## 過去の記録

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 126号室
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室

A Sequential Unit Root Test
[ 講演概要 ]
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.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/18.html

### 2007年01月30日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
John F. Duncan 氏 (Harvard University)
Elliptic genera and some finite groups
[ 講演概要 ]
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.

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 118号室

Jerome Le Rousseau 氏 (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
[ 講演概要 ]
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).

#### 東京無限可積分系セミナー

14:00-15:00   数理科学研究科棟(駒場) 123号室
Michael Lashkevich 氏 (Landau Institute)
Scaling limits for the SOS models and bosonization
[ 講演概要 ]
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年01月29日(月)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 126号室
Li Daqian 氏 (復旦大学)
Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

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

### 2007年01月27日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室

マイクロクラスターの特異なダイナミクス
[ 講演概要 ]

[ 講演概要 ]

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年01月26日(金)

#### 代数幾何学セミナー

16:30-17:30   数理科学研究科棟(駒場) 128号室
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)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 126号室
「魅力ある大学院教育」イニシアティブにより以下の3回の講演を行います。
1月26日(金),1月29日(月),31日(水)

Li Daqian 氏 (復旦大学)
Controllability and Observability:
from ODEs to Quasilinear Hyperbolic Systems

### 2007年01月25日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 056号室
Michael TRIBELSKY 氏 (東大・数理 / モスクワ工科大学)
Soft-mode turbulence as a new type of spatiotemporal chaos at onset

#### 作用素環セミナー

15:15-18:00   数理科学研究科棟(駒場) 126号室

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

A Note on Weak Amenability

#### 関数解析セミナー

14:00-17:00   数理科学研究科棟(駒場) 370号室
Ivana Alexandrova 氏 (East Carolina University)
Semi-Classical Structure of the Scattering Amplitude and the Spectral Function for Schrodinger Operators

### 2007年01月23日(火)

#### トポロジー火曜セミナー

16:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

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

[ 講演概要 ]
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 $Out(F_n)$
[ 講演概要 ]
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年01月22日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Hanjin Lee 氏 (Seoul National University)
Omori-Yau generalized maximum principle

### 2007年01月19日(金)

#### 講演会

10:30-12:00   数理科学研究科棟(駒場) 056号室
Alex Mahalov 氏 (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics

### 2007年01月18日(木)

#### 講演会

13:00-14:30   数理科学研究科棟(駒場) 056号室

Alex Mahalov 氏 (Arizona State University)
3D Navier-Stokes and Euler Equations with Uniformly Large Initial Vorticity: Global Regularity and Three-Dimensional Euler Dynamics
[ 講演概要 ]
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.

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

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

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 056号室
LIANG Xing 氏 (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
[ 講演概要 ]
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年01月17日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Alex Mahalov 氏 (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
[ 講演概要 ]
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.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/

#### 講演会

15:30-17:00   数理科学研究科棟(駒場) 470号室

Hamilton-Jacobi方程式の漸近解とその周辺の話題

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 128号室

Second order optimality for estimators in time series regression models
[ 講演概要 ]
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.
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/17.html

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 122号室
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential in the wave equation via Dirichlet-to-Neumann map.

### 2007年01月16日(火)

#### トポロジー火曜セミナー

16:30-18:30   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

An $SO(3)$-version of $2$-torsion instanton invariants
[ 講演概要 ]
We construct invariants for simply connected, non-spin $4$-manifolds using torsion cohomology classes of moduli spaces of ASD connections on $SO(3)$-bundles. The invariants are $SO(3)$-version of Fintushel-Stern's $2$-torsion instanton invariants. We show that this $SO(3)$-torsion invariant of $2CP^2 \\# -CP^2$ is non-trivial, while it is known that any invariants of $2CP^2 \\# - CP^2$ coming from the Seiberg-Witten theory are trivial
since $2CP^2 \\# -CP^2$ has a positive scalar curvature metric.

On the non-acyclic Reidemeister torsion for knots
[ 講演概要 ]
The Reidemeister torsion is an invariant of a CW-complex and a representation of its fundamental group. We consider the Reidemeister torsion for a knot exterior in a homology three sphere and a representation given by the composition of an SL(2, C)- (or SU(2)-) representation of the knot group and the adjoint action to the Lie algebra.
We will see that this invariant is expressed by the differential coefficient of the twisted Alexander invariant of the knot and investigate some properties of the invariant by using this relation.

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 122号室
Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential from partial Cauchy data for the Schrödinger equation.