Title: Some new applications of the mean curvature to self shrinkers

Abstract: The mean curvature flow, where one deforms a submanifold by its mean curvature vector, is known to in many cases develop singularities. These are points where the curvature along the flow blows up, or in some sense where the submanifold pinches. This makes the study of singularities vital to fully utilize the flow. Arguably the most basic local models for singularities are self shrinkers, called such because they evolve by dilations. In this talk I’ll discuss some applications of the mean curvature flow to self shrinkers in R^3 and R^4.