In Spring 2014, I will be on leave at MSRI.
My research is in algebraic topology and homotopy theory. It is supported in part by NSF Research Grant DMS-1308933.
A large part of my research concerns Goodwillie's homotopy calculus. This theory provides analogues in the world of homotopy theory of ordinary calculus notions such as polynomial approximation, the Taylor series and its convergence, and derivatives. Much of my work is focused on the problem of reconstructing the corresponding 'Taylor tower' from its individual terms. Unlike in ordinary calculus there are many different ways to 'add up' terms.
Operad theory and Koszul duality
The key objects that appear in my work on Goodwillie calculus are operads, and modules over them. Operads provide a way to keep track of complex collections of operations and how they interact. I have developed a geometric version of Ginzburg and Kapranov's 'Koszul' duality between the Lie and commutative operads.
Algebraic K-theory of ring spectra
This is an extension of the K-theory of rings to a topological setting. I would like to apply my work on calculus and operads to make calculations of the `Taylor tower' of the algebraic K-theory functor.
At Amherst College I have taught courses in calculus, analysis, topology and Galois Theory. See my teaching page for more details.
From 2008-2011, I was an Assistant Professor in the Math Department at the University of Georgia.
From 2005-2008, I was a J.J. Sylvester Assistant Professor at Johns Hopkins University.
Before that I grew up in Royston, Herts., UK.