## 過去の記録

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 128号室
Michael Eastwood 氏 (Australian National University)
Invariant differential operators on the sphere (ENGLISH)
[ 講演概要 ]
The circle is acted upon by the rotation group SO(2) and there are plenty of differential operators invariant under this action. But the circle is also acted upon by SL(2,R) and this larger symmetry group cuts down the list of invariant differential operators to something smaller but more interesting! I shall explain what happens and how this phenomenon generalises to spheres. These constructions are part of a general theory but have numerous unexpected applications, for example in suggesting a new stable finite-element scheme in linearised elasticity (due to Arnold, Falk, and Winther).
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood

### 2010年11月05日(金)

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 123号室
Michael Eastwood 氏 (Australian National University)
How to recognise the geodesics of a metric connection (ENGLISH)
[ 講演概要 ]
The geodesics on a Riemannian manifold form a distinguished family of curves, one in every direction through every point. Sometimes two metrics can provide the same family of curves: the Euclidean metric and the round metric on the hemisphere have this property. It is also possible that a family of curves does not arise from a metric at all. Following a classical procedure due to Roger Liouville, I shall explain how to tell these cases apart on a surface. This is joint work with Robert Bryant and Maciej Dunajski.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood

### 2010年11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) 122号室

Nonequilibrium Statistical Mechanics (JAPANESE)

#### 講演会

10:40-12:10   数理科学研究科棟(駒場) 123号室
Jean Meyer 氏, 久松康子 氏 (BNPパリバ証券キャピタルマーケッツ・リスク管理部)
Market, Liquidity and Counterparty Risk (ENGLISH)
[ 講演概要 ]
1. Introduction to the market risk

- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)

3. Risk measure

- Stress test
- Value at risk
- Risks measure for counterparty risk

### 2010年11月02日(火)

#### 講演会

13:00-16:10   数理科学研究科棟(駒場) 122号室
Vladimir Bogachev 氏 (Moscow)
The Malliavin calculus on configuration spaces and applications (ENGLISH)
[ 講演概要 ]
It is planned to discuss first a general scheme of the Malliavin
calculus on an abstract measurable
manifold with minimal assumptions about the manifold.
Then a practical realization of this scheme will be discussed in
several concrete examples with emphasis
on configuration spaces, i.e., spaces of locally finite configurations
in a given manifold (for example, just
a finite-dimensional Euclidean space), which can be alternatively
described as the spaces of integer-valued
discrete measures equipped with suitable differential structures.
No acquaintance with the Malliavin calculus and differential geometry
is assumed.

#### 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
Daniel Ruberman 氏 (Brandeis University)
Periodic-end manifolds and SW theory (ENGLISH)
[ 講演概要 ]
We study an extension of Seiberg-Witten invariants to
4-manifolds with the homology of S^1 \\times S^3. This extension has
many potential applications in low-dimensional topology, including the
study of the homology cobordism group. Because b_2^+ =0, the usual
strategy for defining invariants does not work--one cannot disregard
reducible solutions. In fact, the count of solutions can jump in a
family of metrics or perturbations. To remedy this, we define an
index-theoretic counter-term that jumps by the same amount. The
counterterm is the index of the Dirac operator on a manifold with a
periodic end modeled at infinity by the infinite cyclic cover of the
manifold. This is joint work with Tomasz Mrowka and Nikolai Saveliev.

#### 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
Michael Eastwood 氏 (University of Adelaide)
Twistor theory and the harmonic hull (ENGLISH)
[ 講演概要 ]
Harmonic functions are real-analytic and so automatically extend from being functions of real variables to being functions of complex variables. But how far do they extend? This question may be answered by twistor theory, the Penrose transform, and associated geometry. I shall base the constructions on a formula of Bateman from 1904. This is joint work with Feng Xu.

### 2010年11月01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

How to estimate Seshadri constants (JAPANESE)
[ 講演概要 ]
Seshadri constant is an invariant which measures the positivities of ample line bundles. This relates with adjoint bundles, Nagata conjecture, slope stabilities, Gromov width (an invariant of symplectic manifolds) and so on. But it is very diffiult to compute or estimate Seshadri constants in general, especially in higher dimension.
In this talk, we first study Seshadri constants of toric varieties, and next consider about non-toric cases using toric degenerations. For example, good estimations are obtained for complete intersections in projective spaces.

#### 講演会

16:00-18:15   数理科学研究科棟(駒場) 270号室
Michel Cristofol 氏 (マルセイユ大学) 16:00-17:00
Inverse problems in non linear parabolic equations : Two differents approaches (ENGLISH)
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/abstractTokyo.pdf
Patricia Gaitan 氏 (マルセイユ大学) 17:15-18:15
Inverse Problems for parabolic System
(ENGLISH)
[ 講演概要 ]
I will present a review of stability and controllability results for linear parabolic coupled systems with coupling of first and zeroth-order terms by data of reduced number of components. The key ingredients are global Carleman estimates.

### 2010年10月29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
*** 通常とは部屋が異なります。ご注意ください ***
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。

Robin Graham 氏 (University of Washington)
Ambient metrics and exceptional holonomy (ENGLISH)
[ 講演概要 ]
The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$. The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.

### 2010年10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) 122号室

Type III representations of the infinite symmetric group (ENGLISH)
[ 講演概要 ]
Based on earlier results about the structure of the II$_1$ representations of the infinite symmetric group, we investigate its type III representations and the related inclusion of von Neumann algebras of type III.

#### 講演会

10:40-12:10   数理科学研究科棟(駒場) 123号室
Jean Meyer 氏, 久松康子 氏 (BNPパリバ証券キャピタルマーケッツ・リスク管理部)
Market, Liquidity and Counterparty Risk (ENGLISH)
[ 講演概要 ]
1. Introduction to the market risk

- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks

2. Market & Liquidity Risks –Basics

-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)

3. Risk measure

- Stress test
- Value at risk
- Risks measure for counterparty risk

### 2010年10月26日(火)

#### 複素解析幾何セミナー

13:00-14:30   数理科学研究科棟(駒場) 123号室
Dan Popovici 氏 (Toulouse)
Limits of Moishezon Manifolds under Holomorphic Deformations (ENGLISH)
[ 講演概要 ]
We prove that if all the fibres, except one, of a holomorphic family of compact complex manifolds are supposed to be Moishezon (i.e. bimeromorphic to projective manifolds), then the remaining (limit) fibre is again Moishezon. The two ingredients of the proof are the relative Barlet space of divisors contained in the fibres for which we show properness over the base of the family and the "strongly Gauduchon" (sG) metrics that we have introduced for the purpose of controlling volumes of cycles. These new metrics enjoy stability properties under both deformations and modifications and play a crucial role in obtaining a uniform control on volumes of relative divisors that prove the above-mentioned properness.

#### 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

Quantum fundamental groups and quantum representation varieties for 3-manifolds (JAPANESE)
[ 講演概要 ]
We define a refinement of the fundamental groups of 3-manifolds and
a generalization of representation variety of the fundamental group
of 3-manifolds. We consider the category $H$ whose morphisms are
nonnegative integers, where $n$ corresponds to a genus $n$ handlebody
equipped with an embedding of a disc into the boundary, and whose
morphisms are the isotopy classes of embeddings of handlebodies
compatible with the embeddings of the disc into the boundaries. For
each 3-manifold $M$ with an embedding of a disc into the boundary, we
can construct a contravariant functor from $H$ to the category of
sets, where the object $n$ of $H$ is mapped to the set of isotopy
classes of embedding of the genus $n$ handlebody into $M$, compatible
with the embeddings of the disc into the boundaries. This functor can
be regarded as a refinement of the fundamental group of $M$, and we
call it the quantum fundamental group of $M$. Using this invariant, we
can construct for each co-ribbon Hopf algebra $A$ an invariant of
3-manifolds which may be regarded as (the space of regular functions
on) the representation variety of $M$ with respect to $A$.

#### 数値解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

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

[ 講演概要 ]

【注意】いつもと教室が異なりますのでご注意ください.また,今回より,開催曜日が火曜日に変更になりました.水曜日を予定されていた方々にはお詫びいたします.
[ 講演参考URL ]
http://www.infsup.jp/utnas/

#### 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
Daniel Sternheimer 氏 (Keio University and Institut de Mathematiques de Bourgogne)
Some instances of the reasonable effectiveness (and limitations) of symmetries and deformations in fundamental physics (ENGLISH)
[ 講演概要 ]
In this talk we survey some applications of group theory and deformation theory (including quantization) in mathematical physics. We start with sketching applications of rotation and discrete groups representations in molecular physics (dynamical" symmetry breaking in crystals, Racah-Flato-Kibler; chains of groups and symmetry breaking). These methods led to the use of classification Lie groups" (internal symmetries") in particle physics. Their relation with space-time symmetries will be discussed. Symmetries are naturally deformed, which eventually brought to Flato's deformation philosophy and the realization that quantization can be viewed as a deformation, including the many avatars of deformation quantization (such as quantum groups and quantized spaces). Nonlinear representations of Lie groups can be viewed as deformations (of their linear part), with applications to covariant nonlinear evolution equations. Combining all these suggests an Ansatz based on Anti de Sitter space-time and group, a deformation of the Poincare group of Minkowski space-time, which could eventually be quantized, with possible implications in particle physics and cosmology. Prospects for future developments between mathematics and physics will be indicated.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html

### 2010年10月21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
Benoit Collins 氏 (Univ. Ottawa)
Free probability and entropy additivity problems for Quantum information theory (ENGLISH)

### 2010年10月20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

[ 講演概要 ]
3次元空間に埋め込まれた、厚みのある2次元曲面での粒子の拡散を考察する。

このとき通常の拡散流に加えて、面の厚さ:ε展開において、

さらに、3次元に埋め込まれた1次元の場合(チューブ)を考察し、

### 2010年10月19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) 002号室
Tea: 16:00 - 16:30 コモンルーム
Jinseok Cho 氏 (早稲田大学)
Optimistic limits of colored Jones invariants (ENGLISH)
[ 講演概要 ]
Yokota made a wonderful theory on the optimistic limit of Kashaev
invariant of a hyperbolic knot
that the limit determines the hyperbolic volume and the Chern-Simons
invariant of the knot.
Especially, his theory enables us to calculate the volume of a knot
combinatorially from its diagram for many cases.

We will briefly discuss Yokota theory, and then move to the optimistic
limit of colored Jones invariant.
We will explain a parallel version of Yokota theory based on the
optimistic limit of colored Jones invariant.
Especially, we will show the optimistic limit of colored Jones
invariant coincides with that of Kashaev invariant modulo 2\\pi^2.
This implies the optimistic limit of colored Jones invariant also
determines the volume and Chern-Simons invariant of the knot, and
probably more information.

This is a joint-work with Jun Murakami of Waseda University.

### 2010年10月18日(月)

#### 複素解析幾何セミナー

10:30-11:30   数理科学研究科棟(駒場) 128号室
Sergey Ivashkovitch 氏 (Univ. de Lille)
Limiting behavior of minimal trajectories of parabolic vector fields on the complex projective plane. (ENGLISH)
[ 講演概要 ]
The classical Poincare-Bendixson theory describes the way a trajectory of a vector field on the real plane behaves when accumulating to the singular locus of the vector field. We shall describe, in the first approximation, the way a minimal trajectory of a parabolic complex polynomial vector field (or, a holomorphic foliation) on the complex projective plane approaches the singular locus. In particular we shall prove that if a holomorphic foliation has an exceptional minimal set then its nef model is necessarily hyperbolic.

#### 複素解析幾何セミナー

13:00-14:00   数理科学研究科棟(駒場) 128号室
Philippe Eyssidieux 氏 (Institut Fourier, Grenoble)
Degenerate complex Monge-Ampere equations (ENGLISH)

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Todor Milanov 氏 (IPMU)
Quasi-modular forms and Gromov--Witten theory of elliptic orbifold $\\mathbb{P}^1$ (ENGLISH)
[ 講演概要 ]
This talk is based on my current work with Y. Ruan. Our project is part of the so called Landau--Ginzburg/Calabi-Yau correspondence. The latter is a conjecture, due to Ruan, that describes the relation between the $W$-spin invariants of a Landau-Ginzburg potential $W$ and the Gromov--Witten invariants of a certain Calabi--Yau orbifold. I am planning first to explain the higher-genus reconstruction formalism of Givental. This formalism together with the work of M. Krawitz and Y. Shen allows us to express the Gromov--Witten invariants of the orbifold $\\mathbb{P}^1$'s with weights $(3,3,3)$, $(2,4,4)$, and $(2,3,6)$ in terms of Saito's Frobenius structure associated with the simple elliptic singularities $P_8$, $X_9$, and $J_{10}$ respectively. After explaining Givental's formalism, my goal would be to discuss the Saito's flat structure, and to explain how its modular behavior fits in the Givental's formalism. This allows us to prove that the Gromov--Witten invariants are quasi-modular forms on an appropriate modular group.

#### 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

ガロア拡大と局所コホモロジー間の写像について (JAPANESE)
[ 講演概要 ]

### 2010年10月14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

Nonstandard analysis for operator algebraists (JAPANESE)

### 2010年10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
Andrei Pajitnov 氏 (Univ. de Nantes, 東京大学大学院数理科学研究科)
Asymptotics of Morse numbers of finite coverings of manifolds (ENGLISH)
[ 講演概要 ]
Let X be a closed manifold;
denote by m(X) the Morse number of X
(that is, the minimal number of critical
points of a Morse function on X).
Let Y be a finite covering of X of degree d.

In this survey talk we will address the following question
posed by M. Gromov: What are the asymptotic properties
of m(N) as d goes to infinity?

It turns out that for high-dimensional manifolds with
free abelian fundamental group the asymptotics of
the number m(N)/d is directly related to the Novikov homology
of N. We prove this theorem and discuss related results.