P. O. Box 400137
Localization of Andre-Quillen-Goodwillie towers, and the periodic homology of infinite loopspaces, Advances in Math. 201 (2006), 318-378.
Primitives and central detection numbers in group cohomology, Advances in Math. 216 (2007), 387-442.
My research is centered around algebraic topology and homotopy theory. Over the years, my research interests have broadened to include algebraic K-theory and group representation theory. My work in topology in recent years has concerned the development of a character theory for complex oriented cohomology theories, the stable homotopy groups of spheres, the foundations of H-space theory, iterated loopspace theory, topological realization questions, and the application of Goodwillie polynomial functor theory to classical homotopy. My algebraic work in recent years has been on the topics of modern Steenrod algebra technology over all finite fields, generic representation theory of the finite general linear groups, rational cohomology, and homological stability questions.