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:	919-660-2811
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 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

Curriculum Vitae

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]

Selected Curriculum Innovations

1. Secretary for Graduate Calculus Curriculum Review, January 01, 2007 - May 30, 2007 [pdf]    

Selected Invited Lectures

1. Integrability of 2nd order PDE and GL(2,R) geometry, April, 2009, NC State. AMS special session on geometry of PDE [pdf]    
2. DEs to EDS: How to "solve" PDEs without being clever., November 30, 2007, Duke    
3. GL(2,R) structures and integrability, October 22, 2007, UC--Berkeley    
4. Finsler geometry and the technique of moving frames., April 09, 2007, Duke    

Selected Grant Support

• 2008-2009 Graduate School Teaching Mini-Grant, Duke University Graduate School.      

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