Generic equidistribution of periodic orbits for area-preserving surface diffeomorphisms

I will discuss some recent work showing that a generic area-preserving diffeomorphism of a closed surface has an equidistributed sequence of periodic orbits. The proof uses several properties of spectral invariants from periodic Floer homology, along with a variational argument originating in work of Marques-Neves-Song and Irie regarding equidistribution results for minimal hypersurfaces and Reeb flows, respectively.