Professor • Ph.D. Duke, 1996

Math 321

Geometry of Partial Differential Equations

I work in differential geometry and the application of geometry to the study of partial differential equations. Specifically, my work has focused on conservation laws, Backlund transformations, intermediate equations, and sub-Finsler geometry with applications to control theory.

- Geometry of conservation laws for a class of parabolic partial differential equations,
*Selecta Math. (New Series)***3**(1997) 1-77. - Geometry of conservation laws for a class of parabolic PDEs II: Normal forms for equations with conservation laws.
*Selecta Math. (New Series).***3**(1997) 497-515. - Homogeneous Backlund transformations of hyperbolic Monge-Ampere systems.
*Asian J. Math.***6**(2002) 433-480.} - Parametric Backlund transformations I: Phenomenology, (with T. Ivey).
*Trans. Amer. Math. Soc*.**357**(2005) 1061-1093. - Sub-Finsler geometry in dimension three, (with C. G. Moseley).
*Differential Geometry Appl*.**24**(2006) 628-651.