過去の記録 ~08/15本日 08/16 | 今後の予定 08/17~

Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
池田 暁志 氏 (東京大学大学院数理科学研究科)
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.


10:30-12:00   数理科学研究科棟(駒場) 128号室
相原 義弘 氏 (福島大学)
Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)



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)
松本 眞 氏 (東京大学大学院数理科学研究科)
疑似乱数発生に用いられる数学:メルセンヌ・ツイスターを例に (JAPANESE)
[ 講演概要 ]
[ 参考URL ]



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.


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.



10:30-11:30   数理科学研究科棟(駒場) 056号室
佐崎元 氏 (北海道大学低温科学研究所)
高分解光学顕微法による結晶成長素過程の直接観察 (JAPANESE)
[ 講演概要 ]
近年の光学顕微法の様々な発展により,結晶表面上での分子ス ケール高さ(Å - nm)の単位ステップや個々の分子の動的な振る舞いを,直接観 察することが可能になって来た.講演では,様々な結晶表面上でのステップの協 同的な運動を多数のムービーでご覧いただくことで,数学的な問題と繋げていた だければ幸いである.


16:30-18:00   数理科学研究科棟(駒場) 002号室
小林 健太 氏 (金沢大学 理工学域)
On the interpolation constant over triangular and rectangular elements (JAPANESE)
[ 講演概要 ]
[ 参考URL ]



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

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
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.


16:30-18:00   数理科学研究科棟(駒場) 126号室
奥田 隆幸 氏 (東京大学)
半単純対称空間におけるSL(2,R)の固有な作用 (JAPANESE)
[ 講演概要 ]



16:40-18:10   数理科学研究科棟(駒場) 126号室
松村 慎一 氏 (東大数理)
[ 講演概要 ]
豊富な因子の部分多様体に沿った自己交点数は, 基本的かつ重要である.
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


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.


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.
[ 参考URL ]


16:30-18:00   数理科学研究科棟(駒場) 056号室
波江野 洋 氏 (Memorial Sloan-Kettering Cancer Center)
骨髄増殖性疾患の起源細胞に関する数理的研究 (JAPANESE)
[ 講演概要 ]



13:30-16:00   数理科学研究科棟(駒場) 123号室
宮崎 直 氏 (東京農工大学) 13:30-14:30
$Sp(2,C)$ 上の主系列Whittaker関数 (JAPANESE)
[ 講演概要 ]
原下 秀士 氏 (横浜国立大学) 15:00-16:00
A paving of the Siegel 10-fold of positive characteristic (JAPANESE)
[ 講演概要 ]
種数4の Siegel modular variety の stratification で一般論で扱えない部分を論じる。



16:30-18:00   数理科学研究科棟(駒場) 056号室
Uuganbayar Zunderiya 氏 (Nagoya University)
超幾何微分方程式系の一般化 (ENGLISH)
[ 講演概要 ]


関口(英)はm x m次の行列の行列式として得られるm階の



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.


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.



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.



10:30-11:30   数理科学研究科棟(駒場) 056号室
横山悦郎 氏 (学習院大学計算機センター)
国際宇宙ステーション「きぼう」における「氷の結晶成長における形態不安定化」実験解析ー氷の底面及び樹枝先端の成長速度解析とその理論的考察 (JAPANESE)
[ 講演概要 ]



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.


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)



10:30-12:00   数理科学研究科棟(駒場) 128号室
千葉 優作 氏 (東大数理)
Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space
[ 参考URL ]



16:30-18:00   数理科学研究科棟(駒場) 126号室
加藤周 氏 (京都大学)
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.



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



10:00-15:00   数理科学研究科棟(駒場) 122号室
山本 昌宏 氏 (東大数理) 10:00-10:50
産学連携による新たな数学の課題:非整数階拡散方程式への誘い (JAPANESE)
中村 周 氏 (東大数理) 11:00-11:50
量子力学のスペクトル・散乱理論における数学的手法 (JAPANESE)
伊東 一文 氏 (東大数理、ノースカロライナ州立大学) 13:20-14:10
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

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