Yevgeny Liokumovich, a mathematician at the University of Toronto, presents a proof of Gromov's conjecture that every closed 3-manifold with positive scalar curvature contains a short closed geodesic. Speaking at the Institute for Advanced Study, he builds the argument from Min-Max theory for minimal surfaces combined with a combinatorial version of mean curvature flow, work done jointly with Davi Maximo and Regina Rotman. The talk walks through how minimal surface techniques, originally developed for other geometric problems, can be adapted to bound the length of geodesics using curvature assumptions alone. Time permitting, Liokumovich extends the discussion to further results on the geometry and topology of 3-manifolds obtained through minimal surface methods. The talk assumes familiarity with Riemannian geometry and is aimed at researchers and graduate students working in geometric analysis and low-dimensional topology.