## 過去の記録

### 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.
[ 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.
[ 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.

### 2007年01月15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

Lagragian constructions for various topological invariants of algebraic varieties (東大数理、松井優氏との共同研究)

#### 講演会

16:30-18:00   数理科学研究科棟(駒場) 122号室

「魅力ある大学院教育」イニシアティブにより以下の講演を行います。

Mourad Bellassoued 氏 (Faculte des Sciences de Bizerte)
Recovering a potential from full Cauchy data for the Schrödinger equation.
[ 講演概要 ]
In this lectures we survey recent progress on the problem of determining a potential by measuring the Dirichlet to Neumann map
for the associated Schr\\"odinger equation or wave equation. We make emphasis on the new results obtained with M.Yamamoto which is concerned with the case that the measurements are made on a strict
subset of the boundary for the wave equation.

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 056号室
Antonio DeSimone 氏 (SISSA (International School for Advanced Studies))
Analysis of physical systems involving multiple spatial scales: some case studies
[ 講演概要 ]
Variational methods have recently proved to be a powerful tool in deriving macroscopic models for phenomena whose physics is decided at the sub-miccron scale.
We will use two case studies to illustrate this point, namely, that of liquid crystal elastomers and that of superhydrophobic surfaces.

Liquid crystal elastomers are solids which combine the optical properties of liquid crystals with the mechanical properties of rubbery solids. They display phase transformations, material instabilities, and microstructures in a way simalr to shape-memory alloys.

The richness of the underlying material symmetries makes the mathematical analysis of this system particularly rewarding. Recent progress, ranging from analytical relaxation results to numerical simulations of the macroscopic mechanical response will be reviewed.

### 2007年01月12日(金)

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 123号室
お茶&Coffee&お菓子: 16:00～16:30(コモンルーム)

1、プレート境界で砂と泥に起こる雪だるま現象
2、プレート境界地震は確率共鳴か
[ 講演概要 ]

### 2007年01月11日(木)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 123号室
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.

### 2007年01月10日(水)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 118号室
Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.

### 2007年01月09日(火)

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 118号室

「魅力ある大学院教育」イニシアティブにより以下の講演を行います。

Oleg Yu. Emanouilov 氏 (Colorado State University)
Some Problems of Global Controllability of Burgers Equation and Navier-Stokes system.
[ 講演概要 ]
We show that 1-D Burgers equation is globally uncontrollable with control acting at two endpoints. Then we establish the global controllability of the 2-D Burgers equation. Finally we show that for 2-D Navier-Stokes system the problem of global exact controllability is solvable for the dense set of the initial data with a control acting on part of the boundary.

### 2006年12月28日(木)

#### 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
Roberto Longo 氏 (University of Rome)
Operator Algebras and Conformal Field Theory II