## 過去の記録

### 2010年06月22日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Ivana Alexandrova 氏 (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
[ 講演概要 ]
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions, and we study how a trajectory
oscillating between the two fields gives rise to resonances near the real axis when
the distance between two centers of fields goes to infinity. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.

### 2010年06月21日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室

ファノ多様体の擬指数と端射線の長さの最小値 (JAPANESE)
[ 講演概要 ]
ファノ多様体上の有理曲線と反標準因子の交点数
の最小値は擬指数(pseudo-index)と呼ばれる。ファノ多様体
の構造は端射線によって制御されるという観点から、

#### 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

A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

### 2010年06月17日(木)

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 128号室
Feng Xu 氏 (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)

#### 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
Feng Xu 氏 (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)

#### 古典解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

あるシュレジンジャー系のクラスについて (JAPANESE)
[ 講演概要 ]
シュレジンジャー系は,リーマン球面上にN+3個の確定特異点を持つL連立1階線形常微分方程式の等モノドロミー族を記述する非線形方程式系です。ここでは,線形方程式が『N+3個の特異点のうちN+1点の近傍でL-1次元の正則解を持つ』特別な状況を考えます。対応するシュレジンジャー系は,実はUC階層(=KP階層のある拡張)の相似簡約として自然に現れるものであり,例えば(L,N)=(2,1)の場合としてパンルヴェ第6方程式、L=2,N:一般の場合にガルニエ系を含む興味深いクラスです。講演では,多項式ハミルトン系としての統一的表示や(捻れドラム理論に基づく)超幾何函数解の構成などを紹介します。

### 2010年06月16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
Luc Illusie 氏 (Universite de Paris-Sud)
Vanishing theorems revisited, after K.-W. Lan and J. Suh (ENGLISH)
[ 講演概要 ]
Let k be an algebraically closed field of characteristic p and X,
Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar
type for certain nef and big line bundles L on Y and morphisms f : X -> Y
having semistable reduction along a divisor with simple normal crossings. It
holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2
and dimension assumptions, and generalizes vanishing theorems of Esnault-
Viehweg and of mine. I'll give an outline of the proof and sketch some
applications, due to K.-W. Lan and J. Suh, to the cohomology of certain
automorphic bundles arising from PEL type Shimura varieties.

### 2010年06月15日(火)

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Sato's counterexample and the structure of generalized functions (JAPANESE)
[ 講演概要 ]
In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.

#### 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

On exceptional surgeries on Montesinos knots
(joint works with In Dae Jong and Shigeru Mizushima) (JAPANESE)
[ 講演概要 ]
I will report recent progresses of the study on exceptional
surgeries on Montesinos knots.
In particular, we will focus on how homological invariants (e.g.
khovanov homology,
knot Floer homology) on knots can be used in the study of Dehn surgery.

### 2010年06月14日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Yongnam Lee 氏 (Sogang University)
Slope of smooth rational curves in an anticanonically polarized Fano manifold (ENGLISH)
[ 講演概要 ]
Ross and Thomas introduce the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature metric. Since K-stability implies slope stability, slope stability gives an algebraic obstruction to theexistence of constant scalar curvature. This talk presents a systematic study of slope stability of anticanonically polarized Fano manifolds with respect to smooth rational curves. Especially, we prove that an anticanonically polarized Fano maniold is slope semistable with respect to any free smooth rational curves, and that an anticanonically polarized Fano threefold X with Picard number 1 is slope stable with respect to any smooth rational curves unless X is the project space. It is a joint work with Jun-Muk Hwang and Hosung Kim.

#### 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

C^n の Levi 平坦実超曲面への距離の Levi form の退化条件 (JAPANESE)
[ 講演概要 ]
C^nのC^2級の実超曲面への距離のLevi formは、超曲面の定義関数の2階微分から決まるHermite行列と対称行列を用いて表現できることを示す。また、その結果を用いて、距離のLevi formが至る所退化するLevi平坦実超曲面の性質を導く。その直接的な応用として、n次元複素トーラス内の滑らかな境界を持つ擬凸部分領域がSteinになるための条件が得られる。

### 2010年06月11日(金)

#### 談話会・数理科学講演会

17:00-18:00   数理科学研究科棟(駒場) 123号室

お茶&Coffee&お菓子: 16:30～17:00 (コモンルーム)。

ガウス・ボンネの定理と曲面上の特異点 (JAPANESE)
[ 講演概要 ]

### 2010年06月10日(木)

#### 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
Christian Klingenberg 氏 (Wuerzburg 大学 )
Hydrodynamic limit of microscopic particle systems to conservation laws to fluid models
[ 講演概要 ]
In this talk we discuss the hydrodynamic limit of a microscopic description of a fluid to its macroscopic PDE description.

In the first part we consider flow through porous media, i.e. the macroscopic description is a scalar conservation law. Here the new feature is that we allow sudden changes in porosity and thereby the flux may have discontinuities in space. Microscopically this is described through an interacting particle system having only one conserved quantity, namely the total mass. Macroscopically this gives rise to a scalar conservation laws with space dependent flux functions

u_t + f(u, x)_x = 0 .

We are able to derive the PDE together with an entropy condition as a hydrodynamic limit from a microscopic interacting particle system.

In the second part we consider a Hamiltonian system with boundary conditions. Microscopically this is described through a system of coupled oscillators. Macroscopically this will lead to a system of conservation laws, namely the p-system. The proof of the hydrodynamic limit is restricted to smooth solutions. The new feature is that we can derive this with boundary conditions.

#### 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
Mikael Pichot 氏 (IPMU)
Random groups and nonarchimedean lattices (JAPANESE)

### 2010年06月09日(水)

#### 代数学コロキウム

16:15-17:15   数理科学研究科棟(駒場) 052号室
Richard Hain 氏 (Duke大学)
Universal mixed elliptic motives (ENGLISH)
[ 講演概要 ]
This is joint work with Makoto Matsumoto. A mixed elliptic
motive is a mixed motive (MHS, Galois representation, etc) whose
weight graded quotients are Tate twists of symmetric powers of the the
motive of elliptic curve. A universal mixed elliptic motive is an
object that can be specialized to a mixed elliptic motive for any
elliptic curve and whose specialization to the nodal cubic is a mixed
Tate motive. Universal mixed elliptic motives form a tannakian
category. In this talk I will define universal mixed elliptic motives,
give some fundamental examples, and explain what we know about the
fundamental group of this category. The "geometric part" of this group
is an extension of SL_2 by a prounipotent group that is generated by
Eisenstein series and which has a family of relations for each cusp
form. Although these relations are not known, we have a very good idea
of what they are, thanks to work of Aaron Pollack, who determined
relations between the generators in a very large representation of
this group.

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室
Fabrice Orgogozo 氏 (CNRS, École polytechnique)
エタールコホモロジーの高次順像の一様構成可能性について
(ENGLISH)
[ 講演概要 ]
Z_ℓエタールコホモロジーの捻れとF_ℓコホモロジーの超積の関係を巡り
N. Katz氏の指摘に基づいて、高次順像に於けるℓに対する

(この様な定理は以前よりガバー氏の構想に有った。)
ここでは月並みな方法で有るが、A.J.de Jong氏の定理と

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/saito/

#### GCOEセミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 000号室

Weak convergence of Markov chain Monte Carlo method and its application to Yuima (JAPANESE)
[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/03.html

### 2010年06月08日(火)

#### Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 126号室

Automorphism groups of causal Makarevich spaces (JAPANESE)
[ 講演概要 ]
Let G^ be a simple Lie group of Hermitian type and U^ be a maximal parabolic subgroup of G^ with abelian nilradical. The flag manifold M^= G^/ U^ is the Shilov
boundary of an irreducible bounded symmetric domain of tube type. M^ has the G-invariant causal structure. A causal Makarevich space is, by definition, an open symmetric G-orbit M in M^, endowed with the causal structure induced from that
of the ambient space M^, G being a reductive subgroup of G^. All symmetric cones fall in the class of causal Makarevich spaces.
In this talk, we determine the causal automorphism groups of all causal Makarevich spaces.

### 2010年06月07日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Xavier Roulleau 氏 (東大数理)
Genus 2 curve configurations on Fano surfaces (ENGLISH)

#### 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

[ 講演概要 ]

### 2010年06月03日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Fixed Points in the Stone-Cech boundary of Groups (ENGLISH)
[ 講演概要 ]
We discuss the class of discrete groups which admit fixed points under the adjoint action on the Stone-Cech boundary. Such groups have vanishing $L^2$-Betti numbers, and nonamenable ones fail to have property (AO).

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 470号室
Birgit Speh 氏 (Cornel University)
Introduction to the cohomology of locally symmetric spaces 2
(ENGLISH)
[ 講演概要 ]
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma$.
If $X_\\Gamma$ is cocompact this cohomology can be expressed as the $(\\bg,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2010年06月02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

On some algebraic properties of CM-types of CM-fields and their
reflex fields (JAPANESE)
[ 講演概要 ]
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.

For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \\rtimes S_n$.
Using properties of the embedding, a set of CM-types $\\Phi$ of $K$ and their
dual CM-types $(K, \\Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual
CM-type.

I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.