## Seminar information archive

#### Kavli IPMU Komaba Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Akishi Ikeda (The University of Tokyo)
The correspondence between Frobenius algebra of Hurwitz numbers
and matrix models (JAPANESE)
[ Abstract ]
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.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiro AIHARA (Fukushima Univ.)
Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

### 2010/04/23

#### Colloquium

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

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

### 2010/04/22

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Nigel Higson (Pennsylvania State Univ.)
The Baum-Connes Conjecture and Group Representations (ENGLISH)
[ Abstract ]
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.

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jens Starke (Technical University of Denmark)
Deterministic and stochastic modelling of catalytic surface processes (ENGLISH)
[ Abstract ]
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.

### 2010/04/21

#### Seminar on Mathematics for various disciplines

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Gen Sazaki (Hokkaido University)
Direct observation of elementary processes of crystal growth by advanced optical microscopy (JAPANESE)
[ Abstract ]

#### Numerical Analysis Seminar

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Kenta Kobayashi (Kanazawa University)
On the interpolation constant over triangular and rectangular elements (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/

### 2010/04/20

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Helene Eynard-Bontemps (東京大学大学院数理科学研究科, JSPS)
Homotopy of foliations in dimension 3. (ENGLISH)
[ Abstract ]
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 Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Takayuki Okuda (the University of Tokyo)
Proper actions of SL(2,R) on semisimple symmetric spaces (JAPANESE)
[ Abstract ]
Complex irreducible symmetric spaces which admit proper SL(2,R)-actions were classified by Katsuki Teduka.
In this talk, we generalize Teduka's method and classify semisimple symmetric spaces which admit proper SL(2,R)-actions.

### 2010/04/19

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

(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.

#### Lectures

16:00-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Cyrill Muratov (New Jersey Institute of Technology)
Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions
[ Abstract ]
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.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Filippo Bracci (Universita di Roma, Tor Vergata'')
Loewner's theory on complex manifolds (ENGLISH)
[ Abstract ]
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.
[ Reference URL ]
http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

#### Mathematical Biology Seminar

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Horoshi HAENO (Memorial Sloan-Kettering Cancer Center)

### 2010/04/17

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
MIYAZAKI Tadashi (Tokyo Univ. of agr. and indus.) 13:30-14:30
Principal series Whittaker functions on $Sp(2,C)$ (JAPANESE)
[ Abstract ]
Not given here.
HARASHITA Shushi (Yokohama National Univ.) 15:00-16:00
A paving of the Siegel 10-fold of positive characteristic (JAPANESE)
[ Abstract ]
Not given here.

### 2010/04/15

#### Lie Groups and Representation Theory

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Uuganbayar Zunderiya (Nagoya University)
Generalized hypergeometric systems (ENGLISH)
[ Abstract ]
A new type of hypergeometric differential equations was introduced and studied by H. Sekiguchi. The investigated system of partial differential equation generalizes the Gauss-Aomoto-Gelfand system which in its turn stems from the classical set of differential relations for the solutions to a generic algebraic equation introduced by K.Mayr in 1937. Gauss-Aomoto-Gelfand systems can be expressed as the determinants of $2\\times 2$ matrices of derivations with respect to certain variables. H. Sekiguchi generalized this construction by looking at determinations of arbitrary $l\\times l$ matrices of derivations with respect to certain variables.

In this talk we study the dimension of global (and local) solutions to the generalized systems of Gauss-Aomoto-Gelfand hypergeometric systems. The main results in the talk are a combinatorial formula for the dimension of global (and local) solutions of the generalized Gauss-Aomoto-Gelfand system and a theorem on generic holonomicity of a certain class of such systems.

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Alberto Tesei (University of Rome 1)
Long-time behaviour of solutions of a forward-backward parabolic equation
[ Abstract ]
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.

#### Classical Analysis

16:00-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Claude Mitschi (Univ. de Strasbourg)
The Galois group of projectively isomonodromic deformations (ENGLISH)
[ Abstract ]
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.

### 2010/04/14

#### Number Theory Seminar

17:30-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Gerard Laumon (CNRS, Universite Paris XI - Orsay)
The cohomological weighted fundamental lemma
[ Abstract ]
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。)

#### Seminar on Mathematics for various disciplines

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Etsuro Yokoyama (Gakushuin University)
Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station
--basal plane growth rate and dendritic growth velocity
(JAPANESE)

### 2010/04/13

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Christian Kassel (CNRS, Univ. de Strasbourg)
Torsors in non-commutative geometry (ENGLISH)
[ Abstract ]
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.

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Jean-Marc Bouclet (Toulouse University, France)
Strichartz estimates and the Isozaki-Kitada parametrix
on asymptotically hyperbolic manifolds (ENGLISH)

### 2010/04/12

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

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

### 2010/04/06

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

On the characters of tempered modules of affine Hecke
algebras of classical type
[ Abstract ]
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.

### 2010/04/05

#### Algebraic Geometry Seminar

16:40-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Alexandru Dimca (Université Nice-Sophia Antipolis)
From Lang's Conjecture to finiteness properties of Torelli groups
[ Abstract ]
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.

### 2010/03/30

#### GCOE Seminars

10:00-15:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Masahiro Yamamoto (University of Tokyo) 10:00-10:50

Shu Nakamura (University of Tokyo) 11:00-11:50

Kazufumi Ito (University of Tokyo, North Carolina State University) 13:20-14:10
Semismooth Newton法の理論、及び応用 (JAPANESE)
Georg Weiss (University of Tokyo) 14:10-15:00
TBA (JAPANESE)