I work in the area of applied analysis, studying variational problems and partial differential equations that arise in continuum mechanics, in particular in nonlinear elasticity. A common feature of the problems studied is the often intriguing interplay between the properties of the underlying partial differential equations and the physics of the situation being modelled, with physical considerations yielding insight into the underlying mathematics and vice versa. This often requires the use of tools and concepts from diverse areas of mathematics ranging from analysis, differential equations, geometry, and topology to numerical analysis and continuum physics.

One main area of interest has been to study the existence and properties of singular energy minimisers and their connection with fracture mechanisms observed in polymers. A key problem here, on which I have been working, is to develop new numerical approaches to predicting the formation and location of singularities.

A more recent interest has been to understand the connections between my previous studies in nonlinear elasticity and corresponding phenomena in fluid mechanics.