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Title: Smith theory in Floer homology, persistence, and dynamics
Abstract: Recent years have seen a renewed interest in a classical topological inequality that originated in the work of P. A. Smith, extended to the framework of Floer homology. We describe such inequalities in the setting of persistence modules obtained from Floer homology, and their recent applications to questions in Hamiltonian dynamics. In particular, we show that for a class of symplectic manifolds including complex projective spaces, a Hamiltonian diffeomorphism with more fixed points, counted suitably, than the dimension of the ambient homology, must have an infinite number of simple periodic points. This is a higher-dimensional homological generalization of a celebrated result of Franks from 1992, as conjectured by Hofer and Zehnder in 1994. Time permitting, we may discuss further, very recent, related results