## 過去の記録

### 2008年12月10日(水)

#### 東京幾何セミナー

14:45-18:00   数理科学研究科棟(駒場) 122号室

「今後の予定」欄には、東工大で行われるセミナーは表��

Acyclic polarizations and localization of Riemann-Roch numbers
[ 講演概要 ]

Megumi Harada 氏 (McMaster University) 16:30-18:00
The topology of symplectic and hyperkahler quotients
[ 講演概要 ]
Symplectic geometry lies at the crossroads of many exciting areas of research due to its relationship to geometric representation theory, combinatorics, and algebraic geometry, among others. As often happens in mathematics, the presence of symmetry in these geometric structures -- in this context, a Hamiltonian G-action for a Lie group G, i.e. an action with an associated moment map -- turns out to be crucial in the computation of topological invariants, such as the Betti numbers, the cohomology ring, or the K-theory, of symplectic manifolds which arise as Hamiltonian quotients. In the first part of the talk, I will give a bird's-eye, motivating overview of this subject, and in particular will introduce one of the main technical tools of the field, which is the Morse theory associated to the moment map. In the second part, I will give a more detailed account of recent joint work with Graeme Wilkin, which deals with Nakajima quiver varieties, a special case of hyperkahler Hamiltonian quotients. In particular, we develop a Morse theory for the hyperkahler moment map analogous to the case of the moduli space of Higgs bundles. In particular, we show that the Harder-Narasimhan stratification of spaces of representations of quivers coincide with the Morse-theoretic stratification associated to the norm-square of the real moment map. Our approach also provides insight into the topology of specific examples of small-rank quiver varieties, including hyperpolygon spaces and some ADHM quivers.

### 2008年12月09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
Bertrand Deroin 氏 (CNRS, Orsay, Universit\'e Paris-Sud 11)
Tits alternative in $Diff^1(S^1)$
[ 講演概要 ]
The following form of Tits alternative for subgroups of
homeomorphisms of the circle has been proved by Margulis: or the group
preserve a probability measure on the circle, or it contains a free
subgroup on two generators. We will prove that if the group acts by diffeomorphisms of
class $C^1$ and does not preserve a probability measure on the circle, then
in fact it contains a subgroup topologically conjugated to a Schottky group.
This is a joint work with V. Kleptsyn and A. Navas.

### 2008年12月08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

Critically finite holomorphic maps on projective spaces

### 2008年12月05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

### 2008年12月04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

カッツ環の作用の分類

#### Lie群論・表現論セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
いつもと開始時刻および場所が違いますのでご注意ください
Genkai Zhang 氏 (Chalmers and Gothenburg University)
Realization of quanternionic discrete series as spaces of H-holomorphic
functions
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2008年12月03日(水)

#### 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) 122号室
Freddy Delaben 氏 (ETH)
The structure of dynamic utility functions in a Brownian Filtration

[ 講演概要 ]
The penalty function for monetary dynamic utility functions
has a special form. They can be seen as potentials. In the Brownian Filtration Rao's theorem permits to give a complete description.

#### 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

Mean-periodicity and analytic properties of zeta-functions
[ 講演概要 ]
Mean-periodicityというのは周期性の概念のひとつの一般化である。最近、I. Fesenko, G. Ricottaとの共同研究により、数論的スキームのゼータ関数を含むある複素関数のクラスと、mean-periodicityとの関連性が新しく見出された。
これはHecke-Weilによる, 解析接続と関数等式を持つDirichlet級数と保型形式との対応の一つの拡張ともみなせる. この背景には, I. Fesenkoの高次元アデール上のゼータ積分の理論があり、数論的スキームのHasseゼータ関数の解析接続を高次元アデール上の調和解析から導こうというプログラムの一環となっている。
この講演ではそのような背景にも若干触れた上、ゼータ関数の解析的性質とmean-periodicityの関連、特に解析接続と関数等式との関連について解説する。

### 2008年12月02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) 056号室
トポロジー火曜セミナーと合同で開催します. またいつもと開催時刻および開催場所が違います。

[ 講演概要 ]
The aim of my talk is to reveal an unforeseen link between the classical vanishing theorems of Matsushima and Weil, on the one hand, and rigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank noncompact Lie group, on the other.

The connection is established via "transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the orbit foliation of the Weyl chamber flow that is tangentially closed (and satisfies a certain mild additional condition) can be extended to a closed 1- form on the whole space in a canonical manner. In particular, infinitesimal rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.
[ 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

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:40 - 17:00 コモンルーム (Lie群論・表現論セミナーと合同で開催)

Vanishing and Rigidity
[ 講演概要 ]
The aim of my talk is to reveal an unforeseen link between
the classical vanishing theorems of Matsushima and Weil, on the one hand,
andrigidity of the Weyl chamber flow, a dynamical system arising from a higher-rank
noncompact Lie group, on the other. The connection is established via
"transverse extension theorems": Roughly speaking, they claim that a tangential 1- form of the
orbit foliation of the Weyl chamber flow that is tangentially closed
(and satisfies a certain mild additional condition) can be extended to a closed 1- form on the
whole space in a canonical manner. In particular, infinitesimal
rigidity of the orbit foliation of the Weyl chamber flow is proved as an application.

### 2008年12月01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

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Kentaro Hori 氏 (University of Toronto / IPMU)
A pair of non-birational but derived equivalent Calabi-Yau
manifolds from non-Abelian gauge theories
[ 講演概要 ]
We construct a family of (2,2) supersymmetric gauge theories
in 2-dimensions that flows to a family of (2,2) superconformal fields theories with \\hat{c}=3. The family has two limits and three singular points. The two limits correspond to two Calabi-Yau manifolds which are not birationally equivalent. The two are, however, derived equivalent
by general principle of supersymmetric quantum field theory.

### 2008年11月28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

#### 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)

[ 講演概要 ]

[ 参考URL ]
[開催日にご注意下さい]

#### GCOEレクチャーズ

14:40-16:10   数理科学研究科棟(駒場) 002号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Circle-valued Morse theory
, Lecture 2

### 2008年11月26日(水)

#### 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
Piotr Pragacz
(Banach Institute)
Diagonal subschemes and vector bundles

#### GCOEレクチャーズ

14:40-16:10   数理科学研究科棟(駒場) 002号室
Andrei Pajitnov 氏 (Univ. de Nantes)
Circle-valued Morse theory, Lecture 1
[ 講演概要 ]
Morse theory of circle-valued functions, initiated by S. P. Novikov in 1980-1982 is now a rapidly developing domain with applications and connections to many other fields of geometry and topology such as dynamical systems, Lagrangian intersections,
knots and links in three-dimensional sphere.

We will start with the basics of the theory, discuss the construction of the Novikov complex, relations with the dynamical zeta functions, and the knot theory. We will conclude with a list of the open problems of the theory.

#### 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

Lang's Observation in Diophantine Problems
[ 講演概要 ]
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\\varphi$ be a rational function on $E$. Then, for every point $P\\in E(K)$ where $\\varphi$ does not vanish at $P$, the logarithms of a norm of $\\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.

### 2008年11月25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
Ovidiu Calin 氏 (Eastern Michigan University)
Heat kernels for subelliptic operators
[ 講演概要 ]
Subelliptic operators are differential operators with missing
directions. Their behavior is very different than the behavior or
elliptic operators. Among the most well known subelliptic operators
are the Grusin operator, the Heisenberg operator, and the Kolmogorov
operator. There are several methods of finding the heat kernels of
subelliptic operators. The heat kernels of subelliptic operators are
usually represented in integral form, but in the case of the
Kolmogorov operator we shall show that the heat kernel is of function
type. We shall spend some time on other subelliptic operators too.

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 118号室
Xavier Roulleau 氏 (東大)
Cotangent maps of surfaces of general type
[ 講演概要 ]
Surfaces are usualy studied and classified via the properties of the pluricanonical maps. For surfaces of general type whose cotangent sheaf is generated by global sections, we propose to study an other map, called the cotangent map, in order to obtain geometric informations on the surface. In this way, we obtain informations on the ampleness of the cotangent sheaf of such a surface. We will illustate this talk with the example of the Fano surface of lines of cubic threefolds.

#### 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

$\\mathbb R^n$への$\\mathbb R^2$の固有な作用と周期性
[ 講演概要 ]
Consider $\\R^2$ actions on $\\R^n$ which is free, affine and unipotent. Our concern here is to answer the following question:

"Does the quotient topology admits a manifold structure?"

Under some weak assumption, we classify all actions up to conjugate, and give a complete answer to the question.

If Lipsman's conjecture were true, all of the answer should be affirmative.

But, we shall find a unique action which gives a negative answer for each $n\\geq 5$. And, we also find a periodicity on such counterexamples.

As a key lemma, we use "proper analogue" of the five lemma on
exact sequence.
[ 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) 056号室
Tea: 16:00 - 16:30 コモンルーム
Andrei Pajitnov 氏 (Univ. de Nantes)
Circle-valued Morse theory for knots and links
[ 講演概要 ]
We will discuss several recent developments in
this theory. In the first part of the talk we prove that the Morse-Novikov number of a knot is less than or equal to twice the tunnel number of the knot, and present consequences of this result. In the second part we report on our joint project with Hiroshi Goda on the half-transversal Morse-Novikov theory for 3-manifolds.

### 2008年11月22日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室

Quantum Entanglement in Exactly Solvable Models
[ 講演概要 ]

は、この新しく導入された指標が量子多体系の基本性質を正しく反映しているか
をテストする一種の実験室として重要な役割を果たしてきた。セミナーでは、

1. Affleck-Kennedy-Lieb-Tasaki modelのvalence bond solid基底状態におけるenta
nglementと端状態
2. Calogero-Sutherland modelにおける粒子間entanglementと排他的分数統計
3. Bethe ansatz波動関数の行列積表示

づくものである。

[ 講演概要 ]
KRクリスタルとはアフィンリー環gのディンキン図の0以外の頂点と

の場合には昨年確認された。今年になって、それらの結晶グラフの

についてgが$A_{2n-1}^{(2)}$と$C_n^{(1)}$の場合にお話したい。
また、組合せ論的に与えた結晶グラフが、なぜ表現論的に存在が
わかった結晶基底のグラフと一致するかについての証明の概略に
ついても触れたい。

### 2008年11月21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

デリバティブ・プロダクツの価格付け II

#### 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)

What is Q-curvature?
[ 講演概要 ]

[ 参考URL ]