My primary research area is 3-dimensional topology and knot theory. I am verry interested in invariants of 3-manifolds and knots that are constructed using gauge theory, such as Floer homology, the Casson invariant, and SU(n) generalizations of these invariants. I am also interested in the topological and smooth knot concordance groups and Casson-Gordon invariants, untwisted and twisted Alexander polynomials, Cochran-Teichner-Orr invariants and invariants arising from Heegaard Floer theory which shed light on knot concordance and sliceness.

My work in higher rank Casson invariants has also given rise to an interest in equivariant transversality problems. Many standard foundational results about manifolds and maps between them become either much trickier, not known, or just plain untrue if one insists that the functions preserve some symmetries of the manifolds. In other words, there are many good problems left to work on in this area.

I have also been involved in several interdisciplinary projects recently.

• A project with Kevin Facemyer of the Department of Biochemistry and Molecular Biology studying the way proteins bind together.
• A project with Hans Moosmuller, Rajan Chakrabarty, and Mark Garro, of DRI and the Chemical Physics Program, to model soot particle formation.
• A project with Richard A. Wirtz, Kiran Balantrapu, and Deepti Sarde of UNR's Mechanical Engineering Department, concerning new designs for heat exchangers.

Below are my publications, some of which can be downloaded in pdf form.