Integral Hamiltonian Floer theory

Some years ago, joint with Xu, we resolved the integral version of the Arnold conjecture. Expanding the ad hoc constructions used there, we have developed a package of integral Hamiltonian Floer theory and their mod p reduction, including defining quantum Steenrod operations and their Floer-theoretic counterpart for any closed symplectic manifold. I will present some aspects of this package, highlighting how to efficiently combine global Kuranishi charts and FOP perturbations. Time permitting, I will also present applications to the study of Hamiltonian diffeomorphisms.