I am interested in three different areas: Stochastic Differential Equations, Diversities, and Cognitive Science.
In the field of Stochastic Differential Equations I work on issues both in the modeling of systems with stochastic differential equations and the numerical analysis of stochastic differential equations.
Diversities are a generalization of metric spaces developed by David Bryant and me. We introduced diversities in "Hyperconvexity and Tight Span Theory for Diversities." More recently, we discuss the relation between diversities and some network flow problems in "Diversities and the Geometry of Hypergraphs."
Cognitive Science is a tremendously broad field, and I currently work in only two small corners of it: phonology and dynamic field theory.