## Seminar information archive

Seminar information archive ～02/15｜Today's seminar 02/16 | Future seminars 02/17～

### 2010/06/10

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Hydrodynamic limit of microscopic particle systems to conservation laws to fluid models

**Christian Klingenberg**(Wuerzburg 大学 )Hydrodynamic limit of microscopic particle systems to conservation laws to fluid models

[ Abstract ]

In this talk we discuss the hydrodynamic limit of a microscopic description of a fluid to its macroscopic PDE description.

In the first part we consider flow through porous media, i.e. the macroscopic description is a scalar conservation law. Here the new feature is that we allow sudden changes in porosity and thereby the flux may have discontinuities in space. Microscopically this is described through an interacting particle system having only one conserved quantity, namely the total mass. Macroscopically this gives rise to a scalar conservation laws with space dependent flux functions

u_t + f(u, x)_x = 0 .

We are able to derive the PDE together with an entropy condition as a hydrodynamic limit from a microscopic interacting particle system.

In the second part we consider a Hamiltonian system with boundary conditions. Microscopically this is described through a system of coupled oscillators. Macroscopically this will lead to a system of conservation laws, namely the p-system. The proof of the hydrodynamic limit is restricted to smooth solutions. The new feature is that we can derive this with boundary conditions.

In this talk we discuss the hydrodynamic limit of a microscopic description of a fluid to its macroscopic PDE description.

In the first part we consider flow through porous media, i.e. the macroscopic description is a scalar conservation law. Here the new feature is that we allow sudden changes in porosity and thereby the flux may have discontinuities in space. Microscopically this is described through an interacting particle system having only one conserved quantity, namely the total mass. Macroscopically this gives rise to a scalar conservation laws with space dependent flux functions

u_t + f(u, x)_x = 0 .

We are able to derive the PDE together with an entropy condition as a hydrodynamic limit from a microscopic interacting particle system.

In the second part we consider a Hamiltonian system with boundary conditions. Microscopically this is described through a system of coupled oscillators. Macroscopically this will lead to a system of conservation laws, namely the p-system. The proof of the hydrodynamic limit is restricted to smooth solutions. The new feature is that we can derive this with boundary conditions.

#### Operator Algebra Seminars

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

Random groups and nonarchimedean lattices (JAPANESE)

**Mikael Pichot**(IPMU)Random groups and nonarchimedean lattices (JAPANESE)

### 2010/06/09

#### Number Theory Seminar

16:15-17:15 Room #052 (Graduate School of Math. Sci. Bldg.)

Universal mixed elliptic motives (ENGLISH)

**Richard Hain**(Duke University)Universal mixed elliptic motives (ENGLISH)

[ Abstract ]

This is joint work with Makoto Matsumoto. A mixed elliptic

motive is a mixed motive (MHS, Galois representation, etc) whose

weight graded quotients are Tate twists of symmetric powers of the the

motive of elliptic curve. A universal mixed elliptic motive is an

object that can be specialized to a mixed elliptic motive for any

elliptic curve and whose specialization to the nodal cubic is a mixed

Tate motive. Universal mixed elliptic motives form a tannakian

category. In this talk I will define universal mixed elliptic motives,

give some fundamental examples, and explain what we know about the

fundamental group of this category. The "geometric part" of this group

is an extension of SL_2 by a prounipotent group that is generated by

Eisenstein series and which has a family of relations for each cusp

form. Although these relations are not known, we have a very good idea

of what they are, thanks to work of Aaron Pollack, who determined

relations between the generators in a very large representation of

this group.

This is joint work with Makoto Matsumoto. A mixed elliptic

motive is a mixed motive (MHS, Galois representation, etc) whose

weight graded quotients are Tate twists of symmetric powers of the the

motive of elliptic curve. A universal mixed elliptic motive is an

object that can be specialized to a mixed elliptic motive for any

elliptic curve and whose specialization to the nodal cubic is a mixed

Tate motive. Universal mixed elliptic motives form a tannakian

category. In this talk I will define universal mixed elliptic motives,

give some fundamental examples, and explain what we know about the

fundamental group of this category. The "geometric part" of this group

is an extension of SL_2 by a prounipotent group that is generated by

Eisenstein series and which has a family of relations for each cusp

form. Although these relations are not known, we have a very good idea

of what they are, thanks to work of Aaron Pollack, who determined

relations between the generators in a very large representation of

this group.

#### Number Theory Seminar

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

Constructibilité uniforme des images directes supérieures en

cohomologie étale

(ENGLISH)

**Fabrice Orgogozo**(CNRS, École polytechnique)Constructibilité uniforme des images directes supérieures en

cohomologie étale

(ENGLISH)

[ Abstract ]

Motivé par une remarque de N. Katz sur le lien entre la

torsion de la Z_ℓ-cohomologie étale et les ultraproduits de groupes de

F_ℓ-cohomologie, nous démontrons un théorème d'uniformité en ℓ pour la

constructibilité des images directes supérieures entre schémas de type fini

sur un trait excellent. (Un tel théorème avait été considéré par

O. Gabber il y a plusieurs années déjà.)

La méthode est maintenant classique : on utilise des

théorèmes de A. J. de Jong et un peu de log-géométrie.

(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted from IHES by the internet.)

Motivé par une remarque de N. Katz sur le lien entre la

torsion de la Z_ℓ-cohomologie étale et les ultraproduits de groupes de

F_ℓ-cohomologie, nous démontrons un théorème d'uniformité en ℓ pour la

constructibilité des images directes supérieures entre schémas de type fini

sur un trait excellent. (Un tel théorème avait été considéré par

O. Gabber il y a plusieurs années déjà.)

La méthode est maintenant classique : on utilise des

théorèmes de A. J. de Jong et un peu de log-géométrie.

(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted from IHES by the internet.)

#### Numerical Analysis Seminar

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

A bubble finite-element method with orthogonal property and applications to flow problems (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/saito/

**Junichi Matsumoto**(National Institute of Advanced Industrial Science and Technology)A bubble finite-element method with orthogonal property and applications to flow problems (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/saito/

#### GCOE Seminars

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

直交基底気泡関数有限要素法による流体解析と応用計算 (JAPANESE)

[ Reference URL ]

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

**松本 純一**(産業技術総合研究所)直交基底気泡関数有限要素法による流体解析と応用計算 (JAPANESE)

[ Reference URL ]

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

#### Seminar on Probability and Statistics

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

Weak convergence of Markov chain Monte Carlo method and its application to Yuima (JAPANESE)

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/03.html

**KAMATANI, Kengo**(Graduate school of Mathematical Sciences, Univ. of Tokyo)Weak convergence of Markov chain Monte Carlo method and its application to Yuima (JAPANESE)

[ Abstract ]

We examine some asymptotic properties of Markov chain Monte Carlo methods by the weak convergence framework of MCMC. Our purpose is to compare this framework to the Harris recurrence framework. Numerical illustrations will be given via R. The connection to the YUIMA package will also be discussed.

This talk will be held at IT Studio.

[ Reference URL ]We examine some asymptotic properties of Markov chain Monte Carlo methods by the weak convergence framework of MCMC. Our purpose is to compare this framework to the Harris recurrence framework. Numerical illustrations will be given via R. The connection to the YUIMA package will also be discussed.

This talk will be held at IT Studio.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/03.html

### 2010/06/08

#### Lie Groups and Representation Theory

17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Automorphism groups of causal Makarevich spaces (JAPANESE)

**Soji Kaneyuki**(Sophia University)Automorphism groups of causal Makarevich spaces (JAPANESE)

[ Abstract ]

Let G^ be a simple Lie group of Hermitian type and U^ be a maximal parabolic subgroup of G^ with abelian nilradical. The flag manifold M^= G^/ U^ is the Shilov

boundary of an irreducible bounded symmetric domain of tube type. M^ has the G-invariant causal structure. A causal Makarevich space is, by definition, an open symmetric G-orbit M in M^, endowed with the causal structure induced from that

of the ambient space M^, G being a reductive subgroup of G^. All symmetric cones fall in the class of causal Makarevich spaces.

In this talk, we determine the causal automorphism groups of all causal Makarevich spaces.

Let G^ be a simple Lie group of Hermitian type and U^ be a maximal parabolic subgroup of G^ with abelian nilradical. The flag manifold M^= G^/ U^ is the Shilov

boundary of an irreducible bounded symmetric domain of tube type. M^ has the G-invariant causal structure. A causal Makarevich space is, by definition, an open symmetric G-orbit M in M^, endowed with the causal structure induced from that

of the ambient space M^, G being a reductive subgroup of G^. All symmetric cones fall in the class of causal Makarevich spaces.

In this talk, we determine the causal automorphism groups of all causal Makarevich spaces.

### 2010/06/07

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Genus 2 curve configurations on Fano surfaces (ENGLISH)

**Xavier Roulleau**(The University of Tokyo)Genus 2 curve configurations on Fano surfaces (ENGLISH)

#### Seminar on Geometric Complex Analysis

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

Restricted Bergman kernel asymptotics (JAPANESE)

**Tomoyuki HISAMOTO**(Univ. of Tokyo)Restricted Bergman kernel asymptotics (JAPANESE)

### 2010/06/03

#### Operator Algebra Seminars

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

Fixed Points in the Stone-Cech boundary of Groups (ENGLISH)

**Makoto Yamashita**(Univ. Tokyo)Fixed Points in the Stone-Cech boundary of Groups (ENGLISH)

[ Abstract ]

We discuss the class of discrete groups which admit fixed points under the adjoint action on the Stone-Cech boundary. Such groups have vanishing $L^2$-Betti numbers, and nonamenable ones fail to have property (AO).

We discuss the class of discrete groups which admit fixed points under the adjoint action on the Stone-Cech boundary. Such groups have vanishing $L^2$-Betti numbers, and nonamenable ones fail to have property (AO).

#### GCOE lecture series

16:30-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Introduction to the cohomology of locally symmetric spaces 2

(ENGLISH)

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Birgit Speh**(Cornel University)Introduction to the cohomology of locally symmetric spaces 2

(ENGLISH)

[ Abstract ]

I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma $.

If $X_\\Gamma $ is cocompact this cohomology can be expressed as the $(\\bg,K) $-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.

[ Reference URL ]I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma $.

If $X_\\Gamma $ is cocompact this cohomology can be expressed as the $(\\bg,K) $-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2010/06/02

#### Number Theory Seminar

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

On some algebraic properties of CM-types of CM-fields and their

reflex fields (JAPANESE)

**Ryoko Tomiyasu**(KEK)On some algebraic properties of CM-types of CM-fields and their

reflex fields (JAPANESE)

[ Abstract ]

Shimura and Taniyama proved in their theory of complex

multiplication that the moduli of abelian varieties of a CM-type and their

torsion points generate an abelian extension, not of the field of complex

multiplication, but of a reflex field of the field. In this talk, I

introduce some algebraic properties of CM-types, half norm maps that might

shed new light on reflex fields.

For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,

there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \\rtimes S_n$.

Using properties of the embedding, a set of CM-types $\\Phi$ of $K$ and their

dual CM-types $(K, \\Phi)$ is equipped with a combinatorial structure. This

makes it much easier to handle a whole set of CM-types than an individual

CM-type.

I present a theorem that shows the combinatorial structure of the dual

CM-types is isomorphic to that of a Pfister form.

Shimura and Taniyama proved in their theory of complex

multiplication that the moduli of abelian varieties of a CM-type and their

torsion points generate an abelian extension, not of the field of complex

multiplication, but of a reflex field of the field. In this talk, I

introduce some algebraic properties of CM-types, half norm maps that might

shed new light on reflex fields.

For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,

there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \\rtimes S_n$.

Using properties of the embedding, a set of CM-types $\\Phi$ of $K$ and their

dual CM-types $(K, \\Phi)$ is equipped with a combinatorial structure. This

makes it much easier to handle a whole set of CM-types than an individual

CM-type.

I present a theorem that shows the combinatorial structure of the dual

CM-types is isomorphic to that of a Pfister form.

### 2010/06/01

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On Fatou-Julia decompositions (JAPANESE)

**Taro Asuke**(The University of Tokyo)On Fatou-Julia decompositions (JAPANESE)

[ Abstract ]

We will explain that Fatou-Julia decompositions can be

introduced in a unified manner to several kinds of one-dimensional

complex dynamical systems, which include the action of Kleinian groups,

iteration of holomorphic mappings and complex codimension-one foliations.

In this talk we will restrict ourselves mostly to the cases where the

dynamical systems have a certain compactness, however, we will mention

how to deal with dynamical systems without compactness.

We will explain that Fatou-Julia decompositions can be

introduced in a unified manner to several kinds of one-dimensional

complex dynamical systems, which include the action of Kleinian groups,

iteration of holomorphic mappings and complex codimension-one foliations.

In this talk we will restrict ourselves mostly to the cases where the

dynamical systems have a certain compactness, however, we will mention

how to deal with dynamical systems without compactness.

#### GCOE lecture series

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

Introduction to the cohomology of locally symmetric spaces

(ENGLISH)

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

**Birgit Speh**(Cornel University)Introduction to the cohomology of locally symmetric spaces

(ENGLISH)

[ Abstract ]

I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma $.

If $X_\\Gamma $ is cocompact this cohomology can be expressed as the $(g,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.

[ Reference URL ]I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma $.

If $X_\\Gamma $ is cocompact this cohomology can be expressed as the $(g,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.

http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2010/05/31

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

On Pfaffian Calabi-Yau Varieties and Mirror Symmetry (JAPANESE)

**Atsushi Kanazawa**(The University of Tokyo)On Pfaffian Calabi-Yau Varieties and Mirror Symmetry (JAPANESE)

[ Abstract ]

We construct new smooth CY 3-folds with 1-dimensional Kaehler moduli and

determine their fundamental topological invariants. The existence of CY

3-folds with the computed invariants was previously conjectured. We then

report mirror symmetry for these non-complete intersection CY 3-folds.

We explicitly build their mirror partners, some of which have 2 LCSLs,

and carry out instanton computations for g=0,1.

We construct new smooth CY 3-folds with 1-dimensional Kaehler moduli and

determine their fundamental topological invariants. The existence of CY

3-folds with the computed invariants was previously conjectured. We then

report mirror symmetry for these non-complete intersection CY 3-folds.

We explicitly build their mirror partners, some of which have 2 LCSLs,

and carry out instanton computations for g=0,1.

#### Seminar on Geometric Complex Analysis

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

Singularities and analytic torsion (JAPANESE)

**Ken-ichi YOSHIKAWA**(Kyoto Univ.)Singularities and analytic torsion (JAPANESE)

### 2010/05/28

#### Classical Analysis

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

On solutions of uniformization equations (JAPANESE)

**Jiro Sekiguchi**(Tokyo University of Agriculture and Technology)On solutions of uniformization equations (JAPANESE)

### 2010/05/27

#### Operator Algebra Seminars

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

The C*-algebra of codimension one foliations which are almost without holonomy (ENGLISH)

**Catherine Oikonomides**(Univ. Tokyo)The C*-algebra of codimension one foliations which are almost without holonomy (ENGLISH)

### 2010/05/26

#### Seminar on Probability and Statistics

16:20-17:30 Room #000 (Graduate School of Math. Sci. Bldg.)

Financial data analysis with R-YUIMA (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html

**FUKASAWA, Masaaki**(CSFI, Osaka Univ.)Financial data analysis with R-YUIMA (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html

#### PDE Real Analysis Seminar

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

Hokkaido University)

A SELECTION CRITERION FOR SOLUTIONS OF A

SYSTEM OF EIKONAL EQUATIONS

(ENGLISH)

**Giovanni Pisante**(Department of MathematicsHokkaido University)

A SELECTION CRITERION FOR SOLUTIONS OF A

SYSTEM OF EIKONAL EQUATIONS

(ENGLISH)

[ Abstract ]

We deal with the system of eikonal equations |ðu/ðx1|=1, |ðu/ðx2|=1 in a planar Lipschitz domain with zero boundary condition. Exploiting the classical pyramidal construction introduced by Cellina, it is easy to prove that there exist infinitely many Lipschitz solutions. Then, the natural problem that has arisen in this framework is to find a way to select and characterize a particular meaningful class of solutions.

We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient. More precisely we select an optimal weighted measure for the jump set of the second derivatives of a given solution v of the system and we prove the existence of minimizers of the corresponding variational problem.

We deal with the system of eikonal equations |ðu/ðx1|=1, |ðu/ðx2|=1 in a planar Lipschitz domain with zero boundary condition. Exploiting the classical pyramidal construction introduced by Cellina, it is easy to prove that there exist infinitely many Lipschitz solutions. Then, the natural problem that has arisen in this framework is to find a way to select and characterize a particular meaningful class of solutions.

We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient. More precisely we select an optimal weighted measure for the jump set of the second derivatives of a given solution v of the system and we prove the existence of minimizers of the corresponding variational problem.

#### Numerical Analysis Seminar

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

Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)

[ Reference URL ]

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

**Keisuke Matsuya**(University of Tokyo)Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)

[ Reference URL ]

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

#### GCOE Seminars

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

Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)

[ Reference URL ]

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

**松家 敬介**(東京大学大学院数理科学研究科)Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)

[ Reference URL ]

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

### 2010/05/25

#### Lie Groups and Representation Theory

17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

On endoscopy, packets, and invariants (JAPANESE)

**Kaoru Hiraga**(Kyoto University)On endoscopy, packets, and invariants (JAPANESE)

[ Abstract ]

The theory of endoscopy came out of the Langlands functoriality and the trace formula.

In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.

I would like to talk about the connection between these topics and the endoscopy.

The theory of endoscopy came out of the Langlands functoriality and the trace formula.

In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.

I would like to talk about the connection between these topics and the endoscopy.

### 2010/05/24

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

A counterexample of the birational Torelli problem via Fourier--Mukai transforms (JAPANESE)

**Hokuto Uehara**(Tokyo Metropolitan University)A counterexample of the birational Torelli problem via Fourier--Mukai transforms (JAPANESE)

[ Abstract ]

We study the Fourier--Mukai numbers of rational elliptic surfaces. As

its application, we give an example of a pair of minimal 3-folds $X$

with Kodaira dimensions 1, $h^1(O_X)=h^2(O_X)=0$ such that they are

mutually derived equivalent, deformation equivalent, but not

birationally equivalent. It also supplies a counterexample of the

birational Torelli problem.

We study the Fourier--Mukai numbers of rational elliptic surfaces. As

its application, we give an example of a pair of minimal 3-folds $X$

with Kodaira dimensions 1, $h^1(O_X)=h^2(O_X)=0$ such that they are

mutually derived equivalent, deformation equivalent, but not

birationally equivalent. It also supplies a counterexample of the

birational Torelli problem.

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