The group coordinates its wide-ranging activities through the Centre for Analysis and Nonlinear Partial Differential Equations (CANPDE).

Research covers a broad spectrum from harmonic analysis to pure and applied PDEs. The research carried out can be divided between three broad themes below, with clear links between them:

- Harmonic Analysis: interactions with number theory, combinatorics, discrete and integral geometry, geometric measure theory and PDEs, applications to elliptic BVPs and semilinear and linear PDEs with rough coefficients and/or domains; applications to nonlinear hyperbolic, dispersive and transport equations.
- ODEs, PDEs and dynamical systems: spectral theory of nonlinear (p-Laplacian-type) ODEs with jumping nonlinearities, nonlinear eigenvalue problems for ODEs and PDEs; spectral analysis of linear self-adjoint and non-self-adjoint operators and applications to mathematical physics.
- Nonlinear PDEs and Applications: free-boundary problems, PDEs and variational methods in nonlinear elasticity and other continuum theories, nonlinear dissipative equations including Navier-Stokes and reaction-diffusion equations, transport equations arising in mathematical biology (e.g. chemotaxis), and mathematical general relativity.

There are additional strong synergies with other groups, for example Applied & Computational Mathematics for numerical analysis and Probability, Statistics & Applications for studies in probability theory.