My main current interest is the theory of 'disordered physical systems'. This is the study of stochastic processes in finite-dimensional Euclidean spaces, and is motivated by practical problems arising in more applied sciences including physics and biology. Examples include the percolation model and the contact model, being models respectively for a disordered medium and the spread of epidemics. These systems give insight into the behaviour of models for ferromagnetism, such as the Ising and Potts models. They also provide a host of really captivating and well motivated problems in probability.
A further interest is the application of modern probability to the structure of the integers, thereby obtaining contemporary insight into probabilistic number theory.