Explore upper bounds for the length of the shortest periodic geodesic on closed Riemannian manifolds in this 47-minute lecture by Regina Rotman. Delve into the relationship between curvature bounds and geodesic lengths, focusing on manifolds with positive Ricci curvature and closed Riemannian 3-spheres with positive scalar curvature. Gain insights into joint research with Y. Liokumovich and D. Maximo, examining how various curvature conditions influence the geometry of manifolds and their shortest closed geodesics.