Theatre B, Richard Berry Building
The University of Melbourne
Department of Mathematics
University of Minnesota
This talk will be a gentle introduction to contact structures and the Heat-Flow Method. Contact structures are a subject which has a hundred-year history and has been very active in the last ten years. I will explain what a contact structure is, in comparison to a foliation (which I will also explain). This will require the introduction of differential forms, which will be introduced in an intuitive way. There are some famous theorems by Darboux about these contact structures and some compelling questions that remain open. I will explore some of these using the idea of heat flow.