Research

I was an algebraic topologist, interested in working on problems in unstable homotopy theory using the tools of Goodwillie’s calculus of functors. This theory allows us to approximate functors of spaces by functors of spectra, a kind of homotopy abelianization. The analogue in this theory of a Taylor Series, the Taylor Tower of a functor, encodes homotopical nilpotence information, bearing a strong resemblance to the lower central series filtration of a group, whose associated graded has a Lie algebra structure.

Especially interesting are problems that explore and strengthen this analogy, such as invariants controlled by homotopy nilpotence, the Quillen-style Lie models of chromatic homotopy theory, the Lie-algebra structure of the derivatives of the identity functor. I am also working on applying these tools to hard problems such as calculating the (p-local, stable) homotopy groups of spheres.