Recent results on crystalline curvature flows

In this talk I will describe the construction we set up with M. Morini (U. Parma), M. Novaga (U. Pisa), M. Ponsiglione (U. Roma I) to build and show uniqueness of some types of mean curvature flows driven by an anisotropic, nonsmooth perimeter. In particular a striking result is the convergence of the scheme designed by S. Luckhaus and T. Sturzenhecker to a unique limit in almost all situations (generically, including for nonsmooth distances or surface tensions).