Deparment colloquium

Title: Generic singularities of mean convex mean curvature flows

Abstract: The mean curvature flow evolves a hypersurface in the direction of its mean curvature, and a fundamental problem is to understand the formation of singularities along this process. Work of White showed that for mean convex flows only cylindrical singularities can arise, but this can still be rather complicated. I will discuss recent progress showing that at least at the first singular time, generically only nondegenerate cylindrical singularities appear, and the behavior of these is very well understood by work of Sun-Wang-Xue.