Explore the intricacies of mean curvature flow in this lecture by Carlo Sinestrari from the University of Rome Tor Vergata. Delve into the singularities that arise during the mean curvature flow of mean convex hypersurfaces. Part of the International School on Extrinsic Curvature Flows, this hour-long talk offers a deep dive into advanced mathematical concepts. Gain insights into the behavior of hypersurfaces under mean curvature flow and the formation of singularities in this specialized area of differential geometry.