## Seminar information archive

#### 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.

#### GCOE Seminars

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.

### 2009/01/08

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Stefaan Vaes (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Stefaan Vaes (K. U. Leuven)
Rigidity for II$_1$ factors: fundamental groups, bimodules, subfactors

#### Seminar on Mathematics for various disciplines

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

Calibration problems for Black-Scholes American Options under the GMMY process
[ Abstract ]
The calibration problem is formulated as a control problem for the parabolic variational inequality. The well-posedness of the formulation is discussed and the necessary optimality is derived. A numerical approximation method is also presented.

#### 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

[ Abstract ]
Hecke algebras play an important role in the harmonic analysis of a p-adic reductive group. On the other hand, their representation theory and harmonic analysis can be described almost completely explicitly. This makes affine Hecke algebras an ideal tool to study the harmonic analysis of p-adic groups. We will illustrate this in this series of lectures by explaining how various components of the Bernstein center contribute to the level-0 L-packets of tempered representations, purely from the point of view of harmonic analysis.

We define a "spectral category" of (affine) Hecke algebras. The morphisms in this category are not algebra morphisms but are affine morphisms between the associated tori of unramified characters, which are compatible with respect to the so-called Harish-Chandra μ-functions. We show that such a morphism generates a Plancherel measure preserving correspondence between the tempered spectra of the two Hecke algebras involved. We will discuss typical examples of spectral morphisms.
We apply the spectral correspondences of affine Hecke algebras to level-0 representations of a quasi-split simple p-adic group. We will concentrate on the example of the special orthogonal groups $SO_{2n+1}(K)$. We show that all affine Hecke algebras which arise in this context admit a *unique* spectral morphism to the Iwahori-Matsumoto Hecke algebra, a remarkable phenomenon that is crucial for this method. We will recover in this way Lusztig's classification of "unipotent" representations.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2009.html#20090108opdam

### 2009/01/06

#### Lectures

16:00-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第3回)
[ Abstract ]

・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播

#### Lectures

14:00-15:30   Room #123 (Graduate School of Math. Sci. Bldg.)

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第2回)
[ Abstract ]

・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導

### 2009/01/05

#### Lectures

16:00-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

GCOE連続講演会 「電気生理学における数理モデル」 (3回講演の第1回)
[ Abstract ]

・ 膜電位とイオンチャネル
・ 細胞の体積調節
・ チャネルの開閉
・ Hodgkin-Huxley モデルと興奮性

・ Hodgkin-Huxley モデルとFitzHugh-Nagumo モデル
・ 神経軸策とケーブルモデル
・ 活動電位の伝播
・ 有髄神経と跳躍伝導

・ 心臓の生理学
・ 3次元ケーブルモデル
・ 均質化極限とbidomain モデル
・ 心臓における興奮波の伝播

### 2008/12/26

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On Siegel Eisenstein series of degree two and weight 2
[ Abstract ]
Cups singularities の組み合わせ論的な解析を援用して、あるレベルのモジュラー群に対する表題の空間の次元を決定する。

### 2008/12/19

#### Lecture Series on Mathematical Sciences in Soceity

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