Leonid Polterovich

Abstract:   I shall discuss a link between symplectic topology and a recently emerged branch of functional analysis, the theory of topological quasi-states, which goes back to J. Aarnes. In the symplectic context, quasi-states can be viewed as an algebraic way of packaging certain information contained in Floer theory. I shall present a number of applications to rigidity of symplectic intersections, to function theory on symplectic manifolds and to Hamiltonian dynamics. In addition, I shall discuss a connection between symplectic quasi-states and a group-theoretical notion of a quasi-morphism. The talk is based on joint works with M. Entov and F. Zapolsky.