Monday, July 29, 2019
07/29/2019 - 1:00pm
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.
07/29/2019 - 4:00pm
We study the structure of intrinsic flat limits of manifolds with lower scalar curvature bounds. In particular, in joint work with Sormani and Basilio, we exhibit a sequence of closed positive scalar curvature manifolds intrinsic flat converging to the sphere with a Euclidean metric structure, restricted to the standard embedding of the sphere. This is the first example of an intrinsic flat limit with no geodesics.