トップ > セミナー・特別講義等 >Seminar on Geometry, Dynamics and Foliations

## Seminar on Geometry, Dynamics and Foliations

(ENCOUNTERwithMATHEMATICS番外編)

#
Seminar on Geometry, Dynamics, and Foliations

at CHUO University (BGammaSchool venue)

Building No.6, Room 61225 (12th Floor, Dept. of Math.)

- 21st September (sat) 15:00-17:30 15:00-16:00 Julio Rebelo (U. Toulouse III)

16:30-17:30 Victor Kleptsyn (CNRS, Rennes)

- 23rd September (mon) 15:00-17:30 15:00-16:00 Julio Rebelo (U. Toulouse III)

16:30-17:30 Kai Cieliebak (U. Augsburg)

- 25th September (wed) 15:00-17:30 15:00-16:00 Julio Rebelo (U. Toulouse III)

16:30-17:30 David Martinez Torres (Utrecht U.)

# Titles and abstracts

### Julio Rebero

Title: Methods for extending holonomy maps of holomorphic foliations and applications. 1, 2, 3.Abstract: We shall be concerned with singular holomorphic foliations F defined on an algebraic surface M. The starting point for these lectures will be the problem of classifying those foliations admitting an invariant positive closed current. This problem will lead us to discuss some extension results for certain holonomy maps associated to foliations F as above (regardless of whether or not they admit invariant positive currents). Applications of these results to the initial problem will then be sketched and additional potential applications of them will also be indicated.

### Victor Kleptsyn

Title: Renormalization: an introduction for the beginnersAbstract: The talk will be devoted to the idea of renormalization -- the art of reducing a problem to a problem of the same kind, and getting something out of a chain of such reductions. We will see how it explains Feigenbaum-Coullet-Tresser universality in unimodal maps, as well as will succeed in guessing the power law for the magnetization near the critical temperature.

### Kai Cieliebak

Titles: The topology of rationally and polynomially convex domainsAbstract: Rationally and polynomially convex domains in \C^n are fundamental objects of study in the theory of functions of several complex variables. After defining and illustrating these notions, I will explain joint work with Y.Eliashberg giving a complete characterization of the possible topologies of such domains in complex dimension at least three. The proofs are based on recent progress in symplectic topology, most notably the h-principles for loose Legendrian knots and Lagrangian caps.

### David Martinez Torres

Title: Non-contractible loops in the diffeomorphism group of coadjoint orbits.Abstract: A compact connected semisimple Lie group G acts in a Hamiltonian fashion on its coadjoint orbits, i.e. G maps into the group of Hamiltonian transformations of the coadjoint orbit. McDuff and Tolman showed that the induced map on fundamental groups is injective, answering a question of A. Weinstein. In this talk we will show that this is not quite a symplectic phenomenon, but a topological one, since the (finite) fundamental group of G already injects in the fundamental group of the group of diffeomorphisms. This is joint work with I. Mundet.

連絡先：三松 佳彦

TEL:03-3817-1749

E-MAIL:yoshiATmath.chuo-u.ac.jp