## 過去の記録

### 2008年10月24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) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)
Benoit Collins 氏 (オタワ大学・東京大学大学院数理科学研究科)
On the spectral measure of the sum of elements in a finite von Neumann algebra
[ 講演概要 ]
Given two self-adjoint n×n matrices A and B with prescribed eigenvalues, the set of all possible spectral distributions for A+B has been conjectured by Horn and proved by Knutson, Tao, Klyachko and Totaro.
We address the same question when A and B have prescribed spectral measures but lie in an arbitrary II_1 factor, and we give elements of answers in terms of inequalities between the spectral measures. We explain the relation with the Connes embedding problem.

### 2008年10月23日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Emily Peters 氏 (UC Berkeley)
Planar algebras and the Haagerup subfactor

### 2008年10月22日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室
10月から教室が056号室に変更になります.
Pierre Parent 氏 (Universite Bordeaux 1)
Serre's uniformity in the split Cartan case
[ 講演概要 ]
We show that, for large enough prime number p, the modular curve
X_{split}(p) has no other point with values in Q than CM points and the rational cusp. This gives a partial answer to an old question of J.-P. Serre concerning the uniform surjectivity of Galois representations associated to torsion points on elliptic curves without complex multiplication.
(Joint work with Yuri Bilu.)

### 2008年10月21日(火)

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 126号室
いつもと開始時刻が違います。また同氏による集中講義がこの週に行われます。

Invitation to Atlas combinatorics
[ 講演概要 ]

この講演では、リー群に関する背景説明などは軽く済ませ、Atlas で公開されているプログラムにおける方言、特に入出力の読み方を通常の言葉に言い換えることで、
プログラムを使ってもらう入り口での障壁を減らしたいと考えています。
ふむ、なかなか、使えるな、自分もインストールしてみようか、と思ってもらえれば、成功です。

なお、サーベイトークなので私のオリジナルな結果は含まれていません。また、計算機を使ってデモをする予定です。京都では計算機と板書の切り替えでばたばたしたので、照準を絞って慌てないように話したいと思います。
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### 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) 002号室
Tea: 16:00 - 16:30 コモンルーム

On embeddings of 3-manifolds in 6-manifolds
[ 講演概要 ]
In this talk, we give a simple axiomatic definition of an invariant of
smooth embeddings of 3-manifolds in 6-manifolds.
The axiom is expressed in terms of some cobordisms of pairs of manifolds of
dimensions 6 and 3 (equipped with some cohomology class of the complement) and
the signature of 4-manifolds.
We then show that our invariant gives a unified framework for some classical
invariants in low-dimensions (Haefliger invariant, Milnor's triple
linking number, Rokhlin invariant, Casson invariant,
Takase's invariant, Skopenkov's invariants).

### 2008年10月20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

パンルヴェ方程式と複素力学系

### 2008年10月17日(金)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 128号室

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 570号室

GCOEレクチャー"Holomorphic extensions of unitary representations" その4 "Applications and open problems"
[ 講演概要 ]
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krotz-Stanton), random matrices (Huckleberry-Puttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

#### 代数幾何学セミナー

13:00-14:30   数理科学研究科棟(駒場) 128号室
Yongnam Lee 氏 (Sogang U.)
Construction of surfaces of general type with pg=0 via
Q-Gorenstein smoothing

#### GCOEレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 118号室

Holomorphic extensions of unitary representations その4 Applications and open problems

[ 講演概要 ]
In this lecture we present further applications of the given extension results and describe some open problems. In particular, we will mention estimates for automorphic forms (Krötz-Stanton), random matrices (Huckleberry-Püttmann-Zirnbauer), unitarizability of highest weight representation with non-scalar lowest K-type, and infinite dimensional groups.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

### 2008年10月16日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Scott Morrison 氏 (UC Santa Barbara)
The $D_{2n}$ planar algebras

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 570号室

GCOEレクチャー"Holomorphic extensions of unitary representations" その3 "Highest weight representations"
[ 講演概要 ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Joseph F. Grotowski 氏 (University of Queensland)
Two-dimensional harmonic map heat flow versus four-dimensional Yang-Mills heat flow
[ 講演概要 ]
Harmonic map heat flow and Yang-Mills heat flow are the gradient flows associated to particular energy functionals. In the considered dimension, (i.e. dimension two for the harmonic map heat flow, dimension four for the Yang-Mills heat flow), the associated energy functional is (locally) conformally invariant, that is, the dimension is critical. This leads to a number of interesting phenomena when considering both the functionals and the associated flows. In this talk we discuss qualitative similarities and differences between the flows.

#### GCOEレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 123号室

Holomorphic extensions of unitary representations その3 Highest weight representations
[ 講演概要 ]
In this lecture we explain the extension results in a little more detail and explain how they lead to geometric realizations of singular highest weight representations on nilpotent coadjoint orbits.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

### 2008年10月15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

Asymptotic behavior of solutions for BCF model describing crystal surface growth
[ 講演概要 ]
This talk is concerned with the initial-boundary value problem for a nonlinear parabolic equation which was presented Johnson et al. for describing the process of growth of a crystal surface on the
basis of the BCF theory. We will investigate asymptotic behavior of solutions by construct exponential attractors and a Lyapunov function and by examining a structure of the $\\omega$ limit set.

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 002号室
George Sell 氏 (ミネソタ大学)

[ 講演概要 ]
In both lectures we will examine a new topic of the thin
3D Navier-Stokes equations with Navier boundary conditions.

In the first lecture we will treat the ultimate boundedness
of strong solutions and the related theory of global
attractors.

In the second lecture, which will include a brief summary
of the first lecture, we will examine the role played by the
2D Limit Problem. These issues are a special challenge for
analysis because the 2D Limit Problem is NOT imbedded the
3D problem.

These lectures are based on joint work with Genevieve Raugel,Dragos Iftimie, and Luan Hoang.

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 570号室

GCOEレクチャー"Holomorphic extensions of unitary representations" その2 "Geometric Background"
[ 講演概要 ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

#### GCOEレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 122号室

Holomorphic extensions of unitary representations その2 Geometric background
[ 講演概要 ]
In this lecture we will explain the complex geometry needed to understand the phenomena described in the first lecture. The key words here are Olshanski semigroups, invariant cones in Lie algebras, Akhiezer-Gindikin domain, and coadjoint orbits of convex type.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2008.html#20081014hilgert

### 2008年10月14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
Jeffrey Herschel Giansiracusa 氏 (Oxford University)
Pontrjagin-Thom maps and the Deligne-Mumford compactification
[ 講演概要 ]
An embedding f: M -> N produces, via a construction of Pontrjagin-Thom, a map from N to the Thom space of the normal bundle over M. If f is an arbitrary map then one instead gets a map from N to the infinite loop space of the Thom spectrum of the normal bundle of f. We extend this Pontrjagin-Thom construction of wrong-way maps to differentiable stacks and use it to produce interesting maps from the Deligne-Mumford compactification of the moduli space of curves to certain infinite loop spaces. We show that these maps are surjective on mod p homology in a range of degrees. We thus produce large new families of torsion cohomology classes on the Deligne-Mumford compactification.

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 002号室
George Sell 氏 (ミネソタ大学)

Ultimate boundedness of solutions with large data and global attractors
[ 講演概要 ]
In both lectures we will examine a new topic of the thin 3D Navier-Stokes equations with Navier boundary conditions.

In the first lecture we will treat the ultimate boundedness of strong solutions and the related theory of global attractors.

In the second lecture, which will include a brief summary of the first lecture, we will examine the role played by the 2D Limit Problem. These issues are a special challenge for analysis because the 2D Limit Problem is NOT imbedded the 3D problem.

These lectures are based on joint work with Genevieve Raugel, Dragos Iftimie, and Luan Hoang.

#### 解析学火曜セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
GCOE講演会と共催です.部屋と時間が通常と異なりますのでご注意ください
George Sell 氏 (ミネソタ大学)
Thin 3D Navier-Stokes equations: Ultimate boundedness of solutions with large data and global attractors
[ 講演概要 ]
グローバルCOE連続講演会と共催です.詳細はそちらをご覧ください.

#### 講演会

15:00-16:00   数理科学研究科棟(駒場) 570号室

GCOEレクチャー"Holomorphic extensions of unitary representations" その1 "Overview and Examples"
[ 講演概要 ]
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.
[ 参考URL ]
http://faculty.ms.u-tokyo.ac.jp/users/gcoe/GCOE_lecture0810Hilgert.html

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
The Dirichlet-to-Neumann map as a pseudodifferential
operator
[ 講演概要 ]
Both Dirichlet and Neumann boundary conditions for the Laplace equation are of fundamental importance in Mathematics and Physics. Given a compact connected Riemannian manifold $M$ with boundary $\\partial M$ the Dirichlet-to-Neumann operator $\\Lambda_g$ maps Dirichlet boundary data $f$ to the corresponding Neumann boundary data $\\Lambda_g f =(\\partial_\\nu u)|_{\\partial M}$ where $u$ denotes the unique solution to the Dirichlet problem $\\laplace_g u=0$ in $M$, $u|_{\\partial M} = f$.
The main statement is that this operator is a first order elliptic pseudodifferential operator on the boundary $\\partial M$.

We will first give a brief overview of how to define the Dirichlet-to-Neumann operator as a map $\\Lambda_g:H^{1/2}(\\partial M)\\longrightarrow H^{-1/2}(\\partial M)$ between Sobolev spaces. In order to show that it is actually a pseudodifferential operator we introduce tangential pseudodifferential operators. This allows us to derive a
microlocal factorization of the Laplacian near boundary points. Together with a regularity statement for the heat equation this will finally give the main result.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

#### GCOEレクチャーズ

15:00-16:00   数理科学研究科棟(駒場) 118号室
In this lecture we present the Gelfand-Gindikin program of decomposing $L^2$-spaces into families of irreducible representations using complex geometry. We then briefly outline results due to Olshanski, Hilgert-Olafsson-Orsted, Hilgert-Neeb-Orsted, Krotz-Stanton and others in this direction. In particular, we will explain holomorphic extensions of holomorphic discrete series representations and their relation to Hardy and weighted Bergman spaces.