## 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) 470号室
Birgit Speh 氏 (Cornel University)
Introduction to the cohomology of locally symmetric spaces 2
(ENGLISH)
[ 講演概要 ]
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma$.
If $X_\\Gamma$ is cocompact this cohomology can be expressed as the $(\\bg,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2010年06月02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

On some algebraic properties of CM-types of CM-fields and their
reflex fields (JAPANESE)
[ 講演概要 ]
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.

For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \\rtimes S_n$.
Using properties of the embedding, a set of CM-types $\\Phi$ of $K$ and their
dual CM-types $(K, \\Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual
CM-type.

I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.

### 2010年06月01日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: 16:30 - 17:00 コモンルーム

On Fatou-Julia decompositions (JAPANESE)
[ 講演概要 ]
We will explain that Fatou-Julia decompositions can be
introduced in a unified manner to several kinds of one-dimensional
complex dynamical systems, which include the action of Kleinian groups,
iteration of holomorphic mappings and complex codimension-one foliations.
In this talk we will restrict ourselves mostly to the cases where the
dynamical systems have a certain compactness, however, we will mention
how to deal with dynamical systems without compactness.

#### GCOEレクチャーズ

16:30-18:00   数理科学研究科棟(駒場) 126号室
Birgit Speh 氏 (Cornel University)
Introduction to the cohomology of locally symmetric spaces
(ENGLISH)
[ 講演概要 ]
I will give an introduction to the cohomology of noncompact locally symmetric spaces $X_\\Gamma =K \\backslash G / \\Gamma$.
If $X_\\Gamma$ is cocompact this cohomology can be expressed as the $(g,K)$-cohomology of automorphic representations. I will explain how representation theory and automorphic forms can be used to study the cohomology in this case.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2010年05月31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

On Pfaffian Calabi-Yau Varieties and Mirror Symmetry (JAPANESE)
[ 講演概要 ]
We construct new smooth CY 3-folds with 1-dimensional Kaehler moduli and
determine their fundamental topological invariants. The existence of CY
3-folds with the computed invariants was previously conjectured. We then
report mirror symmetry for these non-complete intersection CY 3-folds.
We explicitly build their mirror partners, some of which have 2 LCSLs,
and carry out instanton computations for g=0,1.

#### 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

Singularities and analytic torsion (JAPANESE)

### 2010年05月28日(金)

#### 古典解析セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
はじめにこれまでに調べてきた3次元アフィン空間の17種類の単純型斎藤自由因子に沿って対数的極をもつ一意化方程式について概観する。つぎにこれらの斎藤自由因子の補空間の基本群と一意化方程式の関係を論じる。Type Biii)の場合に基本群が可換になる。この場合に一意化方程式の解を初等関数をつかって表示することを試みる。

### 2010年05月27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
Catherine Oikonomides 氏 (東大数理)
The C*-algebra of codimension one foliations which are almost without holonomy (ENGLISH)

### 2010年05月26日(水)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 000号室

R-Yuimaパッケージによるファイナンス高頻度データ解析とシミュレーション (JAPANESE)
[ 講演概要 ]
ファイナンス高頻度データなど、必ずしも等間隔でサンプルされていない時系列データを効率的に処理するツールとして、R言語のzoo,
xtsそしてyuimaパッケージをチュートリアル的に紹介する。ヘッジ戦略のバックテストなどを例示する。またyuimaに実装されている新しい確率微分方程式モデルのシミュレーション法を理論的な利点とともに解説する。
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Giovanni Pisante 氏 (Department of Mathematics
Hokkaido University)
A SELECTION CRITERION FOR SOLUTIONS OF A
SYSTEM OF EIKONAL EQUATIONS
(ENGLISH)
[ 講演概要 ]
We deal with the system of eikonal equations |ðu/ðx1|=1, |ðu/ðx2|=1 in a planar Lipschitz domain with zero boundary condition. Exploiting the classical pyramidal construction introduced by Cellina, it is easy to prove that there exist infinitely many Lipschitz solutions. Then, the natural problem that has arisen in this framework is to find a way to select and characterize a particular meaningful class of solutions.
We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient. More precisely we select an optimal weighted measure for the jump set of the second derivatives of a given solution v of the system and we prove the existence of minimizers of the corresponding variational problem.

#### 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

Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ 講演概要 ]

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

#### GCOEセミナー

16:30-18:00   数理科学研究科棟(駒場) 002号室

Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ 講演概要 ]

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

### 2010年05月25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) 126号室
5月24日(月)-28日(金)に平賀氏の集中講義が行われます

(京都大学)
On endoscopy, packets, and invariants (JAPANESE)
[ 講演概要 ]
The theory of endoscopy came out of the Langlands functoriality and the trace formula.
In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.
I would like to talk about the connection between these topics and the endoscopy.

### 2010年05月24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

A counterexample of the birational Torelli problem via Fourier--Mukai transforms (JAPANESE)
[ 講演概要 ]
We study the Fourier--Mukai numbers of rational elliptic surfaces. As
its application, we give an example of a pair of minimal 3-folds $X$
with Kodaira dimensions 1, $h^1(O_X)=h^2(O_X)=0$ such that they are
mutually derived equivalent, deformation equivalent, but not
birationally equivalent. It also supplies a counterexample of the
birational Torelli problem.

### 2010年05月19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 ]

れている現象が数多く存在する。その例として、(1)造影剤の濃度カーブを用い
た腎臓癌の転移危険性及び肝臓における血液灌流の評価、(2)大動脈瘤に対する
ステント治療の予後予測、について紹介する。前者は、血管からの造影剤の浸出

のである。後者は、個人差の大きい大動脈形状による血流の違いを数値シミュ
レーションによって求め、統計学的なクラスタリングと併せて予後を予測するも
のである。どちらも、モデリングにあたっては臨床医療の現場との緊密な連携が

の手順や困難な点、今後の展望などについて報告したい。

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html

### 2010年05月18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

On roots of Dehn twists (JAPANESE)
[ 講演概要 ]
Let $t_{c}$ be the Dehn twist about a nonseparating simple closed curve
$c$ in a closed orientable surface. If a mapping class $f$ satisfies
$t_{c}=f^{n}$ in mapping class group, we call $f$ a root of $t_{c}$ of
degree $n$. In 2009, Margalit and Schleimer constructed roots of $t_{c}$.
In this talk, I will explain the data set which determine a root of
$t_{c}$ up to conjugacy. Moreover, I will explain the minimal and the
maximal degree.

#### 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
B. Speh 氏 (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
[ 講演概要 ]
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.

Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset$ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $X / \\Gamma$ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.

This is joint work with T.N. Venkataramana

### 2010年05月17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

On the GIT stability of Polarized Varieties (JAPANESE)
[ 講演概要 ]
Background:
Original GIT-stability notion for polarized variety is
"asymptotic stability", studied by Mumford, Gieseker etc around 1970s.
Recently a version appeared, so-called "K-stability", introduced by
Tian(1997) and reformulated by Donaldson(2002), by the way of seeking
the analogue of Kobayashi-Hitchin correspondence, which gives
"differential geometric" interpretation of "stability". These two have
subtle but interesting differences in dimension higher than 1.

Contents:
(1*) Any semistable (in any sense) polarized variety should have only
"semi-log-canonical" singularities. (Partly observed around 1970s)
(2) On the other hand, we proved some stabilities, which corresponds to
"Calabi conjecture", also with admitting mild singularities.

As applications these yield
(3*) Compact moduli spaces with GIT interpretations.
(4) Many counterexamples (as orbifolds) to folklore conjecture:
"K-stability implies asymptotic stability".

(*: Some technical points are yet to be settled.
Some parts for (1)(2) are available on arXiv:0910.1794.)

#### 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

On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)

### 2010年05月15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

Strict positivity of the central values of some Rankin-Selberg
L-functions (JAPANESE)
[ 講演概要 ]
この講演では、荒川リフトというGSp(2)の内部形式上の保型形式に対する、
ある次数8のRankin-Selberg型のL関数の中心値が正となる例について紹介
する。このL関数は岡崎武生氏がGO(2,2)からのテータリフトにより

GSp(2)のRankin-Selberg型のL関数の中心値が正となる例も与える。

[ 講演概要 ]

### 2010年05月12日(水)

#### 講演会

15:30-17:00   数理科学研究科棟(駒場) 123号室
3回連続の最終回です。前2回より開始時間が早いのでご注意ください。

Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)
[ 講演概要 ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.

#### 代数学コロキウム

17:30-18:30   数理科学研究科棟(駒場) 056号室

Differences between
Galois representations in outer-automorphisms
of the fundamental groups and those in automorphisms, implied by
topology of moduli spaces (ENGLISH)
[ 講演概要 ]
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number ﬁeld K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:

ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).

Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are inﬁnitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.

This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).

There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.

(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室

Jean-Pierre Puel 氏 (Graduate School of Mathematical Sciences
The University of Tokyo)
Exact controllability for incompressible fluids (ENGLISH)
[ 講演概要 ]
After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.
We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).
We will end up with some important open problems.

#### 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

[ 講演概要 ]

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