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!