My work is in the area of differential geometry. More specifically, I'm interested in riemannian manifolds, homogeneous spaces, compact Lie groups. I'm also interested in the intersection of knot theory with geometry, and the intersection of knot theory with fluid dynamics. .
- Fiberwise homogeneous fibrations of 3-dimensional space forms by geodesics, in preparation.
- Hopf fibrations are characterized by being fiberwise homogeneous, in preparation.
- Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows, part II, with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Clayton Shonkwiler and David Shea Vela-Vick. Algebraic & Geometric Topology 13 (2013) 2897-2923.