Rafe Mazzeo, Stanford University

Title: The flow of networks by curvature

Abstract: This work constitutes a very preliminary step in the study of geometric heat flows on stratified spaces. It concerns the one-dimensional case of singular networks. Work on this goes back several decades (motivated by metallurgy!), and I will review some of the main points of progress, and then discuss a new formulation of the problem which clarifies short-time existence around "irregular vertices", and is expected to be particularly useful for the higher dimensional version. This is joint work with Jorge Lira, Alessandra Pluda and Mariel Saez.