## Seminar information archive

Seminar information archive ～10/03｜Today's seminar 10/04 | Future seminars 10/05～

#### PDE Real Analysis Seminar

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

The University of Tokyo)

Exact controllability for incompressible fluids (ENGLISH)

**Jean-Pierre Puel**(Graduate School of Mathematical SciencesThe University of Tokyo)

Exact controllability for incompressible fluids (ENGLISH)

[ Abstract ]

After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.

We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).

We will end up with some important open problems.

After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.

We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).

We will end up with some important open problems.

#### Numerical Analysis Seminar

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

Accurate factorizations of ill-conditioned matrices and applications (JAPANESE)

[ Reference URL ]

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

**Takeshi Ogita**(Tokyo Woman's Christian University)Accurate factorizations of ill-conditioned matrices and applications (JAPANESE)

[ Reference URL ]

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

#### GCOE Seminars

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

悪条件行列の高精度な分解法とその応用 (JAPANESE)

[ Reference URL ]

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

**荻田 武史**(東京女子大学現代教養学部)悪条件行列の高精度な分解法とその応用 (JAPANESE)

[ Reference URL ]

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

### 2010/05/11

#### Tuesday Seminar on Topology

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

The logarithms of Dehn twists (JAPANESE)

**Nariya Kawazumi**(The University of Tokyo)The logarithms of Dehn twists (JAPANESE)

[ Abstract ]

We establish an explicit formula for the action of (non-separating and

separating) Dehn twists on the complete group ring of the fundamental group of a

surface. It generalizes the classical transvection formula on the first homology.

The proof is involved with a homological interpretation of the Goldman

Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).

We establish an explicit formula for the action of (non-separating and

separating) Dehn twists on the complete group ring of the fundamental group of a

surface. It generalizes the classical transvection formula on the first homology.

The proof is involved with a homological interpretation of the Goldman

Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).

#### Lie Groups and Representation Theory

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

On a finite $W$-algebra module structure on the space of

continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)

**Hisayosi Matumoto**(the University of Tokyo)On a finite $W$-algebra module structure on the space of

continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)

[ Abstract ]

Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.

Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.

### 2010/05/10

#### Algebraic Geometry Seminar

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

Toric degenerations of Grassmannians and mirror symmetry (JAPANESE)

**Makoto Miura**

(The University of Tokyo)Toric degenerations of Grassmannians and mirror symmetry (JAPANESE)

[ Abstract ]

I will talk about toric degenerarions of Grassmannians and

an application to the mirror constructions for complete intersection

Calabi-Yau manifolds in Grassmannians.

In particular, if we focus on toric degenerations by term orderings on

polynomial rings,

we have to choose a term ordering for which the coordinate ring has an

uniformly homogeneous sagbi basis.

We discuss this condition for some examples of ordinary Grassmannians

and a spinor variety.

I will talk about toric degenerarions of Grassmannians and

an application to the mirror constructions for complete intersection

Calabi-Yau manifolds in Grassmannians.

In particular, if we focus on toric degenerations by term orderings on

polynomial rings,

we have to choose a term ordering for which the coordinate ring has an

uniformly homogeneous sagbi basis.

We discuss this condition for some examples of ordinary Grassmannians

and a spinor variety.

#### 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.

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