My research area is algebraic topology. In particular, I am interested in homotopy theory. Most recently I have been pursuing two different threads in my work.

With Jeff Strom (Western Michigan University) I have been thinking about A-cellular spaces. Basically, an A-cellular space is a space that can be built out of A and its suspensions in the way that CW complexes are built out of spheres. Each space A determines a closed class - a collection of spaces which is closed under homotopy colimit operations and contains the space A. These are the so-called A-cellular spaces. Any space X can be approximated by an A-cellular space, and the measure of how difficult it is to construct this approximation is known as the A-complication of X. We have been working on developing some bounds for the A-complication of spaces. We have also been thinking about good spaces - these are spaces A such that the closed class determined by A is also closed under extensions by fibrations. In particular, we have been working to understand bounds for A-complication when A is a good space.

With Brenda Johnson (Union College) and Randy McCarthy (University of Illinois at Urbana-Champaign) I have been thinking about things relating to Goodwillie's calculus of functors. Given a functor of spaces, F, and a nice space X, there is a tower of functors, P_nF, where P_nF is a degree n functor. This tower acts as a Taylor tower for F, expanded around X. That is, the tower converges to the functor F in some range which depends not only on F but also on X. There are also derivatives in this theory - the n^th derivative is the fibre of the map P_nF --> P_n-1F. We have been studying a particular bi-complex whose homology produces the first derivative of F when F is a Gamma module in the hopes of paring down the complex while retaining the convergence to D₁F.

The rank filtration and Robinson's complex, with Brenda Johnson and Randy McCarthy, Journal of Pure and Applied Algebra, 212 (2008) no 4 p735-752.

Homotopical Complexity and Good Spaces, with Jeff Strom, Transactions of the American Mathematical Society, 359 (2007) p687-700.

v_*-torsion spaces and thick classes with Wojciech Chacholski and William G. Dwyer, Mathematische Annalen 336 (2006) no 1, p13-26.

Model Structures on the Category of Ex-Spaces, with Mark W. Johnson, Topology and its Applications, 119 (2002) pp325-353.

The A-Complication of a Space with Wojciech Chacholski and William G. Dwyer, Journal of the London Mathematical Society, (2) 65 (2002) pp204-223.

An equivariant smash spectral sequence and unstable box product, Transactions of the American Mathematical Society 351 (1999) pp2763-2775.

An equivariant van Kampen spectral sequence, Topology and its Applications 79 (1997) pp31-48.

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