## 過去の記録

### 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

#### 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
Chongying Dong 氏 (UC Santa Cruz)
On uniqueness of the moonshine vertex operator algebra

#### 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

(東北大学・大学院理学研究科)

[ 講演概要 ]

### 2006年12月13日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
C. M. Elliott 氏 (University of Sussex)
Computational Methods for Geometric PDEs
[ 講演概要 ]
Computational approaches to evolutionary geometric partial differential equations such as anisotropic motion by mean curvature and surface diffusion are reviewed. We consider methods based on graph, parametric , level set and phase field descriptions of the surface. We also discuss the approximation of partial differential equations which hold on the evolving surfaces. Numerical results will be presented along with some approximation results.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### 数理ファイナンスセミナー

17:30-19:00   数理科学研究科棟(駒場) 118号室

### 2006年12月12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
Maxim Kazarian 氏 (Steklov Math. Institute)
Thom polynomials for maps of curves with isolated singularities
(joint with S. Lando)
[ 講演概要 ]
Thom (residual) polynomials in characteristic classes are used in
the analysis of geometry of functional spaces. They serve as a
tool in description of classes Poincar\\'e dual to subvarieties of
functions of prescribed types. We give explicit universal
expressions for residual polynomials in spaces of functions on
complex curves having isolated singularities and
multisingularities, in terms of few characteristic classes. These
expressions lead to a partial explicit description of a
stratification of Hurwitz spaces.

### 2006年12月11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

Modified deficiencies of holomorphic curves and defect relation

### 2006年12月08日(金)

#### 講演会

10:30-12:00   数理科学研究科棟(駒場) 056号室
Charles M. Elliott 氏 (University of Sussex)
Computational Methods for Surface Partial Differential Equations
[ 講演概要 ]
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.

We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\\Gamma$ in $\\mathbb R^{n+1}$. The key idea is based on the approximation of $\\Gamma$ by a polyhedral surface $\\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\\Phi$ whose zero level set is $\\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.

Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).

#### 代数幾何学セミナー

15:00-16:25   数理科学研究科棟(駒場) 126号室
Stefan Kebekus 氏 氏 (Mathematisches Institut
Universität zu Köln
)
Rationally connected
foliations

### 2006年12月07日(木)

#### 講演会

13:00-14:30   数理科学研究科棟(駒場) 056号室

Charles M. Elliott 氏 (University of Sussex)
Computational Methods for Surface Partial Differential Equations
[ 講演概要 ]
In these lectures we discuss the formulation, approximation and applications of partial differential equations on stationary and evolving surfaces. Partial differential equations on surfaces occur in many applications. For example, traditionally they arise naturally in fluid dynamics, materials science, pattern formation on biological organisms and more recently in the mathematics of images. We will derive the conservation law on evolving surfaces and formulate a number of equations.

We propose a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces $\\Gamma$ in $\\mathbb R^{n+1}$. The key idea is based on the approximation of $\\Gamma$ by a polyhedral surface $\\Gamma_h$ consisting of a union of simplices (triangles for $n=2$, intervals for $n=1$) with vertices on $\\Gamma$. A finite element space of functions is then defined by taking the continuous functions on $\\Gamma_h$ which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on $\\Gamma$. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. We extend this approach to pdes on evolving surfaces. We define an Eulerian level set method for partial differential equations on surfaces. The key idea is based on formulating the partial differential equation on all level set surfaces of a prescribed function $\\Phi$ whose zero level set is $\\Gamma$. We use Eulerian surface gradients to define weak forms
of elliptic operators which naturally generate weak formulations
of Eulerian elliptic and parabolic equations. This results in a degenerate equation formulated in anisotropic Sobolev spaces based on the level set function $\\Phi$. The resulting equation is then solved in one space dimension higher but can be solved on a fixed finite element grid.

Numerical experiments are described for several linear and Nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow. In particular we show how surface level set and phase field models can be used to compute the motion of curves on surfaces. This is joint work with G. Dziuk(Freiburg).
[ 講演参考URL ]
http://www.u-tokyo.ac.jp/campusmap/map02_02_j.html

#### 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

An introduction to analytic endomotives (after Connes-Consani-Marcolli)

### 2006年12月06日(水)

#### 諸分野のための数学研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model
[ 講演概要 ]
Chondrules are small particles of silicate material of the order of a few millimeters in radius, and are the main component of chondritic meteorite.

In this paper, we present a model of the growth starting from a seed crystal at the location of an outer part of pure melt droplet into spherical single crystal corresponding to a chondrule. The formation of rims surrounding a chondrule during solidification is simulated by using the phase field model in three dimensions. Our results display a well developed rim structure when we choose the initial temperature of a melt droplet more than the melting point under the condition of larger supercooling. Furthermore, we show that the size of a droplet plays an important role in the formation of rims during solidification.
[ 講演参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

#### 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
Vincent Maillot 氏 (Jussieu/京大数理研) 16:30-17:30
New applications of the arithmetic Riemann-Roch theorem
Don Blasius 氏 (UCLA) 17:45-18:45
Zariski Closures of Automorphic Galois Representations