The research in this area focuses on a range of topics in analysis ranging from the pure to the applied end.

On the pure side, topics include ergodic theory, functional and fractal analysis, and the rigorous analysis of ordinary and partial differential equations.

On the applied side methods are used to analyse partial differential equations (PDEs) in various contexts such as nonlinear elastostatics, pattern formation, dispersive wave equations, Navier-Stokes equations, and delay equations. Analysis on unbounded domains is of particular interest.

A recent development involves the construction of solutions to the Schrödinger equation that describes the process of electron emission from a metal surface, a process of considerable technological importance in the design of flat displays.

Another dimension is the calculus of variations, a subject with a long history, which has developed fresh new directions in the twenty-first century. A typical example comes from nonlinear elasticity, where the cost of deforming an elastic solid is represented by an energy functional.