I study topological fixed point theory from the perspective of algebraic topology. I'm particularly interested in the connections between fixed point theory and category theory. These connections give new descriptions of classical invariants that readily generalize and also give new categorical definitions that have applications outside fixed point theory.
Fixed Point Theory and Trace for Bicategories Asterisque (333), 2010.
Relative Fixed Point Theory Algebraic & Geometric Topology 11(2011) 839–886.
Duality and traces for indexed monoidal categories with Michael Shulman. Theory and Applications of Categories, Vol. 26, 2012, No. 23, pp 582-659.
Shadows and Traces for Bicategories with Michael Shulman. Journal of homotopy and related structures, DOI 10.1007/s40062-012-0017-0.
J. P. May and K. Ponto. More Concise Algebraic Topology: Localization, Completion and Model Categories. University of Chicago Press, Lecture notes in mathematics.