Branching Floer homology and the Hofer-Zehnder capacity

In several recent works, Hamiltonian Floer theory has been used to calculate the Hofer-Zehnder capacity in new cases. However, these methods are limited by the fact that standard Floer homology can only see one homotopy class of periodic orbits at a time.

In this talk, based on a joint project with Viktor Ginzburg and Basak Gurel, I will describe a method which should allow us to deal with this problem. It uses the notion of Branching Floer homology, an extension of Hamiltonian Floer homology in which periodic orbits in different homotopy classes are allowed to interact via the Floer differential.