## 過去の記録

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 126号室
Thomas W. Roby 氏 (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
[ 講演概要 ]
Many cyclic actions $\\tau$ on a finite set $S$ of
combinatorial objects, along with many natural
statistics $\\phi$ on $S$, exhibitcombinatorial ergodicity'':
the average of $\\phi$ over each $\\tau$-orbit in $S$ is
the same as the average of $\\phi$ over the whole set $S$.
One example is the case where $S$ is the set of
length $n$ binary strings $a_{1}\\dots a_{n}$
with exactly $k$ 1's,
$\\tau$ is the map that cyclically rotates them,
and $\\phi$ is the number of \\textit{inversions}
(i.e, pairs $(a_{i},a_{j})=(1,0)$ for $iJ$ less than $j$).

This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.

This is joint work with Jim Propp.

### 2012年07月21日(土)

#### 保型形式の整数論月例セミナー

13:30-16:00   数理科学研究科棟(駒場) 123号室

degree n の Siegel-Eisenstein 級数の Fourier 係数について (JAPANESE)
[ 講演概要 ]
この話では,まず,あるdegree nのSiegel-Eisenstein級数G_{k,\\chi}を定義し,そのFourier係数の明示公式について述べます.このEisenstein級数G_{k,\\chi}は通常のSiegel-Eisenstein級数E_{k,\\chi}とは定義が違うのですが,G_{k,\\chi}のFourier係数の明示公式から,\\chiが特別な場合のE_{k,\\chi}のFourier係数の明示が得られます.

[ 講演概要 ]

### 2012年07月19日(木)

#### GCOEセミナー

17:00-18:00   数理科学研究科棟(駒場) 370号室
Oleg Emanouilov 氏 (Colorado State Univ.)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ 講演概要 ]
We consider the Dirichlet-to-Neumann map for determining potential in two-dimensional Schroedinger equation. We relax the regularity condition on potentials and establish the uniqueness within L^p class with p > 2.

### 2012年07月18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
Shane Kelly 氏 (Australian National University)
Voevodsky motives and a theorem of Gabber (ENGLISH)
[ 講演概要 ]
The assumption that the base field satisfies resolution of singularities litters Voevodsky's work on motives. While we don't have resolution of singularities in positive characteristic p, there is a theorem of Gabber on alterations which may be used as a substitute if we are willing to work with Z[1/p] coefficients. We will discuss how this theorem of Gabber may be applied in the context of Voevodsky's work and mention some consequences.

#### 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

Free divisors, holonomic systems and algebraic Painlev\\'{e} sixth solutions (ENGLISH)
[ 講演概要 ]
In this talk, I will report an attempt to treat algebraic solutions of Painlev\\'{e} VI equation in a unified manner.
A classification of algebraic solutions of Painlev\\'{e} VI equation was accomplished by O. Lisovyy and Y. Tykhyy after efforts on the construction of such solutions by many authors, K. Iwasaki N. J. Hitchin, P. Boalch, B. Dubrovin, M. Mazzocco, A. V. Kitaev, R. Vidunas and others.
The outline of my approach is as follows.
Let $t$ be a variable and let $w$ be its algebraic function such that $w$ is a solution of Painlev\\'{e} sixth equation. Suppose that both $t$ and $w$ are rational functions of a parameter. Namely $(t,w)$ defines a rational curve.
(1) Find a polynomial $P(u)$ such that $t=\\frac{P(-u)}{P(u)}$.
(2) From $P(u)$, define a weighted homogeneous polynomial $f(x_1,x_2,x_3)=x_3f_1(x_1,x_2,x_3)$ of three variables $x_1,x_2,x_3$, where $(1,2,n)$ is the weight system of $(x_1,x_2,x_3)$ with $n=\\deg P(u)$. The hypersurface $D:f(x)=0$ is a free divisor in ${\\bf C}^3$. Note that $\\deg_{x_3}f_1=2$.
(3) Construct a holonomic system ${\\sl M}$ on ${\\bf C}^3$ of rank two with singularities along $D$.
(4) Construct an ordinary differential equation from the holonomic system ${\\sl M}$ with respect to $x_3$. This differential equation has three singular points $z_0,z_1,a_s$ in $x_3$-line.
(5) Putting $t=\\frac{z_1}{z_0},\\lambda=\\frac{a_s}{z_0}$, we conclude that $(t,\\lambda)$ is equivalent to the pair $(t,w)$.
Our study starts with showing the existence of $P(u)$ in (1). From the classification by Losovyy and Tykhyy, I find that the existence of $P(u)$ is guaranteed for Solutions III, IV, Solutions $k$ ($1\\le k\\le 21$, $k\\not= 4,13,14,20$) and Solution 30. We checked whether (1)-(5) are true or not in these cases separately and as a consequence (1)-(5) hold for the all these cases except Solutions 19, 21.

### 2012年07月17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

Contact structure of mixed links (JAPANESE)
[ 講演概要 ]
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.

#### 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.