Dynamic and Topological Aspects of Hamiltonian Floer Theory on Surfaces

Explore the intricate connections between Hamiltonian dynamics and Floer-theoretic invariants in this advanced mathematics seminar. Delve into the relationship between the dynamics of isotopies generated by Hamiltonians H∈C∞(S1×M) and their associated Floer-theoretic invariants, specifically focusing on closed surfaces. Discover how spectral invariants can be interpreted through purely dynamical perspectives, while examining how certain components of the Hamiltonian Floer complex relate to transverse foliations originally developed by Le Calvez for equivariant Brouwer theory and surface homeomorphisms. Gain insights into the dynamic and topological aspects that bridge symplectic geometry with surface topology through this specialized presentation from the Joint IAS/PU Symplectic Geometry Seminar series.