Egor Shelukhin (University of Montreal)

Title: Smith theory in Floer persistence, and dynamics

Abstract: We describe results related to the Smith inequality in filtered Floer homology, and their applications to questions in dynamics. In particular, we show that for a class of symplectic manifolds including the complex projective spaces, a Hamiltonian diffeomorphism with more fixed points, counted suitably, than the dimension of the ambient rational 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. This talk is partially based on joint work with Jingyu Zhao.