Mathematics Seminar at ICTP - 6 September

[Math]

M A T H E M A T I C S   S E M I N A R S   2007


Thursday, 6 September at 15:00 hrs.


Professor G. Khimshiashvili
(Georgian Academy of Sciences, Tbilisi, Georgia)


"Holomorphic dynamics in loop spaces"

Abstract: Several natural constructions of holomorphic mappings of  
Riemann
surfaces into loop spaces endowed with natural almost complex structures
will be presented. The main attention will be given to based loop spaces
of compact Lie groups and immersed loop spaces of three-dimensional
Riemannian manifolds. In particular case when the source space is the  
unit
disc in complex plane, basic geometric properties of the arising
holomorphic families of loops will be established and their  
interpretation
in dynamical terms will be given. It will be shown that examples of
holomorphic dynamics in loop spaces arise from Seifert fibrations and
isolated singularities of algebraic plane curves. A visual example
provided by the inverse of Hopf fibration will be considered in some
detail. It will be also shown that each Seifert fibration can be turned
into a holomorphic family of loops parameterized by its factor-space.


VENUE:  SEMINAR ROOM (ICTP Main Building, first floor)