## 過去の記録

### 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 ]
http://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

### 2006年12月25日(月)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

なし
[ 講演概要 ]

12月25日午後から27日午後3時くらいまでです。詳細はURL:
http://www.ms.u-tokyo.ac.jp/activity/meeting061225.htm
をご覧下さい。織田孝幸

### 2006年12月21日(木)

#### アジア数学史セミナー

17:00-18:30   数理科学研究科棟(駒場) 123号室

インド数学における証明
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kawazumi/asia.html

#### 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
Susan Friedlander 氏 (University of Illinois-Chicago)
An Inviscid Dyadic Model For Turbulence
[ 講演概要 ]
We discuss properties of a GOY type model for the inviscid fluid equations. We prove that the forced system has a unique equilibrium which a an exponential global attractor. Every solution blows up in H^5/6 in finite time . After this time, all solutions stay in H^s, s<5/6, and "turbulent" dissipation occurs. Onsager's conjecture is confirmed for the model system.

This is joint work with Alexey Cheskidov and Natasa Pavlovic.

#### 作用素環セミナー

14:45-18:00   数理科学研究科棟(駒場) 126号室
Benoit Collins 氏 (Univ. Claude Bernard Lyon 1) 14:45-16:15
Convergence of unitary matrix integrals and free probability
Roberto Longo 氏 (University of Rome) 16:30-18:00
Operator Algebras and Conformal Field Theory

### 2006年12月20日(水)

#### 代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 117号室
2講演です
On the profinite regular inverse Galois problem
[ 講演概要 ]
Given a field $k$ and a (pro)finite group $G$, consider the
following weak version of the regular inverse Galois problem:
(WRIGP/$G$/$k$) \\textit{there exists a smooth geometrically
irreducible curve $X_{G}/k$ and a Galois extension $E/k(X_{G})$
regular over $k$ with group $G$.} (the regular inverse Galois
problem (RIGP/$G$/$k$) corresponding to the case
$X_{G}=\\mathbb{P}^{1}_{k}$). A standard descent argument shows that
for a finite group $G$ the (WRIGP/$G$/$k$) can be deduced from the
(RIGP/$G$/$k((T))$). For
profinite groups $G$, the (WRIGP/$G$/$k((T))$) has been proved for
lots of fields (including the cyclotomic closure of characteristic $0$
fields) but the descent argument no longer works.\\\\
\\indent Let $p\\geq 2$ be a prime, then a profinite group
$G$ is said to be \\textit{$p$-obstructed} if it fits in a profinite group extension
$$1\\rightarrow K\\rightarrow G\\rightarrow G_{0}\\rightarrow 1$$
with $G_{0}$ a finite group and $K\\twoheadrightarrow \\mathbb{Z}_{p}$. Typical examples of such profinite groups $G$ are
universal $p$-Frattini covers of finite $p$-perfect groups or
pronilpotent projective groups.\\\\
\\indent I will show that the (WRIGP/$G$/$k$) - even under
its weaker formulation: (WWRIGP/$G$/$k$) \\textit{there exists a
smooth geometrically irreducible curve $X_{G}/k$ and a Galois
extension $E/k(X_{G}).\\overline{k}$ with group $G$ and field of
moduli $k$.} - fails for the whole class of $p$-obstructed profinite
groups $G$ and any field $k$ which is either a finitely generated
field of characteristic $0$ or a finite field of characteristic
$\\not= p$.\\\\
\\indent The proof uses a profinite generalization of the cohomological obstruction
for a G-cover to be defined over its field of moduli and an analysis of the constrainsts
imposed on a smooth geometrically irreducible curve $X$ by a degree $p^{n}$
cyclic G-cover $X_{n}\\rightarrow X$, constrainsts which are too rigid to allow the
existence of projective systems $(X_{n}\\rightarrow X_{G})_{n\\geq 0}$ of degree $p^{n}$ cyclic G-covers
defined over $k$. I will also discuss other implicsations of these constrainsts
for the (RIGP).
Eric Friedlander 氏 (Northwestern) 17:45-18:45
An elementary perspective on modular representation theory

### 2006年12月19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

Poisson structures on the homology of the spaces of knots
[ 講演概要 ]
We study the homological properties of the space $K$ of (framed) long knots in $\\R^n$, $n>3$, in particular its Poisson algebra structures.
We had known two kinds of Poisson structures, both of which are based on the action of little disks operad. One definition is via the action on the space $K$. Another comes from the action of chains of little disks on the Hochschild complex of an operad, which appears as $E^1$-term of certain spectral sequence converging to $H_* (K)$. The main result is that these two Poisson structures are the same.
We compute the first non-trivial example of the Poisson bracket. We show that this gives a first example of the homology class of $K$ which does not directly correspond to any chord diagrams.

[ 講演概要 ]
Suppose $F$ is an embedded closed surface in $R^4$.
We call $F$ a pseudo-ribbon surface link
if its projection is an immersion of $F$ into $R^3$
whose self-intersection set $\\Gamma(F)$ consists of disjointly embedded circles.
H. Aiso classified pseudo-ribbon sphere-knots ($F$ is a sphere.)
when $\\Gamma(F)$ consists of less than 6 circles.
when $F$ is two spheres and $\\Gamma(F)$ consists of less than 7 circles.

### 2006年12月18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

Height functions and affine space regular automorphisms

### 2006年12月14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

[ 講演概要 ]

を許容する存在定理の枠組みを提供する為に発展してきた。こうして

の方法論を発展させることによって試みる。また特異点周辺の面積密度の