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Research Interests:

Geometry of Partial Differential Equations

Research:

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.

Select Publications:

• 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.