Past work has emphasized General Relativity, studying model spacetimes and their properties, as well as the interface between relativity and quantum physics. Current work investigates applications of the Octonions, the unique non-associative division algebra, to the physics of fundamental particles. Other past and present interests include Algebraic Computing, Asymptotic Structure, Non-Euclidean Geometry, Quantum Field Theory in Curved Space, and Signature Change.

Work in Mathematics Education includes directing the Vector Calculus Bridge Project, co-directing the High Desert Mathematics Partnership and the Paradigms in Physics Project, and designing course content for the Oregon Mathematics Leadership Institute.