Periodic geodesics, geodesic nets, and fillings

I will discuss questions pertaining to existence of periodic geodesics and geodesic nets on complete, non-compact Riemannian manifolds, as well as some upper bounds for the length of a shortest periodic geodesics on closed Riemannian manifolds. I will discuss some of the techniques that help to establish these upper bounds, including “filling techniques” that originate with M. Gromov.