Mathematics Colloquium

Colding and Minicozzi introduce a notion of entropy for hypersurfaces which is defined by the supremum over all Gaussian integrals with varying centers and scales. The entropy is a natural geometric invariant that measures complexity of hypersurfaces. The definition of entropy is motivated by the dynamic approach to the mean curvature flow (a flow of hypersurfaces that decrease the volume in the steepest direction), and has played an important role in the recent progress on Huisken's generic mean curvature flow conjecture. In this talk, I will discuss recent work with J. Bernstein on geometric and topological properties of hypersurfaces of low entropy.