- Topology and geometry

- Mathematics

I'm a stable homotopy theorist and my primary interest is in broad generalizations of the trace of a matrix. At first glance these two ideas don't have a lot in common, but topological fixed point theory provides a really illuminting bridge between them. There is an approach to fixed point theory that makes the invariants formally the same as the trace of a matrix. This formal structure can then be applied in examples well beyond fixed point theory. These new applications are a central focus of my recent work.

I'm also affiliated with the University of Kentucky Math Lab and very happy to discuss our projects - especially our visualization projects!

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.