Mathematics Department Colloquium
Spring 2005

Date: Thursday, April 21
Time: 4:00 p.m.
Location: 215 Thomas Building
Name: Leonid Polterovich
Affiliation: Tel Aviv University
Title: Quasi-morphisms and quasi-states in symplectic topology.

Abstract: A quasi-morphism of a group is "a homomorphism up to a bounded error". This notion was introduced in the 80-ies in connection with bounded cohomology theory (Gromov, Brooks). It proved to be a useful tool in geometry, topology and dynamics. In the present talk I focus on quasi-morphisms on groups of symplectic diffeomorphisms. They come from Floer theory -- the cornerstone of modern symplectic topology. I discuss a link to the theory of quasi-states - a recently emerged branch of functional analysis originated in quantum mechanics. The talk is based on joint works math.SG/0205247, math.SG/0410338 with M.Entov and math.SG/0307011 with P.Biran and M.Entov.