Abstract:

When first introduced to topology, you were probably shown an animation depicting the family of smooth deformations that turn a coffee cup into a donut. One might hope for a way of doing this on a general manifold: perhaps you want to know if your simply connected closed three manifold is homeomorphic to a 3-sphere. One promising answer lies in geometric flows. Drawing heavily on examples from mean curvature flow, I will outline how PDEs and geometry interact to produce brilliant results in differential geometry and topology.