Statement of Research Interest

My research lies in the intersection of three fields of mathematics: stochastic processes, representation theory and the theory of Lie groups; in particular, Lévy processes in nilpotent Lie groups. In Euclidean space, these processes are generated by a particularly nice class of operator, referred to as a pseudo-differential operator. These operators have traditionally been of interest in the study of partial differential equations (PDE). For this reason attempts have been made to extend the notion of pseudo-differential operator to more general spaces. Indeed, for some Lie groups it is known that Lévy processes generate operators with properties analogous to those of pseudo-differential operators.