MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations

Abstract

This tandem workshop with MATRIX in Creswick, Australia, brought together leading experts from the fields of geometric partial differential equations and geometric analysis in general. The focus of the workshop was on recent developments and directions in non-linear geometric diffusion equations. The main flows considered were mean curvature flow, inverse mean curvature flow, Ricci flow, Willmore flow, as well as related flows. A number of the results and methods were in the setting of general relativity, where flows have been very successful in helping solve major problems (for example the resolution of the Penrose conjecture by Huisken/Ilmanen using the inverse mean curvature flow). For four days of the workshop there were combined (with MATRIX) morning talks and extensive discussions.