## 過去の記録

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 056号室
3回連続の第1回です。2回目と3回目は、5月7日(金)4時から5時半と
5月12日(水)3時半から5時です。部屋はどちらも056です。

Luc Illusie 氏 (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility
[ 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 $\\ell$.

#### 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

A Markov process for circular data (JAPANESE)
[ 講演概要 ]
We propose a discrete-time Markov process which takes values on the unit circle. Some properties of the process, including the limiting behaviour and ergodicity, are investigated. Many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers. The proposed model is compared with an existing Markov process for circular data. A simulation study is made to illustrate the mathematical properties of the model. Statistical inference for the process is briefly considered.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/00.html

### 2010年04月27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 the complex volume of hyperbolic knots (JAPANESE)
[ 講演概要 ]
In this talk, we give a formula of the volume and the Chern-Simons invariant of hyperbolic knot complements, which is closely related to the volume conjecture of hyperbolic knots.
We also discuss the volumes and the Chern-Simons invariants of closed 3-manifolds
obtained by Dehn surgeries on hyperbolic knots.

#### 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

Vogan-Zuckerman加群の対称部分群に関する制限 (JAPANESE)
[ 講演概要 ]
We study the restriction of Vogan-Zuckerman derived functor modules $A_\\frak{q}(\\lambda)$ to symmetric subgroups.
An algebraic condition for the discrete decomposability of
$A_\\frak{q}(\\lambda)$ was given by Kobayashi, which offers a framework for the detailed study of branching law.
In this talk, when $A_\\frak{q}(\\lambda)$ is discretely decomposable,
we construct some of irreducible components occurring in the branching law and determine their associated variety.

### 2010年04月26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

The unirationality of the moduli spaces of 2-elementary K3
surfaces (JAPANESE)
[ 講演概要 ]
We prove the unirationality of the moduli spaces of K3 surfaces
with non-symplectic involution. As a by-product, we describe the
configuration spaces of 5, 6, 7, 8 points in the projective plane as
arithmetic quotients of type IV.

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室

The correspondence between Frobenius algebra of Hurwitz numbers
and matrix models (JAPANESE)
[ 講演概要 ]
The number of branched coverings of closed surfaces are called Hurwitz
numbers. They constitute a Frobenius algebra structure, or
two dimensional topological field theory. On the other hand, correlation
functions of matrix models are expressed in term of ribbon graphs
(graphs embedded in closed surfaces).

In this talk, I explain how the Frobenius algebra structure of Hurwitz
numbers are described in terms of matrix models. We use the
correspondence between ribbon graphs and covering of S^2 ramified at
three points, both of which have natural symmetric group actions.

As an application I use Frobenius algebra structure to compute Hermitian
matrix models, multi-variable matrix models, and their large N
expansions. The generating function of Hurwitz numbers is also expressed
in terms of matrix models. The relation to integrable hierarchies and
random partitions is briefly discussed.

#### 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

Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

### 2010年04月23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) 123号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)

[ 講演概要 ]

[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~matumoto/PRESENTATION/tokyo-univ2010-4-23.pdf

### 2010年04月22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
Nigel Higson 氏 (Pennsylvania State Univ.)
The Baum-Connes Conjecture and Group Representations (ENGLISH)
[ 講演概要 ]
The Baum-Connes conjecture asserts a sort of duality between the reduced unitary dual of a group and (a variant of) the classifying space of the group. The conjectured duality occurs at the level of K-theory. For example, for free abelian groups it amounts to a K-theoretic form of Fourier-Mukai duality. The conjecture has well-known applications in topology and geometry, but it also resonates in various ways with Lie groups and representation theory. I'll try to indicate how this comes about, and then focus on a fairly new aspect of the relationship that develops some early ideas of Mackey.

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Jens Starke 氏 (デンマーク工科大学)
Deterministic and stochastic modelling of catalytic surface processes (ENGLISH)
[ 講演概要 ]
Three levels of modelling, the microscopic, the mesoscopic and the macroscopic level are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. The macroscopic description can be derived rigorously for low pressure conditions as limit of the stochastic many particle model for large particle numbers. This is in correspondence with the successful description of experiments under low pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The introduced models include a new approach for the platinum phase transition which allows for a unification of existing models for Pt(100) and Pt(110).

The rich nonlinear dynamical behaviour of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pattern formation, so-called raindrop patterns which are not captured by earlier models, can be reproduced and are shown in simulations.
This is joint work with M. Eiswirth, H. Rotermund, G. Ertl,
Frith Haber Institut, Berlin, K. Oelschlaeger, University of
Heidelberg and C. Reichert, INSA, Lyon.

### 2010年04月21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 ]

#### 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

On the interpolation constant over triangular and rectangular elements (JAPANESE)
[ 講演概要 ]

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

### 2010年04月20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
Helene Eynard-Bontemps 氏 (東京大学大学院数理科学研究科, JSPS)
Homotopy of foliations in dimension 3. (ENGLISH)
[ 講演概要 ]
We are interested in the connectedness of the space of
codimension one foliations on a closed 3-manifold. In 1969, J. Wood proved
the fundamental result:

Theorem: Every 2-plane field on a closed 3-manifold is homotopic to a
foliation.

W. R. gave a new proof of (and generalized) this result in 1973 using
local constructions. It is then natural to wonder if two foliations with
homotopic tangent plane fields can be linked by a continuous path of
foliations.
A. Larcanch\\'e gave a positive answer in the particular case of
"sufficiently close" taut foliations. We use the key construction of her
proof (among other tools) to show that this is actually always true,
provided one is not too picky about the regularity of the foliations of
the path:

Theorem: Two C^\\infty foliations with homotopic tangent plane fields can
be linked by a path of C^1 foliations.

#### 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

[ 講演概要 ]
SL(2,R)が固有に作用しうる複素既約対称空間は、手塚勝貴氏によって分類されてい
る。この講演ではその一般化として、複素でない場合も含めた半単純対称空間で、SL(2,R)が固有に作用しうるものの分類を紹介する。

### 2010年04月19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

[ 講演概要 ]

(部分多様体に沿った)自己交点数の巨大な因子への一般化である制限型体積は,

また, 時間が許せば, 元々の問題意識であった制限型体積の複素解析的な側面に
ついても触れたい.

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 122号室
Cyrill Muratov 氏 (New Jersey Institute of Technology)
Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions
[ 講演概要 ]
In this talk I will present an analysis of the behavior of the minimal energy in non-local Ginzburg-Landau models with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. As a first step, I will show that under suitable scaling the energy of minimizers becomes asymptotically equal to that of a sharp interface energy with screened Coulomb interaction. I will then show that the minimizers of the corresponding sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. Finally, I will show that in a suitable limit these droplets become uniformly distributed throughout the domain. The analysis allows to obtain precise asymptotic behaviors of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density in the considered limit.

#### 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
Filippo Bracci 氏 (Universita di Roma, Tor Vergata'')
Loewner's theory on complex manifolds (ENGLISH)
[ 講演概要 ]
Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.
[ 講演参考URL ]
http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

#### 数理人口学・数理生物学セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

くの研究者の間で、造血幹細胞から白血病が起こると考えられてきた。そ
こで、幹細胞集団とそれが分化してできる自己複製能を持たない前駆細胞

は細胞の異常増殖を引き起こす特有の突然変異(JAK2V617F)が知られてお
り、この突然変異と、前駆細胞に自己複製能を与える特定の突然変異を仮

た。実験から得られた現実的なパラメータを用いた結果、幹細胞に比べて

### 2010年04月17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

$Sp(2,C)$ 上の主系列Ｗｈｉttaker関数 (JAPANESE)
[ 講演概要 ]

A paving of the Siegel 10-fold of positive characteristic (JAPANESE)
[ 講演概要 ]

### 2010年04月15日(木)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
いつもと場所・時刻が違います
Uuganbayar Zunderiya 氏 (Nagoya University)

[ 講演概要 ]

この偏微分方程式系はガウス-青本-ゲルファント系を高階に一般化したものであり、
それは1937年にMayrが導入したgenericな代数方程式の解に対する微分関係式
にも端を発する。

ガウス-青本-ゲルファント系は偏微分作用素を成分とする
2x2の行列の行列式として得られる2階の微分作用素を主要項とする。

この講演ではガウス-青本-ゲルファントの超幾何微分方程式系の

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室
Alberto Tesei 氏 (University of Rome 1)
Long-time behaviour of solutions of a forward-backward parabolic equation
[ 講演概要 ]
We discuss some recent results concerning the asymptotic behaviour of entropy measure-valued solutions for a class of ill-posed forward-backward parabolic equations, which arise in the theory of phase transitions.

#### 古典解析セミナー

16:00-17:00   数理科学研究科棟(駒場) 122号室
Claude Mitschi 氏 (Univ. de Strasbourg)
The Galois group of projectively isomonodromic deformations (ENGLISH)
[ 講演概要 ]
Isomonodromic families of regular singular differential equations over $\\mathbb C(x)$ are characterized by the fact that their parametrized differential Galois group is conjugate to a (constant) linear algebraic group over $\\mathbb C$. We will describe properties of this differential group that reflect a special type of monodromy evolving deformation of Fuchsian differential equations.

### 2010年04月14日(水)

#### 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
Gerard Laumon 氏 (CNRS, Universite Paris XI - Orsay)
The cohomological weighted fundamental lemma
[ 講演概要 ]
Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

#### 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 ]
2008年12月から2009年2月にかけて国際宇宙ステーション「きぼう」において「氷の結晶成長における形態不安定化」という実験が実施された(研究代表者・北大研・古川義純)。そこでは、微小重力下において重水から成長する氷単結晶のその場観察が130回以上行うことができた。得られた明視野及び干渉縞の動画像の記録を解析し、次の2つの結果を得た。1)氷の底面の成長速度(c軸方向の速度)は、成長が測定できる臨界過冷却度(約0.1K)が存在し、臨界過冷却度以上では成長速度は過冷却度の2乗に比例する。2)樹枝先端の成長速度(a軸方向の速度)は、0.2K以上で過冷却度の2.5乗に比例する。このセミナーでは、得られた結果が理論モデルと一致することについて解説する。

### 2010年04月13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
Christian Kassel 氏 (CNRS, Univ. de Strasbourg)
Torsors in non-commutative geometry (ENGLISH)
[ 講演概要 ]
G-torsors or principal homogeneous spaces are familiar objects in geometry. I'll present an extension of such objects to "non-commutative geometry". When the structural group G is finite, non-commutative G-torsors are governed by a group that has both an arithmetic component and a geometric one. The arithmetic part is given by a classical Galois cohomology group; the geometric input is encoded in a (not necessarily abelian) group that takes into account all normal abelian subgroups of G of central type. Various examples will be exhibited.