that shift the eigenvalues

of the coefficient matrices by integers. By discrete Schlesinger equations

we mean the evolution equations on the matrix coefficients describing

such transformations. We derive these equations, show how they can be

split into the evolution equations on the space of eigenvectors of the

coefficient matrices, and explain how to write the latter equations in

the discrete Hamiltonian form. We also consider some reductions of those

equations to the difference Painlevé equations, again in complete parallel

to the differential case.

This is a joint work with H. Sakai (the University of Tokyo) and

T.Takenawa (Tokyo Institute of Marine Science and Technology).

### 2014/03/14

#### GCOE Seminars

16:00-16:50 Room #118 (Graduate School of Math. Sci. Bldg.)

A new finite difference scheme based on staggered grids for Navier Stokes equations (ENGLISH)

**Kazufumi Ito**(North Carolina State Univ.)A new finite difference scheme based on staggered grids for Navier Stokes equations (ENGLISH)

[ Abstract ]

We develop a new method that uses the staggered grid only for the pressure node, i.e., the pressure gird is the center of the square cell and the velocities are at the node. The advantage of the proposed method compared to the standard staggered grid methods is that it is very straight forward to treat the boundary conditions for the velocity field, the fluid structure interaction, and to deal with the multiphase flow using the immersed interface methods. We present our analysis and numerical tests.

We develop a new method that uses the staggered grid only for the pressure node, i.e., the pressure gird is the center of the square cell and the velocities are at the node. The advantage of the proposed method compared to the standard staggered grid methods is that it is very straight forward to treat the boundary conditions for the velocity field, the fluid structure interaction, and to deal with the multiphase flow using the immersed interface methods. We present our analysis and numerical tests.

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