Singularities in Mean Curvature Flow

Mean curvature flow is a nonlinear geometric flow where a hypersurface evolves to decrease its area as efficiently as possible. Singularities are unavoidable and the point is to understand the possible singularities and the behavior of the flow near a singularity. I will talk about recent joint work with Toby Colding and Tom Ilmanen where we prove strong rigidity and uniqueness theorems for generic singularities in all dimensions.