Minimal surfaces and Gromov’s conjecture on the length of closed geodesics in PSC

Abstract:
I will prove Gromov's conjecture that every 3-manifold of positive scalar curvature contains a short closed geodesic.
The proof uses Min-Max theory of minimal surfaces and a combinatorial version of mean curvature flow.
This is a joint work with Davi Maximo and Regina Rotman.