Abstract: We say a family of hypersurfaces are flowed by mean curvature if the velocity equals the mean
curvature of the hypersurfaces. Mean curvature flow is the geometric flow modelling the motion of interfaces
in the natural world. A central topic in mean curvature flow is studying the singularities. In this talk, I will
introduce some basic properties of the mean curvature flow, and the formation of the singularities. In
particular, I will discuss the generic mean curvature flow introduced by Colding-Minicozzi and how to use the generic flow to study the singularities and the dynamics of mean curvature flow.
