## Seminar information archive

Seminar information archive ～11/05｜Today's seminar 11/06 | Future seminars 11/07～

#### Lectures

15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Quasi-homomorphism rigidity with noncommutative targets (ENGLISH)

Ruelle-Lanford functions for quantum spin systems (ENGLISH)

**Narutaka Ozawa**(Univ. Tokyo) 15:00-16:00Quasi-homomorphism rigidity with noncommutative targets (ENGLISH)

**Yoshiko Ogata**(Univ. Tokyo) 16:30-17:30Ruelle-Lanford functions for quantum spin systems (ENGLISH)

### 2010/06/24

#### Operator Algebra Seminars

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

Strong solidity of factors from lattices in SO(n,1) and SU(n,1) (ENGLISH)

**Thomas Sinclair**(Vanderbilt Univ.)Strong solidity of factors from lattices in SO(n,1) and SU(n,1) (ENGLISH)

[ Abstract ]

Generalizing techniques found in Ozawa and Popa,

``On a class of II$_1$ factors with at most one Cartan subalgebra, II''

(Amer. J. Math., to appear), we show that the group factors of ICC

lattices in SO(n,1) and SU(n,1), $n\\ge2$, are strongly solid. If

time permits, we will also discuss applications to $L^2$-rigidity.

Generalizing techniques found in Ozawa and Popa,

``On a class of II$_1$ factors with at most one Cartan subalgebra, II''

(Amer. J. Math., to appear), we show that the group factors of ICC

lattices in SO(n,1) and SU(n,1), $n\\ge2$, are strongly solid. If

time permits, we will also discuss applications to $L^2$-rigidity.

#### Applied Analysis

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

Reaction-diffusion approximation to nonlinear diffusion problems (JAPANESE)

**Hideki Murakawa**(University of Toyama)Reaction-diffusion approximation to nonlinear diffusion problems (JAPANESE)

#### GCOE Seminars

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

非線形拡散問題の反応拡散系近似 (JAPANESE)

**村川 秀樹**(富山大学大学院理工学研究部)非線形拡散問題の反応拡散系近似 (JAPANESE)

[ Abstract ]

氷の融解・水の凝固の過程を記述するステファン問題、地下水の流れを表す多孔質媒体流方程式、2種生物種の競合問題における互いの動的な干渉作用を記述する重定-川崎-寺本交差拡散系など、様々な問題を含む非線形拡散問題を取り扱う。本講演では、非線形拡散問題の解が、拡散が線形である半線形反応拡散系の解により近似されることを示す。この結果は、非線形拡散問題の解構造が、ある種の半線形反応拡散系の中に再現されることを示唆するものである。一般に、非線形問題を扱うよりも半線形問題を取り扱う方が容易であるため、本研究は非線形問題の解析や数値解析に応用できることが期待される。

氷の融解・水の凝固の過程を記述するステファン問題、地下水の流れを表す多孔質媒体流方程式、2種生物種の競合問題における互いの動的な干渉作用を記述する重定-川崎-寺本交差拡散系など、様々な問題を含む非線形拡散問題を取り扱う。本講演では、非線形拡散問題の解が、拡散が線形である半線形反応拡散系の解により近似されることを示す。この結果は、非線形拡散問題の解構造が、ある種の半線形反応拡散系の中に再現されることを示唆するものである。一般に、非線形問題を扱うよりも半線形問題を取り扱う方が容易であるため、本研究は非線形問題の解析や数値解析に応用できることが期待される。

### 2010/06/23

#### GCOE Seminars

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

非線形交差拡散系の数値解法―反応拡散系近似理論の応用― (JAPANESE)

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

**村川 秀樹**(富山大学大学院理工学研究部(理学))非線形交差拡散系の数値解法―反応拡散系近似理論の応用― (JAPANESE)

[ Abstract ]

多成分反応拡散系において、他の成分同士、拡散が相互に依存しあっているときに、拡散が交差していると言い、そのような系は交差拡散系と呼ばれる。2種生物種の競合問題におけるお互いの動的な干渉作用を記述する重定-川崎-寺本モデルは非線形交差拡散を含む問題の代表例である。非線形交差拡散系に対する効果的な数値解法は個別の問題に対して構成され、解析されるのが現状である。現象のモデリングを行う場合など、パラメータの変更のみでなく、非線形項そのものを変えて多くの数値実験を行いたい場合がある。この様な状況に対応するために、汎用的で簡便な数値解法が望まれる。講演では、非線形交差拡散系を近似するある半線形反応拡散系を媒介することにより、そのような数値解法を導出、解析し、数値計算を通してその有用性を示す。時間が許せば、半線形反応拡散系を用いた退化放物型方程式の数値解法についても触れたい。

[ Reference URL ]多成分反応拡散系において、他の成分同士、拡散が相互に依存しあっているときに、拡散が交差していると言い、そのような系は交差拡散系と呼ばれる。2種生物種の競合問題におけるお互いの動的な干渉作用を記述する重定-川崎-寺本モデルは非線形交差拡散を含む問題の代表例である。非線形交差拡散系に対する効果的な数値解法は個別の問題に対して構成され、解析されるのが現状である。現象のモデリングを行う場合など、パラメータの変更のみでなく、非線形項そのものを変えて多くの数値実験を行いたい場合がある。この様な状況に対応するために、汎用的で簡便な数値解法が望まれる。講演では、非線形交差拡散系を近似するある半線形反応拡散系を媒介することにより、そのような数値解法を導出、解析し、数値計算を通してその有用性を示す。時間が許せば、半線形反応拡散系を用いた退化放物型方程式の数値解法についても触れたい。

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

#### Numerical Analysis Seminar

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

Numerical methods for nonlinear cross diffusion system: application of reaction-diffusion approximation theory (JAPANESE)

[ Reference URL ]

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

**Hideki Murakawa**(University of Toyama)Numerical methods for nonlinear cross diffusion system: application of reaction-diffusion approximation theory (JAPANESE)

[ Reference URL ]

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

### 2010/06/22

#### Tuesday Seminar of Analysis

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

Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)

**Ivana Alexandrova**(East Carolina University)Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)

[ Abstract ]

We consider the problem of quantum resonances in magnetic scattering by two

solenoidal fields at large separation in two dimensions, and we study how a trajectory

oscillating between the two fields gives rise to resonances near the real axis when

the distance between two centers of fields goes to infinity. We give a sharp lower

bound on resonance widths in terms of backward amplitudes calculated explicitly for

scattering by each solenoidal field. The study is based on a new type of complex

scaling method. As an application, we also discuss the relation to semiclassical

resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.

We consider the problem of quantum resonances in magnetic scattering by two

solenoidal fields at large separation in two dimensions, and we study how a trajectory

oscillating between the two fields gives rise to resonances near the real axis when

the distance between two centers of fields goes to infinity. We give a sharp lower

bound on resonance widths in terms of backward amplitudes calculated explicitly for

scattering by each solenoidal field. The study is based on a new type of complex

scaling method. As an application, we also discuss the relation to semiclassical

resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.

### 2010/06/21

#### Algebraic Geometry Seminar

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

Pseudo-index and minimal length of extremal rays for Fano manifolds (JAPANESE)

**Toru Tsukioka**(Osaka Prefecture University)Pseudo-index and minimal length of extremal rays for Fano manifolds (JAPANESE)

[ Abstract ]

The minimum of intersection numbers of the anticanonical

divisor with rational curves on a Fano manifold is called pseudo-index.

In view of the fact that the geometry of Fano manifolds is governed by

its extremal rays, it is important to consider the extremal rational

curves. In this talk, we show that for Fano 4-folds having birational

contractions, the minimal length of extremal rays coincides with the

pseudo-index.

The minimum of intersection numbers of the anticanonical

divisor with rational curves on a Fano manifold is called pseudo-index.

In view of the fact that the geometry of Fano manifolds is governed by

its extremal rays, it is important to consider the extremal rational

curves. In this talk, we show that for Fano 4-folds having birational

contractions, the minimal length of extremal rays coincides with the

pseudo-index.

#### Seminar on Geometric Complex Analysis

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

A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

**Sachiko HAMANO**(Fukushima Univ)A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

### 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

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