## Seminar information archive

### 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 ]
http://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 ]
http://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

#### Applied Analysis

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

On a phase field model for mode III crack growth
[ Abstract ]
2次元弾性体の面外変形による亀裂の進展を記述する,ある
フェイズ・フィールド・モデルについて考える.モデルの

Griffithの破壊基準をもとに,Ambrosio-Tortorelliに
よるエネルギー正則化のアイデアを用いてなされる.

#### 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

#### Lie Groups and Representation Theory

13:30-17:20   Room #050 (Graduate School of Math. Sci. Bldg.)

Quantization of complex manifolds
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/index.files/oshima60th200901.html

Global geometry on locally symmetric spaces — beyond the Riemannian case
[ Abstract ]
The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

In this talk, I plan to give an exposition on the recent developments on the question about the global natures of locally non-Riemannian homogeneous spaces, with emphasis on the existence problem of compact forms, rigidity and deformation.

Classification of Fuchsian systems and their connection problem
[ Abstract ]
We explain a classification of Fuchsian systems on the Riemann sphere together with Katz's middle convolution, Yokoyama's extension and their relation to a Kac-Moody root system discovered by Crawley-Boevey.
Then we present a beautifully unified connection formula for the solution of the Fuchsian ordinary differential equation without moduli and apply the formula to the harmonic analysis on a symmetric space.

### 2009/01/14

#### Lectures

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

[ Abstract ]
ニューロンの興奮性の調節やシナプス可塑性において重要な役割を担っているC型タンパク質リン酸化酵素(PKC)は,その酵素活性と関連して細胞内局在が変化する性質を有する(トランスロケーション).GFP-γPKC融合タンパクを発現させたマウス小脳プルキンエ細胞において,平行線維シナプスの高頻度刺激に伴い,刺激部位近傍から樹状突起に沿ってトランスロケーションが伝播する現象が報告されている.最近,坪川は,同じ刺激条件で樹状突起内をほぼ同速度で伝播する細胞内Ca2+波が生じることを見出し,これがγPKCトランスロケーション波をリードしている可能性を指摘した.本研究では,生理学的・解剖学的知見に基づいたプルキンエ細胞の数理モデルを構築し,Ca2+波の再現を試みた.その結果に基づき,トランスロケーション伝播のメカニズムと機能的意義について考察する.

### 2009/01/13

#### Lectures

10:30-11:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Gieri Simonett (Vanderbilt University, USA)
Analytic semigroups, maximal regularity and nonlinear parabolic problems
[ Reference URL ]
http://www.math.sci.hokudai.ac.jp/sympo/090113/index.html

#### Tuesday Seminar on Topology

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

Compactification of the homeomorphism group of a graph
[ Abstract ]
Topological properties of homeomorphism groups, especially of finite-dimensional manifolds,
have been of interest in the area of infinite-dimensional manifold topology.
For a locally finite graph $\\Gamma$ with countably many components,
the homeomorphism group $\\mathcal{H}(\\Gamma)$
and its identity component $\\mathcal{H}_+(\\Gamma)$ are topological groups
with respect to the compact-open topology. I will define natural compactifications
$\\overline{\\mathcal{H}}(\\Gamma)$ and
$\\overline{\\mathcal{H}}_+(\\Gamma)$ of these groups and describe the
topological type of the pair $(\\overline{\\mathcal{H}}_+(\\Gamma), \\mathcal{H}_+(\\Gamma))$
using the data of $\\Gamma$. I will also discuss the topological structure of
$\\overline{\\mathcal{H}}(\\Gamma)$ where $\\Gamma$ is the circle.

### 2009/01/12

#### Lie Groups and Representation Theory

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

[ Abstract ]

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Jacob S. Christiansen
(コペンハーゲン大学)
Finite gap Jacobi matrices (joint work with Barry Simon and Maxim Zinchenko)

### 2009/01/09

#### GCOE lecture series

17:00-18:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (University of Amsterdam)
The spectral category of Hecke algebras and applications 第2講 Affine Hecke algebras and harmonic analysis.

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

#### Lectures

16:00-17:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Leevan Ling (Hong Kong Baptist University)
Effective Condition Numbers and Laplace Equations

[ Abstract ]
The condition number of a matrix is commonly used for investigating the
stability of solutions to linear algebraic systems. Recent meshless
techniques for solving PDEs have been known to give rise to
ill-conditioned matrices, yet are still able to produce results that are
close to machine accuracy. In this work, we consider the method of
fundamental solutions (MFS), which is known to solve, with extremely high
accuracy, certain
partial differential equations, namely those for which a fundamental
solution is known. To investigate the applicability of the MFS, either when
the boundary is not analytic or when the boundary data is not harmonic, we
examine the relationship between its accuracy and the effective condition
number.