## 過去の記録

#### 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.

#### 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
Jean-Marc Bouclet 氏 (トゥールーズ大学,フランス)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)

### 2010年04月12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) 128号室

Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space
[ 講演参考URL ]
http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

### 2010年04月06日(火)

#### 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

On the characters of tempered modules of affine Hecke
algebras of classical type
[ 講演概要 ]
We present an inductive algorithm to compute the characters
of tempered modules of an affine Hecke algebras of classical
types, based on a new class of representations which we call
"tempered delimits". They have some geometric origin in the
eDL correspondence.

Our new algorithm has some advantage to the Lusztig-Shoji
algorithm (which also describes the characters of tempered
modules via generalized Green functions) in the sense it
enables us to tell how the characters of tempered modules
changes as the parameters vary.

This is a joint work with Dan Ciubotaru at Utah.

### 2010年04月05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
Alexandru Dimca 氏 (Université Nice-Sophia Antipolis)
From Lang's Conjecture to finiteness properties of Torelli groups
[ 講演概要 ]
First we recall one of Lang's conjectures in diophantine geometry
on the interplay between subvarieties and translated subgroups in a
commutative algebraic group
(proved by M. Laurent in the case of affine tori in 1984).

Then we present the technique of resonance and characteristic varieties,
a powerful tool in the study of fundamental groups of algebraic varieties.

Finally, using the two ingredients above, we show that the Torelli
groups $T_g$
have some surprising finiteness properties for $g>3$.
In particular, we show that for any subgroup $N$ in $T_g$ containing
the Johnson kernel $K_g$, the complex vector space $N_{ab} \\otimes C$
is finite dimensional.

All the details are available in our joint preprint with S. Papadima
arXiv:1002.0673.

### 2010年03月30日(火)

#### GCOEセミナー

10:00-15:00   数理科学研究科棟(駒場) 122号室

Semismooth Newton法の理論、及び応用 (JAPANESE)
ゲオク・ヴァイス 氏 (東大数理) 14:10-15:00

### 2010年03月29日(月)

#### 統計数学セミナー

13:00-14:10   数理科学研究科棟(駒場) 002号室
Catherine Laredo 氏 (MIA, INRA)
Inference for partially observed Markov processes and applications
[ 講演概要 ]
We present some statistical methods for estimating the param- eters of a population dynamics model of annual plants. It is modelled using multitype branching processes with immigration. The data consist of counts in each type that are measured in several populations for a few consecu- tive years. Parametric inference is first carried out when count data of all types are observed. We prove statistical identifiability for all the parameters ruling the population dynamics model and derive consistent and asymptot- ically Gaussian estimators. However, it often occurs that, in practice, one or more types cannot be observed, leading to partially observed processes. Parametric inference is first studied in the case of Poisson distributions. We characterize the parameter subset where identifiability holds and de- rive consistent and asymptotically normal estimators for this parameter subset. Theses results are then extended to other distributions.

We apply these results to feral oilseed data. The model takes account of reproduction, immigration, and seed survival in a seed bank. The data consist of the number of plants in several developmental stages that were measured in a number of populations for few consecutive years. They are incomplete since seeds could not be counted.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/17.html

### 2010年03月25日(木)

#### 講演会

17:00-18:00   数理科学研究科棟(駒場) 370号室
Dr Bangti Jin 氏 (Center for Industrial Mathematics University of Bremen, Germany)
Heuristic Choice Rules for Convex Variational Regularization
[ 講演概要 ]
In this talk we shall consider heuristic rules for choosing regularization parameters for general convex variational regularization of linear inverse problems. Several rules of recent origin are described, and some theoretical issues, e.g. existence, convergence, and a posteriori error estimates, are discussed. Numerical examples will be presented to demonstrate their accuracy and practical utility.

#### 講演会

16:00-17:00   数理科学研究科棟(駒場) 370号室
M.M. Lavrentiev, Jr. 氏 (Sobolev Institute of Mathematics, Novosibirsk, Russia)
Modern computer architectures for tsunami simulation
[ 講演概要 ]
Simulation of tsunami wave propagation over the deep water is one of the most time consuming tasks of the tsunami warning system. The authors utilize Method of Splitting Tsunami (MOST) package, accepted by the National Ocean & Atmospheric Administration (NOAA), USA. The software generates calculation of wave propagation at deep water by splitting along coordinate axis. Nonlinear shallow water system is used as the governing equations. Some tasks of the algorithm could be executed in parallel mode, however, direct application of multi processor systems results only in two times performance gain. After a number of optimizations, the authors achieved 16 times performance gain. OpenMP technology was applied. When utilizing Sony PlayStation3 platform (IBM CELL BE architecture) 60 times code acceleration was accomplished. The best result was achieved with modern GPU (GForce 8800 and TESLA), 100 times performance gain.

### 2010年03月23日(火)

#### GCOEセミナー

15:00-17:15   数理科学研究科棟(駒場) 370号室
Mourad Bellassoued 氏 (Univ. of Bizerte) 15:00-16:00
Stability estimates for the anisotropic wave and Schrodinger equations from
the Dirichlet to Neumann map
[ 講演概要 ]
In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in a wave or Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the wave equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1.
Johannes Elschner 氏 (Weierstrass Institute Berlin, Germany) 16:15-17:15
On uniqueness in inverse elastic obstacle scattering
[ 講演概要 ]
The talk is on joint work with M. Yamamoto on the third and fourth exterior boundary value problems of linear isotropic elasticity. We present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves.
Our approach is essentially based on a reflection principle for the Navier equation.