Symplectic Dynamics Working Group

We will discuss several examples where ideas from persistent homology have applications to the study of the coarse geometry of groups of Hamiltonian diffeomorphisms, equipped with the Hofer norm..

The key idea is to consider Hamiltonian Floer Theory as a filtered object and extract quantitative data from the filtration. This viewpoint is particularly fruitful when the total Floer homology is zero, for example if one takes as chain level generators the periodic trajectories in a fixed nontrivial free homotopy class. Time permitting, we will review applications of persistence modules in other areas of symplectic and contact topology.