Leonid Polterovich: Hamiltonian diffeomorphisms and persistence modules

I'll discuss robust obstructions to representing a Hamiltonian diffeomorphism as a full power, with applications to geometry and dynamics. The robustness is understood in the sense of Hofer's metric.
The approach is based on the theory of persistence modules applied in the context of filtered Floer homology. Joint work with Egor Shelukhin.