## 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) 118号室
George Elliott 氏 (University of Toronto)
An introduction to C*-algebra classification theory (ENGLISH)

#### 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

2次元円環領域におけるLiouville-Gel\\'fand方程式の非球対称解の構造 (JAPANESE)
[ 講演概要 ]

#### 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
Eric Opdam 氏 (Universiteit van Amsterdam)
Dirac induction for graded affine Hecke algebras (ENGLISH)
[ 講演概要 ]
In recent joint work with Dan Ciubotaru and Peter Trapa we
constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.
We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.

### 2012年07月14日(土)

#### 調和解析駒場セミナー

13:30-17:00   数理科学研究科棟(駒場) 128号室
このセミナーは,月に1度程度,不定期に開催されます.

(岐阜大学) 13:30-15:00

(JAPANESE)
[ 講演概要 ]

その結果、対応するTrudigner-Moser型不等式、対数型Hardyの不等式及び対数型Young関数による一般化されたMorrey空間への埋込み定理を導出する。

) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
(JAPANESE)
[ 講演概要 ]
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.

### 2012年07月12日(木)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 370号室
M. Lavrentiev 氏 (Sobolev Institute of Mathematics)
Real time tsunami parameters evaluation (ENGLISH)
[ 講演概要 ]
We would like to propose several improvements to the existing software tools for tsunami modeling. Combination of optimaly located system of sensors with advantages of modern hardware architectures will make it possible to deliver calculated parameters of tsunami wave in 12-15 minutes after seismic event.

### 2012年07月11日(水)

#### 古典解析セミナー

14:00-17:30   数理科学研究科棟(駒場) 128号室

On a q-analog of Painlevé III (D_7^{(1)}) and its algebraic function solutions (Joint work with N. Nakazono) (JAPANESE)

First order systems of linear ordinary differential equations and
representations of quivers (ENGLISH)

### 2012年07月10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

Hadamard variational formula for the Green function
of the Stokes equations with the boundary condition (JAPANESE)
[ 講演概要 ]

#### 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
Marcus Werner 氏 (Kavli IPMU)
Topology in Gravitational Lensing (ENGLISH)
[ 講演概要 ]
General relativity implies that light is deflected by masses
due to the curvature of spacetime. The ensuing gravitational
lensing effect is an important tool in modern astronomy, and
topology plays a significant role in its properties. In this
talk, I will review topological aspects of gravitational lensing
theory: the connection of image numbers with Morse theory; the
interpretation of certain invariant sums of the signed image
magnification in terms of Lefschetz fixed point theory; and,
finally, a new partially topological perspective on gravitational
light deflection that emerges from the concept of optical geometry
and applications of the Gauss-Bonnet theorem.

### 2012年07月09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) 126号室

[ 講演概要 ]
We describe the volume of a graded linear series by the Monge-Ampere mass of the associated equilibrium metric. We relate this formula to the question whether the weak geodesic ray associated to a test configuration of given polarized manifold recovers the Donaldson-Futaki invariant.

### 2012年07月06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)。

S.R.Srinivasa Varadhan 氏 (Courant Institute of Mathematical Sciences, New York University)
Large Deviations of Random Graphs and Random Matrices (ENGLISH)
[ 講演概要 ]
A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.

### 2012年07月04日(水)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
Patrick Forré 氏 (東京大学数理科学研究科)
A cohomological Hasse principle of varieties over higher local fields and applications to higher dimensional class field theory (ENGLISH)
[ 講演概要 ]
In this talk I will give an overview of the necessary tools for a description of the class field theory of varieties over higher local fields developed by sevaral mathematicians. On this I will motivate the importance of the proposal and verification of a cohomological Hasse principle for varieties over higher local fields, a generalization of Kato's conjectures, and sketch the recent progress on this.

#### 古典解析セミナー

15:30-17:00   数理科学研究科棟(駒場) 128号室

Symmetries of quantum Lax equations for the Painlev\\'e equations (JAPANESE)

### 2012年06月27日(水)

#### 古典解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

### 2012年06月26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

Absence of embedded eigenvalues for the Schr\\"odinger operator on manifold with ends (JAPANESE)
[ 講演概要 ]
We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of $L^2$-eigenvalues for the Schr\\"odinger operator above some critical value. The critical value is computed from the volume growth rate of the end and the potential behavior at infinity. The end structure is formulated abstractly in terms of some convex function, and the examples include asymptotically Euclidean and hyperbolic ends. The proof consists of a priori superexponential decay estimate for eigenfunctions and the absence of superexponentially decaying eigenfunctions, both of which employs the Mourre-type commutator argument. This talk is based on the recent joint work with E.Skibsted (Aarhus University).

### 2012年06月25日(月)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

Automorphism groups of Calabi-Yau manifolds of Picard number two (JAPANESE)
[ 講演概要 ]
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\\"ahler manifolds and birational automorphism groups, as I shall explain. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation for a Calabi-Yau threefold of Picard number two, together with exsistence of rational curve, expected by the cone conjecture.

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室

スライス構造を持つCR多様体のCR同値問題 (JAPANESE)

### 2012年06月20日(水)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室

On the reduction modulo p of representations of a quaternion
division algebra over a p-adic field (JAPANESE)
[ 講演概要 ]
The p-adic Langlands correspondence and the mod p Langlands correspondence for GL_2(Q_p) are known to be compatible with the reduction modulo p in many cases.
In this talk, we examine whether a similar compatibility exists for the composition of the local Langlands correspondence and the local Jacquet-Langlands correspondence.
The simplest case has already been treated by Vign¥'eras. We deal with more cases.

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Paolo Maremonti 氏 (Seconda Università degli Studi di Napoli)
On the Navier-Stokes Cauchy problem with nondecaying data (ENGLISH)
[ 講演概要 ]
We prove the well posedeness of the Navier-Stokes Cauchy problem for nondecaying initial data u_0 \\in C (R^n) \\cap L^\\infty (R^n), n >= 3. This problem is studied by Giga, Inui and Matsui for n >= 3, and Giga, Matsui and Sawada in the two dimensional case. The aims of our paper are slight different since we also find pointwise estimates for the pressure field. Via a uniqueness theorem, we give a sort of structure theorem to GIM solutions.

### 2012年06月19日(火)

#### トポロジー火曜セミナー

17:10-18:10   数理科学研究科棟(駒場) 056号室
Tea: 16:50 - 17:10 コモンルーム

On the universal degenerating family of Riemann surfaces
over the D-M compactification of moduli space (JAPANESE)
[ 講演概要 ]
It is usually understood that over the Deligne-
Mumford compactification of moduli space of Riemann surfaces of
genus > 1, there is a family of stable curves. However, if one tries to
construct this family precisely, he/she must first take a disjoint union
of various types of smooth families of stable curves, and then divide
them by their automorphisms to paste them together. In this talk we will
show that once the smooth families are divided, the resulting quotient
family contains not only stable curves but virtually all types of
degeneration of Riemann surfaces, becoming a kind of universal
degenerating family of Riemann surfaces.

#### 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

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

(JAPANESE)
[ 講演概要 ]

[ 参考URL ]
http://www.infsup.jp/utnas/

### 2012年06月18日(月)

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 122号室

アルバネーゼ次元最大の複素射影多様体の特殊集合について (JAPANESE)
[ 講演概要 ]
アルバネーゼ次元が最大の複素射影多様体の中に含まれる代数的あるいは超越的な複

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 126号室

CR Q曲率流とCR Paneitz作用素について (JAPANESE)
[ 講演概要 ]
3次元CR多様体上のCR Paneitz作用素とQ-曲率に関するCR幾何学の研究について幾何解析的な視点から最近得られた結果などについて話をしたいと思います。

#### 講演会

09:45-12:30   数理科学研究科棟(駒場) 002号室

James Nolen 氏 (Duke University) 09:45-10:45
Fluctuation of solutions to PDEs with random coefficients (Part 2) (ENGLISH)
[ 講演概要 ]
This is continuation of the previous day's lecture.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
Leonid Ryzhik 氏 (Stanford University) 11:00-12:30
Weak coupling limits for particles and PDEs (Part 2) (ENGLISH)
[ 講演概要 ]
This is continuation of the previous day's lecture.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

### 2012年06月17日(日)

#### 講演会

09:45-17:30   数理科学研究科棟(駒場) 002号室

James Nolen 氏 (Duke University) 09:45-17:30
Fluctuation of solutions to PDEs with random coefficients (Part 1) (JAPANESE)
[ 講演概要 ]
For PDEs with random coefficients, it is interesting to understand whether the solutions exhibit some universal statistical behavior that is independent of the details of the coefficients. In particular, how do solutions fluctuate around the mean behavior? We will discuss this issue in the context of three examples:

(1) Traveling fronts in random media in one dimension.
(2) Elliptic homogenization problems.
(3) Random Hamilton-Jacobi equations.

The relation between PDE tools and probabilistic ideas will be
explained.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

Leonid Ryzhik 氏 (Stanford Univeristy) 13:00-14:45
Weak coupling limits for particles and PDEs (Part 1) (JAPANESE)
[ 講演概要 ]
Weak random fluctuations in medium parameters may lead to a non-trivial effect after large times and propagation over long distances. We will consider several examples when the large time limit can be treated:

(1) a particle in a weakly random velocity field.
(2) weak random fluctuations of Hamilton equations, and
(3) the linear Scrhoedinger equation with a weak random potential.

The role of long range correlation of the random fluctuations will also be discussed.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/
Gregoire Nadin 氏 (CNRS / Paris 6) 15:15-17:15
Asymptotic spreading for heterogeneous Fisher-KPP reaction-diffusion equations (JAPANESE)
[ 講演概要 ]
The solutions of the heterogeneous Fisher-KPP equation associated with compactly supported initial data are known to take off from the unstable steady state 0 and to converge to the steady state 1 for large times. The aim of this lecture is to estimate the speed at which the interface between 0 and 1 spreads.

Using the new notion of generalized principal eigenvalues for non-compact elliptic operators, we will derive such estimates which will be proved to be optimal for several classes of heterogeneity such as periodic, almost periodic or random stationary ergodic ones.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

### 2012年06月16日(土)

#### 講演会

13:15-17:00   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

この講演では,確率論の基礎的な概念や用語を簡単にまとめた上で,ランダムな項を持つ偏微分方程式の研究において重要な役割を果たす確率場の定常性とエルゴード性について解説する.その後ブラウン運動を導入し,いくつかの例を与える.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/

[ 講演概要 ]

(1) 線形の2階放物型方程式との関係
(2) これを常微分方程式に雑音を加えたモデルという立場でとらえると,例えば非線形項がヘルダー連続でしかない常微分方程式に一意性が回復するなど,粘性消去の考え方が自然に表れることへの注意
(3) (主に放物型の)方程式に雑音項を加える,いわゆる確率偏微分方程式の定式化について簡単に紹介し,雑音効果による一意性の回復の問題や解の爆発の消滅などについても触れる.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~matano/SDE2012/