Differential geometry originated as the study of curved or bent spaces fixed in time; over the last 4 decades, however, geometers have overseen huge developments in the study of spaces which are not fixed but change, or flow, over time. One of the simplest and perhaps most natural examples is curve shortening flow, the topic I did my master’s dissertation on, where essentially a curve moves inwards with speed proportional to its bendiness. In this talk we will give an introduction to curve shortening flow and look at some of the (surprising?) ways in which it behaves, starting in the plane before moving onto surfaces. We will then briefly touch on mean curvature flow, a generalisation of curve shortening flow to higher dimensions, and see some of the applications of curve shortening flow in both pure maths and the real world.
There will be some equations and overviews of proofs, but it won’t be super technical, and there’ll also be nice pictures and diagrams so it should be possible to follow the talk without any knowledge of differential geometry at all!