The atomic structure of ancient flows

In many physical systems, a geometric structure (such as an interface or a Riemannian metric) changes over time in a manner dependent on its curvature. Examples include erosion processes like stones tumbling on the beach and the propagation of bushfire fronts. Often, these evolutionary processes are highly nonlinear, and form 'singularities', the onset of which is an obstruction to a classical analysis. A robust method to understand (and overcome) singularity formation involves the characterisation of 'ancient solutions'. This project addresses the research gap in the analytical understanding of ancient solutions to a general class of (both extrinsic and intrinsic) curvature driven geometric flows. The mathematical understanding of these processes developed in this project could lead to improvements in applications such as bushfire modelling, of critical significance in Australia. Resear