Research Interests for Abraham D. Smith

I am interested in the geometry of PDE and local differential geometry, especially in the sense of Cartan.

Currently, I am studying GL(2,R) structures on manifolds, which correspond to distributions of rational normal cones. These structures arise in the context of exotic holonomies and hydrodynamic PDE. The existence of certain sub-manifolds in these structures correspond to the integrability of certain second-order PDE, and my goal is to locally classify all such integrable GL(2,R) structures.

Keywords:

Exterior , Differential, Geometry, Finsler

Current projects:

GL(2,R) structures, exotic holonomies and related systems of PDE

Finsler manifolds of Randers type

Recent Publications

1. Rann Bar-On, Paul Bendich, Benjamin Cooke, Michael Gratton, Timothy Lucas, Michael Nicholas, Nicholas Robbins, Abraham Smith, Joseph Spivey, Graduate Calculus Curriculum Review, Spring 2007 (March, 2007) [pdf] [abs]