Speaker
Description
Mean curvature flow is the gradient flow of the area functional where an
embedded hypersurface evolves in direction of its mean curvature vector. This
constitutes a natural geometric heat equation for hypersurfaces, which ideally will
evolve the embedding into a nicer shape. But due to the nonlinear nature of the
equation singularities are guaranteed to form. Nevertheless, a key observation in
geometry and physics is that generic solutions, obtained by small perturbations, can
exhibit simpler singularities. In this direction, a conjecture of Huisken posits
that a generic mean curvature flow encounters only the simplest singularities. We
will discuss work together with Chodosh, Choi and Mantoulidis which together with
recent work of Bamler-Kleiner establishes this conjecture for embedded hypersurfaces
in R^3.
