Current research interests:
My primary research interests are within mathematical physics, in particular quantum field theory and statistical mechanics and some topics related to string theory. A main theme has been the investigation of various discrete approximations to models of quantum field theories, including models of quantum gravity in low dimensions. In recent years this work has lead to an interest in topics in random graph theory, in particular in random planar maps and random trees. Recently I have done some work on non-commutative field theory. The main results are proofs of existence and stability of static solutions to so-called non-commutative, non-linear wave equations (also called non-commutative solitons), as well as existence and uniqueness results for solutions to the Cauchy problem for such equations.