## 過去の記録

### 2010年12月07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
Raphael Ponge 氏 (東京大学大学院数理科学研究科)
Diffeomorphism-invariant geometries and noncommutative geometry (ENGLISH)
[ 講演概要 ]
In many geometric situations we may encounter the action of
a group $G$ on a manifold $M$, e.g., in the context of foliations. If
the action is free and proper, then the quotient $M/G$ is a smooth
manifold. However, in general the quotient $M/G$ need not even be
Hausdorff. Furthermore, it is well-known that a manifold has structure
invariant under the full group of diffeomorphisms except the
differentiable structure itself. Under these conditions how can one do
diffeomorphism-invariant geometry?

Noncommutative geometry provides us with the solution of trading the
ill-behaved space $M/G$ for a non-commutative algebra which
essentially plays the role of the algebra of smooth functions on that
space. The local index formula of Atiyah-Singer ultimately holds in
the setting of noncommutative geometry. Using this framework Connes
and Moscovici then obtained in the 90s a striking reformulation of the
local index formula in diffeomorphism-invariant geometry.

An important part the talk will be devoted to reviewing noncommutative
geometry and Connes-Moscovici's index formula. We will then hint to on-
going projects about reformulating the local index formula in two new
geometric settings: biholomorphism-invariant geometry of strictly
pseudo-convex domains and contactomorphism-invariant geometry.

#### 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

http://www.ms.u-tokyo.ac.jp/gcoe/index.html

(JAPANESE)
[ 講演概要 ]

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

### 2010年12月06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

[ 講演概要 ]

### 2010年12月04日(土)

#### 古典解析セミナー

09:30-10:30   数理科学研究科棟(駒場) 056号室

#### 古典解析セミナー

10:40-11:40   数理科学研究科棟(駒場) 056号室

ホインの微分方程式における積分変換とその応用 (JAPANESE)

#### 古典解析セミナー

13:00-14:00   数理科学研究科棟(駒場) 056号室

#### 古典解析セミナー

14:10-15:10   数理科学研究科棟(駒場) 056号室

アフィン・ルート系とモノドロミー保存変形系、超幾何関数 (JAPANESE)

#### 古典解析セミナー

15:30-16:30   数理科学研究科棟(駒場) 056号室

### 2010年12月03日(金)

#### GCOEセミナー

11:00-12:00   数理科学研究科棟(駒場) 270号室
Jarmo Hietarinta 氏 (University of Turku)
Discrete Integrability and Consistency-Around-the-Cube (CAC) (ENGLISH)
[ 講演概要 ]
For integrable lattice equations we can still apply many integrability criteria that are regularly used for continuous systems, but there are also some that are specific for discrete systems. One particularly successful discrete integrability criterion is the multidimensional consistency, or CAC. We review the classic results of Nijhoff and of Adler-Bobenko-Suris and then present some extensions.

#### GCOEセミナー

13:30-14:30   数理科学研究科棟(駒場) 370号室
Nalini Joshi 氏 (University of Sydney)
Geometric asymptotics of the first Painleve equation (ENGLISH)
[ 講演概要 ]
I will report on my recent collaboration with Hans Duistermaat on the geometry of the space of initial values of the first Painleve equation, which was first constructed by Okamoto. We show that highly accurate information about solutions can be found by utilizing the regularized and compactified space of initial values in Boutroux's coordinates. I will also describe numerical explorations based on this work obtained in collaboration with Holger Dullin.

#### 古典解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Painleve第3方程式と箙多様体 (JAPANESE)
[ 講演概要 ]
Painleve方程式の初期値空間を与える線型常微分方程式系のモジュライ空間は,2, 4, 5, 6型の場合,岡本Dynkin図に付随する中島箙多様体で記述できる事が知られている.

### 2010年12月01日(水)

#### 代数学コロキウム

16:30-18:45   数理科学研究科棟(駒場) 056号室

On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves (JAPANESE)
[ 講演概要 ]
In this talk, we will discuss the following problem posed by Makoto Matsumoto and Akio Tamagawa concerning monodromic fullness of hyperbolic curves.

For a hyperbolic curve X over a number field, are the following three conditions equivalent?
(A) For any prime number l, X is quasi-l-monodromically full.
(B) There exists a prime number l such that X is l-monodromically full.
(C) X is l-monodromically full for all but finitely many prime numbers l.

The property of being (quasi-)monodromically full may be regarded as an analogue for hyperbolic curves of the property of not admitting complex multiplication for elliptic curves, and the above equivalence may be regarded as an analogue for hyperbolic curves of the following result concerning the Galois representation on the Tate module of an elliptic curve over a number field proven by Jean-Pierre Serre.

For an elliptic curve E over a number field, the following four conditions are equivalent:
(0) E does not admit complex multiplication.
(1) For any prime number l, the image of the l-adic Galois representation associated to E is open.
(2) There exists a prime number l such that the l-adic Galois representation associated to E is surjective.
(3) The l-adic Galois representation associated to E is surjective for all but finitely many prime numbers l.

In this talk, I will present some results concerning the above problem in the case where the given hyperbolic curve is of genus zero. In particular, I will give an example of a hyperbolic curve of type (0,4) over a number field which satisfies condition (C) but does not satisfy condition (A).
Marco Garuti 氏 (University of Padova) 17:45-18:45
Galois theory for schemes (ENGLISH)
[ 講演概要 ]
We discuss some aspects of finite group scheme actions: the Galois correspondence and the notion of Galois closure.

### 2010年11月30日(火)

#### 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

http://www.ms.u-tokyo.ac.jp/gcoe/index.html

[ 講演概要 ]

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

#### 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

Pin^-(2)-monopole equations and intersection forms with local coefficients of 4-manifolds (JAPANESE)
[ 講演概要 ]
We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and explain its applications to intersection forms with local coefficients of 4-manifolds.
The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients.
The second one is a local coefficient version of Furuta's 10/8-inequality.
As a corollary, we construct nonsmoothable spin 4-manifolds satisfying Rohlin's theorem and the 10/8-inequality.

#### 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
Yi-Jun Yao 氏 (Fudan Univ.)
Noncommutative geometry and Rankin-Cohen brackets (ENGLISH)

### 2010年11月29日(月)

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Scott Carnahan 氏 (IPMU)
Borcherds products in monstrous moonshine. (ENGLISH)
[ 講演概要 ]
During the 1980s, Koike, Norton, and Zagier independently found an
infinite product expansion for the difference of two modular j-functions
on a product of half planes. Borcherds showed that this product identity
is the Weyl denominator formula for an infinite dimensional Lie algebra
that has an action of the monster simple group by automorphisms, and used
this action to prove the monstrous moonshine conjectures.

I will describe a more general construction that yields an infinite
product identity and an infinite dimensional Lie algebra for each element
of the monster group. The above objects then arise as the special cases
assigned to the identity element. Time permitting, I will attempt to
describe a connection to conformal field theory.

#### 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

K3 surfaces and log del Pezzo surfaces of index three (JAPANESE)
[ 講演概要 ]
Alexeev and Nikulin have classified log del Pezzo surfaces of index 1 and 2 by using the classification of non-symplectic involutions on K3 surfaces. We want to discuss the generalization of this result to the index 3 cases. In this case we are also able to construct log del Pezzos $Z$ from K3 surfaces $X$, but the converse is not necessarily true. The condition on $Z$ is exactly the "multiple smooth divisor property", which we will define. Our theorem is the classification of log del Pezzo surfaces of index 3 with this property.

The idea of the proof is similar to that of Alexeev and Nikulin, but the methods are different because of the existence of singularities: although the singularity is mild, the description of nef cone by reflection groups cannot be used. Instead
we construct and analyze good elliptic fibrations on K3 surfaces $X$ and use it to obtain the classification. It includes a partial but geometric generalization of the classification of non-symplectic automorphisms of order three, recently done by Artebani, Sarti and Taki.

### 2010年11月26日(金)

#### Kavli IPMU Komaba Seminar

14:40-16:10   数理科学研究科棟(駒場) 002号室

Hamiltonian torus actions on orbifolds and orbifold-GKM theorem (joint
work with T. Holm) (JAPANESE)
[ 講演概要 ]
When a symplectic manifold M carries a Hamiltonian torus R action, the
injectivity theorem states that the R-equivariant cohomology of M is a
subring of the one of the fixed points and the GKM theorem allows us
to compute this subring by only using the data of 1-dimensional
orbits. The results in the first part of this talk are a
generalization of this technique to Hamiltonian R actions on orbifolds
and an application to the computation of the equivariant cohomology of
toric orbifolds. In the second part, we will introduce the equivariant
Chen-Ruan cohomology ring which is a symplectic invariant of the
action on the orbifold and explain the injectivity/GKM theorem for this ring.

### 2010年11月25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

Kac 環の作用の分類 (JAPANESE)

### 2010年11月18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
Jean Roydor 氏 (Univ. Tokyo)
Perturbation of dual operator algebras and similarity (ENGLISH)

### 2010年11月17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

F_2-線形擬似乱数発生法の評価に用いる格子の簡約基底計算の高速化 (JAPANESE)
[ 講演概要 ]
(部分的に松本眞氏、斎藤睦夫氏との共同研究)

の一つとして、高次元均等分布性がしばしば用いられる。メルセンヌツイスター法
を含む二元体上の線形擬似乱数発生法に対しては、上位ビットの均等分布の次元を

L'Ecuyer-Tezuka(1993)およびTezuka(1994))。本研究では、前述の格子を用いた

(i) 冪級数成分の格子点を擬似乱数発生器の状態ベクトルで表現する、
(ii) 射影を用いてv次元簡約基底からv-1次元簡約基底を計算する、
(iii) 効率的な格子簡約アルゴリズムを適用する、
などの手法を導入し、均等分布の次元計算の高速化を提案する。この方法は、
Couture-L'Ecuyer(2000)による双対格子を用いた改良よりも計算量が少なく、計算機

### 2010年11月16日(火)

#### 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

http://www.ms.u-tokyo.ac.jp/gcoe/index.html

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

#### 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 a colored Khovanov bicomplex (JAPANESE)
[ 講演概要 ]
Jones 多項式の Khovanov ホモロジーと関連理論が近年活発に

Khovanov により対応するコホモロジーが導入され,特に Mackaay と Turner
や Beliakova とWehrli の研究を通し発展した.しかし,このコホモロジーが持つ
2つの境界作用素によって,Khovanov型の複体で2重複体となるものが構成
できるのかは問題として残されていた.もしあるならば Khovanov 型のホモロジーが
Total complexのコホモロジーに収束するスペクトル系列の第2項として理解される.
この問題意識は Beliakova と Wehliの論文によって紹介された.今回はそれに

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
いつもと曜日・時間・場所が異なります
Viacheslav Nikulin 氏 (Univ Liverpool and Steklov Moscow)
Self-corresponences of K3 surfaces via moduli of sheaves (ENGLISH)
[ 講演概要 ]
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室
Viacheslav Nikulin 氏 (Univ Liverpool and Steklov Moscow)
Self-corresponences of K3 surfaces via moduli of sheaves (ENGLISH)
[ 講演概要 ]
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.