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
|BS with Honors in the Major||University of Wisconsin||2003|
- Research Interests: Differential Geometry, Geometric PDE, Exterior Differential Systems, Mathematics Education
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.
- Exterior • Differential • Geometry • Finsler
- Curriculum Vitae
- Recent Publications
- 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
- 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, UC--Berkeley
- 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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