## Seminar information archive

### 2007/01/31

#### Seminar on Mathematics for various disciplines

10:30-11:30   Room #123 (Graduate School of Math. Sci. Bldg.)

ガラスに吸着した色素分子の一分子観察――ランダムウォークと拡散――
[ Abstract ]

ガラスの上に希薄に吸着した蛍光性の色素を使って分子の表面拡散をしらべた。平均自乗偏位は時間に比例して増大するようにみえ、これから拡散係数を見積もることができる。

このようにして求めた拡散係数は測定環境の湿度に大きく依存することがわかった。こうして、問題はガラス表面にある数ナノメートルの吸着水のなかでの色素分子の運動の議論になってきた。拡散係数に場所ムラはあるのか、時間依存性はあるのか、実験は進行中である。
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### Number Theory Seminar

15:15-18:45   Room #117 (Graduate School of Math. Sci. Bldg.)
Dennis Eriksson (東大数理/Paris) 15:15-16:15
Towards a proof of a metrized Deligne-Riemann-Roch theorem

CM楕円曲線の超特異点における2変数p進L関数
(A two variable p-adic L-function for CM elliptic curves at supersingular primes)
Frans Oort (Utrecht) 17:45-18:45
Irreducibility of strata and leaves in the moduli space of abelian varieties

#### Lectures

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Li Daqian (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

A Sequential Unit Root Test
[ Abstract ]
It is well known that conventional unit root tests such as Dickey=Fuller and its variants do not have good power properties when sample size is not large. Lai and Siegmund (1983, AS) proved that OLS estimator of the AR(1) coefficient is asymptotically normally distributed in a sequential framework even if the time series has a unit root unlike the OLS estimator under a standard sampling scheme. We pursue this direction to propose a unit root test under a sequential sampling. The proposed test uses not only the OLS estimator of the AR(1) coefficient, which is asymptotically normal, but also the stopping time to construct the critical region, anticipating a better power property. We obtain analytic expressions of the joint distribution of the two statistics as well as its marginals under the null. We also consider the distribution of the statistics under local alternatives. The properties of the stopping time, to the best of our knowledge, have not been studied in the unit root literature. We calculate its expectation and variance.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/18.html

### 2007/01/30

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
John F. Duncan (Harvard University)
Elliptic genera and some finite groups
[ Abstract ]
Recent developments in the representation theory of sporadic groups
suggest new formulations of moonshine' in which Jacobi forms take on the
role played by modular forms in the monstrous case. On the other hand,
Jacobi forms arise naturally in the study of elliptic genera. We review
the use of vertex algebra as a tool for constructing the elliptic genus of
a suitable vector bundle, and illustrate connections between this and
vertex algebraic representations of certain sporadic simple groups.

#### Lectures

16:30-18:00   Room #118 (Graduate School of Math. Sci. Bldg.)
Jerome Le Rousseau (Laboratoire d'Analyse Topologie Probabilit\'es
Universit\'e de Provence / CNRS)
Controllability of parabolic equations with non-smooth coefficients by means of global Carleman estimates
[ Abstract ]
We shall review the different concepts of controllability for parabolic equations and a fix-point method to achieve null-controllability of classes of semilinear equations. It is mainly based on observability inequalities and a precise knowledge of the observability constant. These inequalities are obtained by means of global Carleman estimates. We shall review their derivations and how they can be obtained in the case of non-smooth coefficients. We shall also present some open questions.
Part of this work is in collaboration with Assia Benabdallah and Yves Dermenjian (also from Universit\\'e de Provence).

#### Infinite Analysis Seminar Tokyo

14:00-15:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Michael Lashkevich (Landau Institute)
Scaling limits for the SOS models and bosonization
[ Abstract ]
Two different scaling limits in the SOS models are considered. The scaling limits of the bosonic construction for form factors provide form factors of some classes of operators in the scaling SOS/RSOS models and the sine-Gordon model.

### 2007/01/29

#### Lectures

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Li Daqian (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

#### Seminar on Geometric Complex Analysis

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

Radial cluster set of a bounded holomorphic map in the unit ball of C^n

### 2007/01/27

#### Infinite Analysis Seminar Tokyo

13:30-16:00   Room #117 (Graduate School of Math. Sci. Bldg.)

マイクロクラスターの特異なダイナミクス
[ Abstract ]

[ Abstract ]

この問題にアプローチするために、キリロフ・レシェティヒン加群$W_s^{(r)}$ (以下略してKR加群)を研究したい。これはアフィンリー環のディンキン図形の頂点$0$を除く頂点の番号$r$と、任意の正整数$s$の組によってパラメトライズされる。KR加群に関して、`フェルミ型公式''に起源をもつ以下の予想がある。尚, 現在までにこの予想の反例は見つかっていない。

さらに$s$が$t_r:=max(1,2/(\\alpha_r \\vert \\alpha_r))$の倍数ならば、KR加群$W_s^{(r)}$の結晶基底$B^{r,s}$は、レベル$s/t_r$の完全結晶である。ただし, $(\\cdot \\vert \\cdot)$はウェイト格子上の標準線形形式。」

### 2007/01/26

#### Algebraic Geometry Seminar

16:30-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Professor Frans Oort
(Department of Mathematics
University of Utrecht
)
Irreducibility of strata and leaves in the moduli space of
abelian varieties I (a survey of results)

#### Lectures

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Li Daqian (復旦大学)
Controllability and Observability:
from ODEs to Quasilinear Hyperbolic Systems

### 2007/01/25

#### Applied Analysis

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Michael TRIBELSKY (東大・数理 / モスクワ工科大学)
Soft-mode turbulence as a new type of spatiotemporal chaos at onset

#### Operator Algebra Seminars

15:15-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

The Pimsner-Voiculescu AF-embedding of the irrational rotation $C^*$-algebra and its subalgebra

A Note on Weak Amenability

#### Functional Analysis Seminar

14:00-17:00   Room #370 (Graduate School of Math. Sci. Bldg.)
Ivana Alexandrova (East Carolina University)
Semi-Classical Structure of the Scattering Amplitude and the Spectral Function for Schrodinger Operators

### 2007/01/23

#### Tuesday Seminar on Topology

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

The twistor correspondence for self-dual Zollfrei metrics
----their singularities and reduction

[ Abstract ]
C. LeBrun and L. J. Mason investigated a twistor-type correspondence
between indefinite conformal structures of signature (2,2) with some properties
and totally real embeddings from RP^3 to CP^3.
In this talk, two themes following LeBrun and Mason are explained.

First we consider an additional structure:
the conformal structure is equipped with a null surface foliation
which has some singularity.
We establish a global twistor correspondence for such structures,
and we show that a low dimensional correspondence
between some quotient spaces is induced from this twistor correspondence.

Next we formulate a certain singularity for the conformal structures.
We generalize the formulation of LeBrun and Mason's theorem
admitting the singularity, and we show explicit examples.

On the homology group of $Out(F_n)$
[ Abstract ]
Suppose $F_n$ is the free group of rank $n$,
$Out(F_n) = Aut(F_n)/Inn(F_n)$ the outer automorphism group of $F_n$.
We compute $H_*(Out(F_n);\\mathbb{Q})$ for $n\\leq 6$ and conclude
that non-trivial classes in this range are generated
by Morita classes $\\mu_i \\in H_{4i}(Out(F_{2i+2});\\mathbb{Q})$.
Also we compute odd primary part of $H^*(Out(F_4);\\mathbb{Z})$.

### 2007/01/22

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hanjin Lee (Seoul National University)
Omori-Yau generalized maximum principle

### 2007/01/19

#### Lectures

10:30-12:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Alex Mahalov (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics

### 2007/01/18

#### Lectures

13:00-14:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Alex Mahalov (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics
[ Abstract ]
We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes Equations for fully three-dimensional initial data characterized by uniformly large vorticity; smoothness assumptions for initial data are the same as in local existence theorems. There are no conditional assumptions on the properties of solutions at later times, nor are the global solutions close to any 2D manifold. The global existence is proven using techniques of fast singular oscillating limits, Lemmas on restricted convolutions and the Littlewood-Paley dyadic decomposition. In the second part of the talk, we analyze regularity and dynamics of the 3D Euler equations in cylindrical domains with weakly aligned large initial vorticity.

#### Operator Algebra Seminars

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

Twisted Bernoulli shift actions of $Z^2 \\rtimes SL(2,Z)$

#### Applied Analysis

16:00-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)
LIANG Xing (東京大学大学院数理科学研究科 / 日本学術振興会)
Asymptotic Speeds of Spread and Traveling Waves for Monotone Semiflows with Applications
[ Abstract ]
The theory of asymptotic speeds of spread and monotone traveling waves is established for a class of monotone discrete and continuous-time semiflows and is applied to a functional differential equation with diffusion, a time-delayed lattice population model and a reaction-diffusion equation in an infinite
cylinder.

### 2007/01/17

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Alex Mahalov (Department of Mathematics and Statistics, Department of Mechanical and Aerospace Engineering, Program in Environmental Fluid Dynamics, Arizona State University )
Fast Singular Oscillating Limits of Hydrodynamic PDEs: application to 3D Euler, Navier-Stokes and MHD equations
[ Abstract ]
Methods of harmonic analysis and dispersive properties are applied
to 3d hydrodynamic equations to obtain long-time and/or global existence results to the Cauchy problem for special classes of 3d initial data. Smoothness assumptions for initial data are the same as in local existence theorems. Techniques for fast singular oscillating limits are used and large and/or infinite time regularity is obtained by bootstrapping from global regularity of the limit equations.
The latter gain regularity from 3d nonlinear cancellation of oscillations.
Applications include Euler, Navier-Stokes, Boussinesq and MHD equations, in infinite, periodic and bounded cylindrical domains.
[ Reference URL ]
http://coe.math.sci.hokudai.ac.jp/

#### Lectures

15:30-17:00   Room #470 (Graduate School of Math. Sci. Bldg.)

Hamilton-Jacobi方程式の漸近解とその周辺の話題

#### Seminar on Probability and Statistics

16:20-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

Second order optimality for estimators in time series regression models
[ Abstract ]
We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator $\\hat{\\beta}$ proposed by Hannan (1963). This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of $\\hat{\\beta}$. Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that $\\hat{\\beta}$ has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of $\\hat{\\beta}$. Numerical studies are given to confirm the theoretical results.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/17.html

#### Lectures

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Mourad Bellassoued (Faculte des Sciences de Bizerte)
Recovering a potential in the wave equation via Dirichlet-to-Neumann map.