## Seminar information archive

#### Lectures

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Bendong LOU (婁 本東) (同済大学)
Traveling waves of a curvature flow in almost periodic media
[ Abstract ]
In a plane media with almost periodic vertical striations, we study a curvature flow and construct two kinds of traveling waves, one having a straight line like profile and the other having a V shaped profile. For each of the first kind of traveling waves, its profile is the graph of a function whose derivative is almost periodic. For each of the second kind of traveling waves, its profile is like a pulsating cone, with tails asymptotically approach the first kind of traveling waves.
Also we consider a homogenization problem and provide an explicit formula for the homogenized traveling speed.
This is joint work with Xinfu Chen.

#### Seminar on Probability and Statistics

13:40-14:50   Room #128 (Graduate School of Math. Sci. Bldg.)
Stefano Maria Iacus (Universita degli Studi di Milano)
Applications of Iterated Function Systems to Inference and Simulation
[ Abstract ]
The Iterated Function Systems (IFSs) were born in mid eighties as applications of the theory of discrete dynamical systems and as useful tools for buildings fractals and other similar sets or to produce image compression algorithms. The fundamental result on which the IFS method is based is the Banach contraction theorem because IFSs are defined as operators with some contractive property. In practical applications the crucial point is to solve the inverse problem: given an element f in some metric space (S,d), find a contraction T:S -> S that admits a unique fixed point p such that d(f,p)< eps. When eps=0 the inverse problem is solved exactly and the fixed point p can be identified with the operator T, but in most cases T is an approximation of the target f and T takes linear forms. We present applications of the IFS technique to the problem of estimation of distribution and density functions and to the simulation of L2 stochastic processes.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/12.html

### 2009/02/03

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Gombodorj Bayarmagnai (東京大学数理科学研究科)
The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)
[ Abstract ]
In this talk the basic object will be the principal series representataion of $SU(2, 2)$,
parabolically induced by the minimal parabolic subgroup. We discuss about the $(\\mathfrak g,K)$-module structure on that type of principal series explicitely, and provide various integral expressions of some smooth Whittaker functions with certain $K$-types.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009/02/02

#### Lectures

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Erwin Bolthausen (University of Zurich)
On a perceptron version of the Generalized Random Energy Model

### 2009/01/30

#### GCOE Seminars

16:15-17:15   Room #370 (Graduate School of Math. Sci. Bldg.)
F. Cakoni (University of Delaware)
Faber-Krahn Type Inequalities in Inverse Scattering Theory
[ Abstract ]
We first consider the scattering of time harmonic plane waves by a perfectly conducting infinite cylinder of cross section D. We observe that the Dirichlet eigenvalues for the Laplacian in D can be determined from the far field pattern of the scattered wave and hence from the Faber-Krahn inequality we can obtain a lower bound for the area of D. We then consider the corresponding problem for a dielectric medium. Here we observe that a relatively new type of spectra called transmission eigenvalues can be determined from the far field pattern of the scattered wave and show that transmission eigenvalues exist and form a discrete set. We then obtain a Faber-Krahn type inequality for transmission eigenvalues which, if D is known, provide a lower bound on the index of refraction n(x). Of special interest is the case when cavities may be present,i.e. regions where n(x)=1.We consider both isotropic and anisotropic materials.

#### GCOE Seminars

15:10-16:10   Room #370 (Graduate School of Math. Sci. Bldg.)
Lucie Baudouin (LAAS-CNRS groupe MAC)
Use of Carleman estimates for stability in some inverse problems
[ Abstract ]
In this presentation, we shall present how global Carleman inequalities can be used to prove the well-posedness of inverse problems related to various partial differential equations. This lecture will gather joint works with J.-P. Puel, A. Osses and A. Mercado. We focus here on stability results for the determination of potential from Neumann boundary measurements by using the Bukhgeim-Klibanov method. We will begin with the simplest models: the Schrodinger and wave equations, and then present some more recent results for transmission problems (same equations with discontinuous main coefficient).

### 2009/01/29

#### Applied Analysis

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

Extension and Unification of Singular Perturbation Methods for ODE's Based on the Renormalization Gourp Method
[ Abstract ]
くりこみ群の方法は微分方程式に対する特異摂動法の一種であり,多重尺度法、平均化法、normal forms, 中心多様体縮約、位相縮約、WKB解析などの古くから知られる摂動法を統一的に扱うことができる.ここではくりこみ群の方法を数学的定式化を与え,結合振動子系などへのいくつかの応用も紹介したい.

### 2009/01/28

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #122 (Graduate School of Math. Sci. Bldg.)

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Pierre Colmez (École polytechnique)
On the p-adic local Langlands correspondence

### 2009/01/27

#### Tuesday Seminar on Topology

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

Lagrangian Floer homology and quasi homomorphism
from the group of Hamiltonian diffeomorphism

[ Abstract ]
Entov-Polterovich constructed quasi homomorphism
from the group of Hamiltonian diffeomorphisms using
spectral invariant due to Oh etc.
In this talk I will explain a way to study this
quasi homomorphism by using Lagrangian Floer homology.
I will also explain its generalization to use quantum
cohomology with bulk deformation.
When applied to the case of toric manifold, it
gives an example where (infinitely) many quasi homomorphism
exists.
(Joint work with Oh-Ohta-Ono).

### 2009/01/26

#### Seminar on Geometric Complex Analysis

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

#### GCOE lecture series

17:15-18:15   Room #470 (Graduate School of Math. Sci. Bldg.)
Vladimir Romanov (Sobolev Instutite of Mathematics)
ASYMPTOTIC EXPANSIONS FOR SOME HYPERBOLIC EQUATIONS 第1講
[ Abstract ]
For a linear second-order hyperbolic equation with variable coefficients the fundamental solution for the Cauchy problem is considered. An asymptotic expansion of this solution in a neighborhood of the characteristic cone is introduced and explicit formulae for coefficients of this expansion are derived. Similar questions are discussed for the elasticity equations related to an inhomogeneous isotropic medium.

#### GCOE Seminars

16:00-17:00   Room #470 (Graduate School of Math. Sci. Bldg.)
Vilmos Komornik (University of Strasbourg)
Ingham-Beurling type inequalities
[ Abstract ]
We present a self-contained constructive proof for a multidimensional generalization of Beurling's optimal condition for the validity of Ingham type estimates. We illustrate the usefulness of the result on a particular observability problem.

### 2009/01/24

#### Infinite Analysis Seminar Tokyo

11:00-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]
Young図形における hook formula は、組合せ論的には、その Young 図形の standar
d tableau の総数を数え上げる公式である。R. P. Stanley は reverse plane parti
tion のなす母関数を考えることにより、この公式をq-hook formula に拡張し、E. R
. Gansner はそれをさらに多変数に一般化した。

n の hook formula の証明も与える。

Catalan numbers and level 2 weight structures of $A^{(1)}_{p-1}$
[ Abstract ]
Motivated by a connection between representation theory of
the degenerate affine Hecke algebra of type A and
Lie theory associated with $A^{(1)}_{p-1}$, we determine the complete
set of representatives of the orbits for the Weyl group action on
the set of weights of level 2 integrable highest weight representations of $\\widehat{\\mathfrak{sl}}_p$.
Applying a crystal technique, we show that Catalan numbers appear in their weight multiplicities.

Here "a crystal technique" means a result based on a joint work with S.Ariki and V.Kreiman,
which (as an application of the Littelmann's path model) combinatorially characterize
the connected component (usually called Kleshchev bipartition in the representation theoretic context)
$B(\\Lambda_0+\\Lambda_s)\\subseteq B(\\Lambda_0)\\otimes B(\\Lambda_s)$ in the tensor product.

On a dimer model with impurities
[ Abstract ]
We consider the dimer problem on a non-bipartite graph $G$, where there are two types of dimers one of which we regard impurities. Results of simulations using Markov chain seem to indicate that impurities are tend to distribute on the boundary, which we set as a conjecture. We first show that there is a bijection between the set of dimer coverings on
$G$ and the set of spanning forests on two graphs which are made from $G$, with configuration of impurities satisfying a pairing condition, and this bijection can be regarded as a extension of the Temperley bijection. We consider local move consisting of two operations, and by using the bijection mentioned above, we prove local move connectedness. Finally, we prove that the above conjecture is true,
in some spacial cases.

### 2009/01/23

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

#### GCOE lecture series

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (University of Amsterdam )
The spectral category of Hecke algebras and applications 第4講 Example: Lusztig's unipotent representations for classical groups.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

### 2009/01/22

#### Operator Algebra Seminars

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

On the electron-phonon interacting system

#### GCOE lecture series

17:00-18:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (University of Amsterdam)
The spectral category of Hecke algebras and applications 第3講 The spectral category and correspondences of tempered representations.

[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

### 2009/01/21

#### Lectures

16:50-17:50   Room #123 (Graduate School of Math. Sci. Bldg.)
Erwin Bolthausen (University of Zurich)
The quenched critical point of a diluted disordered polymer model and the related question for the random copolymer

### 2009/01/20

#### Tuesday Seminar of Analysis

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

Generating function of eigenvalues of Daubechies Localization Operator
[ Abstract ]
Daubechies Localization Operator の 固有値の母関数から symbol 関数を再現する公式について

#### Tuesday Seminar on Topology

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

Five dimensional $K$-contact manifolds of rank 2
[ Abstract ]
A $K$-contact manifold is an odd dimensional manifold $M$ with a contact form $\\alpha$ whose Reeb flow preserves a Riemannian metric on $M$. For examples, the underlying manifold with the underlying contact form of a Sasakian manifold is $K$-contact. In this talk, we will state our results on classification up to surgeries, the existence of compatible Sasakian metrics and a sufficient condition to be toric for closed $5$-dimensional $K$-contact manifolds with a $T^2$ action given by the closure of the Reeb flow, which are obtained by the application of Morse theory to the contact moment map for the $T^2$ action.

#### Tuesday Seminar on Topology

17:30-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)

Surface links which are coverings of a trivial torus knot (JAPANESE)
[ Abstract ]
We consider surface links which are in the form of coverings of a
trivial torus knot, which we will call torus-covering-links.
spun $T^2$-knots, turned spun $T^2$-knots, and symmetry-spun tori.
We see some properties of torus-covering-links.

### 2009/01/19

#### Seminar on Geometric Complex Analysis

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

### 2009/01/16

#### Lecture Series on Mathematical Sciences in Soceity

16:20-17:50   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2009/01/15

#### Operator Algebra Seminars

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Alin Ciuperca (Univ. Toronto)
Isomorphism of Hilbert modules over stably finite $C^*$-algebras