Generic Mean Curvature Flow and Generalizations of Entropy

Mean curvature flow entropy was introduced by Colding-Minicozzi, and it is a very important quantity in the study of mean curvature flow and related geometric problem. In particular, mean curvature flow entropy plays a crucial role in the study of generic mean curvature flow. In this talk, I will discuss two generalizations of mean curvature flow entropy: one is a localized version of entropy, another one is entropy in a closed manifold. I will discuss how to use these generalizations of entropy to rule out some pathological asymptotic behaviors of mean curvature flow.