My current and planned research divides into three areas: the relationship between stable and unstable cohomology operations, the differential topology of loop spaces, and the properties of two--vector bundles. This research lies in the areas of algebraic topology, differential topology, and differential geometry and it has further application to mathematical physics. In addition to the techniques of the areas already mentioned, my research uses theory from functional analysis and category theory.

More details are available in my research plan: PDF or PostScript.