## Seminar information archive

Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～

#### Seminar on Geometric Complex Analysis

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

Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)

**Yoshihiko MATSUMOTO**(Univ. of Tokyo)Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)

[ Abstract ]

To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.

To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.

### 2010/05/07

#### Lectures

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Independence of families of $\\ell$-adic representations and uniform constructibility

**Luc Illusie**(東京大学/Paris南大学)Independence of families of $\\ell$-adic representations and uniform constructibility

[ Abstract ]

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

#### Colloquium

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

Why to study controllability problems and the mathematical tools involved (ENGLISH)

**Jean-Pierre Puel**(The University of Tokyo, Universite de Versailles Saint-Quentin)Why to study controllability problems and the mathematical tools involved (ENGLISH)

[ Abstract ]

We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.

We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.

### 2010/05/06

#### Operator Algebra Seminars

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

Connes-Landi Deformation of Spectral Triples (ENGLISH)

**Makoto Yamashita**(Univ. Tokyo)Connes-Landi Deformation of Spectral Triples (ENGLISH)

[ Abstract ]

We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic K-theoretic invariants independent of the deformation parameter.

We describe a way to deform spectral triples with a 2-torus action and a real deformation parameter, motivated by deformation of manifolds after Connes-Landi. Such deformations are shown to have naturally isomorphic K-theoretic invariants independent of the deformation parameter.

### 2010/04/28

#### PDE Real Analysis Seminar

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

)

GLOBAL AND SINGULAR SOLUTIONS TO SOME

HYDRODYNAMIC EVOLUTION EQUATIONS

**Marcus Wunsch**(Kyoto University)

GLOBAL AND SINGULAR SOLUTIONS TO SOME

HYDRODYNAMIC EVOLUTION EQUATIONS

[ Abstract ]

The two-component Hunter-Saxton system is a recently derived system of evolution equations modeling, e.g., the nonlinear dynamics of nondissipative dark matter and the propagation of orientation waves in nematic liquid crystals. It is imbedded into a parameterized family of systems called the generalized Hunter-Saxton (2HS) system [2] reducing, if one component is omitted, to the generalized Proudman-Johnson(gPJ) equation [1] modeling three-dimensional vortex dynamics.

After demonstrating, by means of Kato's semigroup theory, the local-in-time existence of classical solutions, the blow-up scenarios for the 2HS system and the gPJ equation are described. The explicit construction of weak dissipative solutions for both models is discussed in detail.

Finally, global existence in time of these weak solutions is proved.

The two-component Hunter-Saxton system is a recently derived system of evolution equations modeling, e.g., the nonlinear dynamics of nondissipative dark matter and the propagation of orientation waves in nematic liquid crystals. It is imbedded into a parameterized family of systems called the generalized Hunter-Saxton (2HS) system [2] reducing, if one component is omitted, to the generalized Proudman-Johnson(gPJ) equation [1] modeling three-dimensional vortex dynamics.

After demonstrating, by means of Kato's semigroup theory, the local-in-time existence of classical solutions, the blow-up scenarios for the 2HS system and the gPJ equation are described. The explicit construction of weak dissipative solutions for both models is discussed in detail.

Finally, global existence in time of these weak solutions is proved.

#### Lectures

16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Independence of families of $\\ell$-adic representations and uniform constructibility

**Luc Illusie**(東京大学/Paris南大学)Independence of families of $\\ell$-adic representations and uniform constructibility

[ Abstract ]

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

#### Seminar on Probability and Statistics

15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)

A Markov process for circular data (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html

**KATO, Shogo**(The Institute of Statistical Mathematics)A Markov process for circular data (JAPANESE)

[ Abstract ]

We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.

[ Reference URL ]We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html

### 2010/04/27

#### Tuesday Seminar on Topology

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

On the complex volume of hyperbolic knots (JAPANESE)

**横田 佳之**(首都大学東京)On the complex volume of hyperbolic knots (JAPANESE)

[ Abstract ]

In this talk, we give a formula of the volume and the Chern-Simons invariant of hyperbolic knot complements, which is closely related to the volume conjecture of hyperbolic knots.

We also discuss the volumes and the Chern-Simons invariants of closed 3-manifolds

obtained by Dehn surgeries on hyperbolic knots.

In this talk, we give a formula of the volume and the Chern-Simons invariant of hyperbolic knot complements, which is closely related to the volume conjecture of hyperbolic knots.

We also discuss the volumes and the Chern-Simons invariants of closed 3-manifolds

obtained by Dehn surgeries on hyperbolic knots.

#### Lie Groups and Representation Theory

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

Restriction of Vogan-Zuckerman's derived functor modules to symmetric subgroups (JAPANESE)

**Yoshiki Oshima**(the University of Tokyo)Restriction of Vogan-Zuckerman's derived functor modules to symmetric subgroups (JAPANESE)

[ Abstract ]

We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.

An algebraic condition for the discrete decomposability of

$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.

In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,

we construct some of irreducible components occurring in the branching law and determine their associated variety.

We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.

An algebraic condition for the discrete decomposability of

$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.

In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,

we construct some of irreducible components occurring in the branching law and determine their associated variety.

### 2010/04/26

#### Algebraic Geometry Seminar

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

The unirationality of the moduli spaces of 2-elementary K3

surfaces (JAPANESE)

**Shouhei Ma**(The University of Tokyo)The unirationality of the moduli spaces of 2-elementary K3

surfaces (JAPANESE)

[ Abstract ]

We prove the unirationality of the moduli spaces of K3 surfaces

with non-symplectic involution. As a by-product, we describe the

configuration spaces of 5, 6, 7, 8 points in the projective plane as

arithmetic quotients of type IV.

We prove the unirationality of the moduli spaces of K3 surfaces

with non-symplectic involution. As a by-product, we describe the

configuration spaces of 5, 6, 7, 8 points in the projective plane as

arithmetic quotients of type IV.

#### Kavli IPMU Komaba Seminar

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

The correspondence between Frobenius algebra of Hurwitz numbers

and matrix models (JAPANESE)

**Akishi Ikeda**(The University of Tokyo)The correspondence between Frobenius algebra of Hurwitz numbers

and matrix models (JAPANESE)

[ Abstract ]

The number of branched coverings of closed surfaces are called Hurwitz

numbers. They constitute a Frobenius algebra structure, or

two dimensional topological field theory. On the other hand, correlation

functions of matrix models are expressed in term of ribbon graphs

(graphs embedded in closed surfaces).

In this talk, I explain how the Frobenius algebra structure of Hurwitz

numbers are described in terms of matrix models. We use the

correspondence between ribbon graphs and covering of S^2 ramified at

three points, both of which have natural symmetric group actions.

As an application I use Frobenius algebra structure to compute Hermitian

matrix models, multi-variable matrix models, and their large N

expansions. The generating function of Hurwitz numbers is also expressed

in terms of matrix models. The relation to integrable hierarchies and

random partitions is briefly discussed.

The number of branched coverings of closed surfaces are called Hurwitz

numbers. They constitute a Frobenius algebra structure, or

two dimensional topological field theory. On the other hand, correlation

functions of matrix models are expressed in term of ribbon graphs

(graphs embedded in closed surfaces).

In this talk, I explain how the Frobenius algebra structure of Hurwitz

numbers are described in terms of matrix models. We use the

correspondence between ribbon graphs and covering of S^2 ramified at

three points, both of which have natural symmetric group actions.

As an application I use Frobenius algebra structure to compute Hermitian

matrix models, multi-variable matrix models, and their large N

expansions. The generating function of Hurwitz numbers is also expressed

in terms of matrix models. The relation to integrable hierarchies and

random partitions is briefly discussed.

#### Seminar on Geometric Complex Analysis

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

Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

**Yoshihiro AIHARA**(Fukushima Univ.)Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

### 2010/04/23

#### Colloquium

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

疑似乱数発生に用いられる数学:メルセンヌ・ツイスターを例に (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~matumoto/PRESENTATION/tokyo-univ2010-4-23.pdf

**松本 眞**(東京大学大学院数理科学研究科)疑似乱数発生に用いられる数学:メルセンヌ・ツイスターを例に (JAPANESE)

[ Abstract ]

疑似乱数生成法とは、あたかも乱数であるかのようにふるまう数列を、計算機内で高速に、再現性があるように生成する方法の総称です。確率的事象を含む現象の計算機シミュレーションには、疑似乱数は欠かせません。たとえば、核物理シミュレーション、株価に関する商品の評価、DNA塩基配列からのたんぱく質の立体構造推定など、広い範囲で疑似乱数は利用されています。講演者と西村拓士氏が97年に開発したメルセン・ツイスタ―生成法は、生成が高速なうえ周期が$2^19937-1$で623次元空間に均等分布することが証明されており、ISO規格にも取り入れられるなど広く利用が進んでいます。ここでは、メルセンヌ・ツイスターとその後の発展において、(初等的・古典的な)純粋数学(有限体、線形代数、多項式、べき級数環、格子など)がどのように使われたかを、非専門家向けに解説します。学部1年生を含め、他学部・他専攻の方の参加を期待して講演を準備します。

[ Reference URL ]疑似乱数生成法とは、あたかも乱数であるかのようにふるまう数列を、計算機内で高速に、再現性があるように生成する方法の総称です。確率的事象を含む現象の計算機シミュレーションには、疑似乱数は欠かせません。たとえば、核物理シミュレーション、株価に関する商品の評価、DNA塩基配列からのたんぱく質の立体構造推定など、広い範囲で疑似乱数は利用されています。講演者と西村拓士氏が97年に開発したメルセン・ツイスタ―生成法は、生成が高速なうえ周期が$2^19937-1$で623次元空間に均等分布することが証明されており、ISO規格にも取り入れられるなど広く利用が進んでいます。ここでは、メルセンヌ・ツイスターとその後の発展において、(初等的・古典的な)純粋数学(有限体、線形代数、多項式、べき級数環、格子など)がどのように使われたかを、非専門家向けに解説します。学部1年生を含め、他学部・他専攻の方の参加を期待して講演を準備します。

https://www.ms.u-tokyo.ac.jp/~matumoto/PRESENTATION/tokyo-univ2010-4-23.pdf

### 2010/04/22

#### Operator Algebra Seminars

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

The Baum-Connes Conjecture and Group Representations (ENGLISH)

**Nigel Higson**(Pennsylvania State Univ.)The Baum-Connes Conjecture and Group Representations (ENGLISH)

[ Abstract ]

The Baum-Connes conjecture asserts a sort of duality between the reduced unitary dual of a group and (a variant of) the classifying space of the group. The conjectured duality occurs at the level of K-theory. For example, for free abelian groups it amounts to a K-theoretic form of Fourier-Mukai duality. The conjecture has well-known applications in topology and geometry, but it also resonates in various ways with Lie groups and representation theory. I'll try to indicate how this comes about, and then focus on a fairly new aspect of the relationship that develops some early ideas of Mackey.

The Baum-Connes conjecture asserts a sort of duality between the reduced unitary dual of a group and (a variant of) the classifying space of the group. The conjectured duality occurs at the level of K-theory. For example, for free abelian groups it amounts to a K-theoretic form of Fourier-Mukai duality. The conjecture has well-known applications in topology and geometry, but it also resonates in various ways with Lie groups and representation theory. I'll try to indicate how this comes about, and then focus on a fairly new aspect of the relationship that develops some early ideas of Mackey.

#### Applied Analysis

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

Deterministic and stochastic modelling of catalytic surface processes (ENGLISH)

**Jens Starke**(Technical University of Denmark)Deterministic and stochastic modelling of catalytic surface processes (ENGLISH)

[ Abstract ]

Three levels of modelling, the microscopic, the mesoscopic and the macroscopic level are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. The macroscopic description can be derived rigorously for low pressure conditions as limit of the stochastic many particle model for large particle numbers. This is in correspondence with the successful description of experiments under low pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The introduced models include a new approach for the platinum phase transition which allows for a unification of existing models for Pt(100) and Pt(110).

The rich nonlinear dynamical behaviour of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, so-called raindrop patterns which are not captured by earlier models, can be reproduced and are shown in simulations.

This is joint work with M. Eiswirth, H. Rotermund, G. Ertl,

Frith Haber Institut, Berlin, K. Oelschlaeger, University of

Heidelberg and C. Reichert, INSA, Lyon.

Three levels of modelling, the microscopic, the mesoscopic and the macroscopic level are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. The macroscopic description can be derived rigorously for low pressure conditions as limit of the stochastic many particle model for large particle numbers. This is in correspondence with the successful description of experiments under low pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The introduced models include a new approach for the platinum phase transition which allows for a unification of existing models for Pt(100) and Pt(110).

The rich nonlinear dynamical behaviour of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, so-called raindrop patterns which are not captured by earlier models, can be reproduced and are shown in simulations.

This is joint work with M. Eiswirth, H. Rotermund, G. Ertl,

Frith Haber Institut, Berlin, K. Oelschlaeger, University of

Heidelberg and C. Reichert, INSA, Lyon.

### 2010/04/21

#### Seminar on Mathematics for various disciplines

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

Direct observation of elementary processes of crystal growth by advanced optical microscopy (JAPANESE)

**Gen Sazaki**(Hokkaido University)Direct observation of elementary processes of crystal growth by advanced optical microscopy (JAPANESE)

[ Abstract ]

#### Numerical Analysis Seminar

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

On the interpolation constant over triangular and rectangular elements (JAPANESE)

[ Reference URL ]

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

**Kenta Kobayashi**(Kanazawa University)On the interpolation constant over triangular and rectangular elements (JAPANESE)

[ Reference URL ]

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

### 2010/04/20

#### Tuesday Seminar on Topology

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

Homotopy of foliations in dimension 3. (ENGLISH)

**Helene Eynard-Bontemps**(東京大学大学院数理科学研究科, JSPS)Homotopy of foliations in dimension 3. (ENGLISH)

[ Abstract ]

We are interested in the connectedness of the space of

codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved

the fundamental result:

Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a

foliation.

W. R. gave a new proof of (and generalized) this result in 1973 using

local constructions. It is then natural to wonder if two foliations with

homotopic tangent plane fields can be linked by a continuous path of

foliations.

A. Larcanch\\'e gave a positive answer in the particular case of

"sufficiently close" taut foliations. We use the key construction of her

proof (among other tools) to show that this is actually always true,

provided one is not too picky about the regularity of the foliations of

the path:

Theorem: Two C^\\infty foliations with homotopic tangent plane fields can

be linked by a path of C^1 foliations.

We are interested in the connectedness of the space of

codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved

the fundamental result:

Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a

foliation.

W. R. gave a new proof of (and generalized) this result in 1973 using

local constructions. It is then natural to wonder if two foliations with

homotopic tangent plane fields can be linked by a continuous path of

foliations.

A. Larcanch\\'e gave a positive answer in the particular case of

"sufficiently close" taut foliations. We use the key construction of her

proof (among other tools) to show that this is actually always true,

provided one is not too picky about the regularity of the foliations of

the path:

Theorem: Two C^\\infty foliations with homotopic tangent plane fields can

be linked by a path of C^1 foliations.

#### Lie Groups and Representation Theory

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

Proper actions of SL(2,R) on semisimple symmetric spaces (JAPANESE)

**Takayuki Okuda**(the University of Tokyo)Proper actions of SL(2,R) on semisimple symmetric spaces (JAPANESE)

[ Abstract ]

Complex irreducible symmetric spaces which admit proper SL(2,R)-actions were classified by Katsuki Teduka.

In this talk, we generalize Teduka's method and classify semisimple symmetric spaces which admit proper SL(2,R)-actions.

Complex irreducible symmetric spaces which admit proper SL(2,R)-actions were classified by Katsuki Teduka.

In this talk, we generalize Teduka's method and classify semisimple symmetric spaces which admit proper SL(2,R)-actions.

### 2010/04/19

#### Algebraic Geometry Seminar

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

制限型体積と因子的ザリスキー分解

**松村 慎一**(東大数理)制限型体積と因子的ザリスキー分解

[ Abstract ]

豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.

(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,

多くの状況で出現する重要な概念である.

様々な部分多様体に沿った制限型体積の振る舞いと

巨大な因子のザリスキー分解可能性の関係について考察したい.

また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に

ついても触れたい.

豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.

(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,

多くの状況で出現する重要な概念である.

様々な部分多様体に沿った制限型体積の振る舞いと

巨大な因子のザリスキー分解可能性の関係について考察したい.

また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に

ついても触れたい.

#### Lectures

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

**Cyrill Muratov**(New Jersey Institute of Technology)Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions

[ Abstract ]

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

#### Seminar on Geometric Complex Analysis

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

Loewner's theory on complex manifolds (ENGLISH)

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**Filippo Bracci**(Universita di Roma, ``Tor Vergata'')Loewner's theory on complex manifolds (ENGLISH)

[ Abstract ]

Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

[ Reference URL ]Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

#### Mathematical Biology Seminar

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

骨髄増殖性疾患の起源細胞に関する数理的研究 (JAPANESE)

**Horoshi HAENO**(Memorial Sloan-Kettering Cancer Center)骨髄増殖性疾患の起源細胞に関する数理的研究 (JAPANESE)

### 2010/04/17

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

Principal series Whittaker functions on $Sp(2,C)$ (JAPANESE)

A paving of the Siegel 10-fold of positive characteristic (JAPANESE)

**MIYAZAKI Tadashi**(Tokyo Univ. of agr. and indus.) 13:30-14:30Principal series Whittaker functions on $Sp(2,C)$ (JAPANESE)

[ Abstract ]

Not given here.

Not given here.

**HARASHITA Shushi**(Yokohama National Univ.) 15:00-16:00A paving of the Siegel 10-fold of positive characteristic (JAPANESE)

[ Abstract ]

Not given here.

Not given here.

### 2010/04/15

#### Lie Groups and Representation Theory

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

Generalized hypergeometric systems (ENGLISH)

**Uuganbayar Zunderiya**(Nagoya University)Generalized hypergeometric systems (ENGLISH)

[ Abstract ]

A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\\times l$ matrices of derivations with respect to certain variables.

In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.

A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\\times l$ matrices of derivations with respect to certain variables.

In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.

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