UBC Department of Mathematics Graduate Research Award: Thomas Hughes

Superprocesses are measure-valued Markov processes describing the evolution of populations undergoing random spatial motion and independent branching (reproduction). In this talk I will discuss the dual relationship of superprocesses with certain nonlinear PDE and explore how properties of solutions to the dual PDE can be used to infer path properties of the superprocess, and vice-versa. In particular, I will describe some new hitting properties of the (\alpha,\beta)-superprocess, and how these properties correspond to a new (partial) characterization of the admissible initial traces for a fractional nonlinear PDE.