A Weyl law for PFH spectral invariants

Rohil Prasad, Princeton University

Zoom link:https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09

Hutchings' periodic Floer homology (PFH) is a Floer-theoretic invariant associated to an area-preserving diffeomorphism of a closed, oriented surface. It has a set of associated quantitative invariants, called "PFH spectral invariants", which encode information about periodic orbits of this diffeomorphism. The main topic of this talk is a "Weyl law" for PFH spectral invariants, which relates the asymptotics of PFH spectral invariants to the Calabi invariant of Hamiltonian surface diffeomorphisms. We will state the Weyl law and discuss a bit of its proof, which relies on a quantitative analysis of the Lee-Taubes isomorphism of PFH and monopole Floer homology. Time permitting, we will discuss some applications to the dynamics of area-preserving surface diffeomorphisms. This talk is based on joint work with Dan Cristofaro-Gardiner and Boyu Zhang