Abraham D Smith, Graduate Student
Starting August 2009, I will be a MSRI postdoctoral fellow at McGill University in Montreal. Please note: Abraham has left the Mathematics department at Duke University; some info here might not be up to date.  Contact Info:
Office Location:  210 Physics  Office Phone:  9196602811  Email Address:    Office Hours:
 By Appointment
 Education:
PhD  Duke University  2009 
MA  Duke University  2004 
BS with Honors in the Major  University of Wisconsin  2003 
 Specialties:

Geometry
 Research Interests: Differential Geometry, Geometric PDE, Exterior Differential Systems, Mathematics Education
Current projects:
GL(2,R) structures, exotic holonomies and related systems of PDE, Finsler manifolds of Randers type
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 submanifolds in these structures correspond to the integrability of certain secondorder PDE, and my goal is to locally classify all such integrable GL(2,R) structures.
 Keywords:
Exterior • Differential • Geometry • Finsler
 Curriculum Vitae
 Recent Publications
 Rann BarOn, 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]
 Selected Curriculum Innovations
 Secretary for Graduate Calculus Curriculum Review, January 01, 2007  May 30, 2007 [pdf]
 Selected Invited Lectures
 Integrability of 2nd order PDE and GL(2,R) geometry, April, 2009, NC State. AMS special session on geometry of PDE [pdf]
 DEs to EDS: How to "solve" PDEs without being clever., November 30, 2007, Duke
 GL(2,R) structures and integrability, October 22, 2007, UCBerkeley
 Finsler geometry and the technique of moving frames., April 09, 2007, Duke
 Selected Grant Support
 20082009 Graduate School Teaching MiniGrant, Duke University Graduate School.
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