My research interests are in category theory, algebraic topology, and homotopy theory. I am specifically interested in using homotopical or “derived” algebra, in the form of operads, spectra, and infinity categories, to understand and classify structures that naturally arise in geometry and topology. Some geometric structures that I have specifically studied in previous work or am currently interested in include: cohomological invariants of topological spaces, the stable homotopy groups of spheres, the relationships between cobordism rings as the structure group is varied, A-infinity categories.