# Nonlinear Partial Differential Equations and Geometric Evolution Equations

**Project level:** PhD, Masters, Honours, Summer

A number of projects are offered in the areas of Nonlinear Partial Differential Equations and Geometric Evolution Equations. These include topics in partial regularity theory for elliptic and parabolic systems, the evolution equations associated with liquid crystals, Yang-Mills flow and work on the Mumford-Shah functional, which arises in image segmentation. Some projects can also be arranged with a numerical emphasis, in particular in cooperation with Associate Professor Tony Roberts and Dr Vivien Challis, in the area of Topology Optimization.

## Project members

### Professor Joseph Grotowski

Head of School

School of Mathematics and Physics