Explore Gromov's conjecture regarding the existence of short closed geodesics in 3-manifolds with positive scalar curvature in this mathematical physics lecture. Learn how Min-Max theory of minimal surfaces and a combinatorial version of mean curvature flow provide the tools to prove this fundamental result in differential geometry. Discover the collaborative research approach that led to this breakthrough, involving joint work with Davi Maximo and Regina Rotman. Gain insights into additional geometric and topological properties of 3-manifolds that can be established through minimal surface techniques. Examine the intersection of analysis and mathematical physics as applied to understanding the geometric structure of curved spaces, with particular focus on how positive scalar curvature constrains the behavior of geodesics in three-dimensional manifolds.