Fully nonlinear geometric flows. Geometric flows describe geometries changing through heat flow and diffusion. They arise naturally in many fields, from phase change and tumbling stones to string theo

Description

Fully nonlinear geometric flows. Geometric flows describe geometries changing through heat flow and diffusion. They arise naturally in many fields, from phase change and tumbling stones to string theory, and provide new tools for understanding questions in geometry and physics. This project aims to develop techniques for the design and analysis of highly nonlinear geometric flows, and apply them to understand long term behaviour of these processes. The new methods will contribute to the theory of nonlinear partial differential equations, enable the application of geometric flows to resolve important geometric and topological questions, and produce new theoretical tools applicable to similar systems arising in areas such as image processing, finance and material science.. Scheme: Discovery Projects. Field: 4904 - Pure Mathematics. Lead: Dr Mat Langford