Research

My current research is on a motivic version of a result of Haynes Miller which says that there is a filtration on the unitary groups (more generally, the Stiefel manifolds over R, C, and the quaternions) which splits in the stable homotopy category. It is conjectured that an analogous splitting exists in the motivic stable homotopy category of Morel and Voevodsky for GL_n over a field. I am working towards a splitting analogous to Miller's in the context of Voevodsky's category of motives.  

My master's thesis was on the topology of the classifying space of PGL_n(C) and how this relates to the study of the number of generators of an Azumaya algebra.