Dynamic and Topological Aspects of Hamiltonian Floer Theory on Surfaces

Given a Hamiltonian H∈C∞(S1×M), what is the relationship between the dynamics of the isotopy generated by H and the various Floer-theoretic invariants associated to H? In this talk I will discuss how — in the case where M is a closed surface —one can interpret certain spectral invariants in purely dynamical terms,in addition to interpreting certain parts of the Hamiltonian Floer complex in terms of particularly nice transverse foliations initially introduced by Le Calvez in his study of equivariant Brouwer theory and surface homeomorphisms.