- energy minimization of 3-d vector fields
- helicity of 3-d vector fields
- writhe of knots & other geometric knot theory concerns
- ropelength of knots & their applications
Papers: (in preparation)
- The Biot-Savart operator on bounded domains of the three-sphere
- Helicity of vector fields on the three-sphere
- The Geometry of the Taylor Problem
Dissertation: The Biot-Savart operator and electrodynamics on the three-sphere (pdf)
Master's Thesis: The Taylor problem in plasma physics (pdf)
My two advisors and me, April 2004
Herman Gluck, me, and Dennis DeTurck