From Filtered Floer Homology to Dynamics

The structure and growth of various types of Floer homology persistence modules are intimately connected to the dynamics of the underlying Hamiltonian system. For instance, systems with exponential barcode growth have positive topological and metric entropy, while a polynomial growth rate is indicative of complete integrability. Reeb pseudo-rotations tend to have a rigid “minimal” persistence module. In this talk, we discuss these connections and also point out some open questions, drawing mainly on a series of joint results with Erol Barut, Erman Cineli, Basak Gurel, and Marco Mazzucchelli.