Geometry and Topology of Hamiltonian Floer Complexes in Low-Dimension - Dustin Connery-Grigg

The course covers the geometry and topology of Hamiltonian Floer complexes in low-dimension. The learning outcomes include understanding the qualitative dynamics of non-degenerate Hamiltonian isotopies on surfaces and the structure of their Floer complexes. The course teaches a topological characterization of Floer chains representing the fundamental class in CF∗(H,J) and a symplectically bi-invariant norm on the group of Hamiltonian diffeomorphisms. The teaching method involves presenting two results related to the dynamics of Hamiltonian isotopies and their Floer complexes. The intended audience includes individuals interested in symplectic geometry, topology, and Hamiltonian dynamics.