Given the success of the Ricci flow it is natural to want to understand the behaviour of other geometric flows. The Bach flow is a higher order non-linear geometric flow. This project aims to study the Bach flow on non-product homogeneous four manifolds. In particular, we wish to understand the long term behaviour of the flow on the unique, simply connected non-product nilpotent Lie group which is four dimensional and study the geometric properties of any limiting spaces.
The University of Queensland
Adam Thompson is mathematics student at the University of Queensland. When Adam was in kindergarten he enjoyed playing with shapes; now Adam is in university and he continues to enjoy playing with shapes, albeit slightly more complicated ones.
Adam is interested in the differential geometry. In particular, he is interested in what the curvature of a shape can tell us about its underlying topology. Currently he is focused on geometric flows which involve deforming a shape according to a given partial differential equation.