Mean curvature flow of generic initial data

Mean curvature flow is the analogue of the heat equation in extrinsic differential geometry. Because mean curvature flow is nonlinear, there are necessarily singularities. In general, the singular behavior of the flow could be extremely complicated and is not well understood. I will discuss recent work with K. Choi, C. Mantoulidis, and F. Schulze concerning the mean curvature flow of a “generic” initial surface. In particular, we show that certain singularities do not arise in the case of a generic initial surface.