## Seminar information archive

Seminar information archive ～09/14｜Today's seminar 09/15 | Future seminars 09/16～

### 2010/06/17

#### GCOE lecture series

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

On a relative version of Wall's conjecture (ENGLISH)

**Feng Xu**(UC Riverside)On a relative version of Wall's conjecture (ENGLISH)

#### Operator Algebra Seminars

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

On a relative version of Wall's conjecture (ENGLISH)

**Feng Xu**(UC Riverside)On a relative version of Wall's conjecture (ENGLISH)

#### Classical Analysis

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

On a class of the Schlesinger systems (JAPANESE)

**Teruhisa Tsuda**(University of Kyushu)On a class of the Schlesinger systems (JAPANESE)

### 2010/06/16

#### Number Theory Seminar

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

Vanishing theorems revisited, after K.-W. Lan and J. Suh (ENGLISH)

**Luc Illusie**(Universite de Paris-Sud)Vanishing theorems revisited, after K.-W. Lan and J. Suh (ENGLISH)

[ Abstract ]

Let k be an algebraically closed field of characteristic p and X,

Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar

type for certain nef and big line bundles L on Y and morphisms f : X -> Y

having semistable reduction along a divisor with simple normal crossings. It

holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2

and dimension assumptions, and generalizes vanishing theorems of Esnault-

Viehweg and of mine. I'll give an outline of the proof and sketch some

applications, due to K.-W. Lan and J. Suh, to the cohomology of certain

automorphic bundles arising from PEL type Shimura varieties.

Let k be an algebraically closed field of characteristic p and X,

Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar

type for certain nef and big line bundles L on Y and morphisms f : X -> Y

having semistable reduction along a divisor with simple normal crossings. It

holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2

and dimension assumptions, and generalizes vanishing theorems of Esnault-

Viehweg and of mine. I'll give an outline of the proof and sketch some

applications, due to K.-W. Lan and J. Suh, to the cohomology of certain

automorphic bundles arising from PEL type Shimura varieties.

### 2010/06/15

#### Tuesday Seminar of Analysis

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

Sato's counterexample and the structure of generalized functions (JAPANESE)

**Takashi Takiguchi**(Department of Mathematics, National Defense Academy)Sato's counterexample and the structure of generalized functions (JAPANESE)

[ Abstract ]

In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.

In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.

#### Tuesday Seminar on Topology

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

On exceptional surgeries on Montesinos knots

(joint works with In Dae Jong and Shigeru Mizushima) (JAPANESE)

**Kazuhiro Ichihara**(Nihon University)On exceptional surgeries on Montesinos knots

(joint works with In Dae Jong and Shigeru Mizushima) (JAPANESE)

[ Abstract ]

I will report recent progresses of the study on exceptional

surgeries on Montesinos knots.

In particular, we will focus on how homological invariants (e.g.

khovanov homology,

knot Floer homology) on knots can be used in the study of Dehn surgery.

I will report recent progresses of the study on exceptional

surgeries on Montesinos knots.

In particular, we will focus on how homological invariants (e.g.

khovanov homology,

knot Floer homology) on knots can be used in the study of Dehn surgery.

### 2010/06/14

#### Algebraic Geometry Seminar

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

Slope of smooth rational curves in an anticanonically polarized Fano manifold (ENGLISH)

**Yongnam Lee**(Sogang University)Slope of smooth rational curves in an anticanonically polarized Fano manifold (ENGLISH)

[ Abstract ]

Ross and Thomas introduce the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature metric. Since K-stability implies slope stability, slope stability gives an algebraic obstruction to theexistence of constant scalar curvature. This talk presents a systematic study of slope stability of anticanonically polarized Fano manifolds with respect to smooth rational curves. Especially, we prove that an anticanonically polarized Fano maniold is slope semistable with respect to any free smooth rational curves, and that an anticanonically polarized Fano threefold X with Picard number 1 is slope stable with respect to any smooth rational curves unless X is the project space. It is a joint work with Jun-Muk Hwang and Hosung Kim.

Ross and Thomas introduce the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature metric. Since K-stability implies slope stability, slope stability gives an algebraic obstruction to theexistence of constant scalar curvature. This talk presents a systematic study of slope stability of anticanonically polarized Fano manifolds with respect to smooth rational curves. Especially, we prove that an anticanonically polarized Fano maniold is slope semistable with respect to any free smooth rational curves, and that an anticanonically polarized Fano threefold X with Picard number 1 is slope stable with respect to any smooth rational curves unless X is the project space. It is a joint work with Jun-Muk Hwang and Hosung Kim.

#### Seminar on Geometric Complex Analysis

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

Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n (JAPANESE)

**Kazuko MATSUMOTO**(Osaka Prefecture University)Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n (JAPANESE)

### 2010/06/11

#### Colloquium

17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The Gauss-Bonnet Theorem and singular points on surfaces (JAPANESE)

**Masaaki Umehara**(Osaka University)The Gauss-Bonnet Theorem and singular points on surfaces (JAPANESE)

[ Abstract ]

We generalize the classical Gauss-Bonnet formula for closed surfaces as wave fronts. Using it, we can find a new view point of inflection points and the topology of immersed surfaces in Euclidean 3-space via the singularities of their Gauss maps.

We generalize the classical Gauss-Bonnet formula for closed surfaces as wave fronts. Using it, we can find a new view point of inflection points and the topology of immersed surfaces in Euclidean 3-space via the singularities of their Gauss maps.

### 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)

https://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.

https://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)

https://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.

https://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)

https://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.

https://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.

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