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Robert L Bryant, Professor

Robert L Bryant
Contact Info:
Office Location:  103 Physics
Office Phone:  (919) 660-2800, (919) 660-2817
Email Address: send me a message

Teaching (Spring 2014):  (typical courses)

  • MATH 621.01, DIFFERENTIAL GEOMETRY Synopsis
    Physics 205, TuTh 08:30 AM-09:45 AM
Teaching (Fall 2014):

  • MATH 690-20.01, DIFFERENTIAL GEOMETRY (TOP) Synopsis
    Physics 227, TuTh 08:30 AM-09:45 AM
Office Hours:

By appointment. (No formal office hours for Fall 2013)
Education:

PhDUniversity of North Carolina at Chapel Hill1979
BSNorth Carolina State University at Raleigh1974
Specialties:

Geometry
Mathematical Physics
Research Interests: Nonlinear Partial Differential Equations and Differential Geometry

I'm interested in the geometry of partial differential equations (as always), but, more specifically, I have been thinking about conservation laws for PDE, Finsler geometry, calibrations, holonomy, and trying to learn more about Seiberg-Witten invariants and symplectic geometry.

Areas of Interest:

exterior differential systems
differential geometry
algebraic geometry
Finsler geometry

Keywords:

calibrations • solitons • CR hypersurfaces • exterior differential systems • Finsler

Curriculum Vitae
Current Ph.D. Students   (Former Students)

  • Benjamin McMillan  
Recent Publications   (More Publications)   (search)

  1. with Michael G. Eastwood, A. Rod. Gover, Katharina Neusser, Some differential complexes within and beyond parabolic geometry (Accepted, December, 2011) [arXiv:1112.2142v2]  [abs] [author's comments]
  2. Non-embedding and non-extension results in special holonomy, in The many facets of geometry, edited by Jean-Pierre Bourguignon, Simon Salamon, and Oscar Garcia Prada (Fall, 2010), pp. 346--367, Oxford University Press, Oxford [MR2681703]
  3. with M. Dunajski, M. Eastwood, Metrisability of two-dimensional projective structures, J. Differential Geometry, vol. 83 no. 3 (2009), pp. 465--499, ISSN 0022-040X [MR2581355], [arXiv:0801.0300v1 [math.DG]]  [abs]
  4. Gradient Kähler Ricci Solitons, in Géométrie différentielle, physique mathématique, mathématiques et société. I., Astérisque, vol. 321 (Spring, 2008), pp. 51--97, ISBN 978-285629-258-7 [MR2010i:53138], [math.DG/0407453]  [abs]
  5. with G. Manno, V. Matveev, A solution of a problem of Sophus Lie: Normal forms of 2-dimensional metrics admitting two projective vector fields, Mathematische Annalen, vol. 340 no. 2 (Spring, 2008), pp. 437--463 [3592]  [abs]
Selected Invited Lectures

  1. Parking Cars, Rolling Balls, and Falling Cats: The Concept of Holonomy, May 22, 2013, Simons Foundation in New York City [available here]    
  2. Geometry Old and New: From Euclid to String Theory, November 1, 2012, Humboldt State University, Arcata, CA [1433]    
  3. Applications of Cartan's generalization of Lie's Third Theorem, June 13, 2011, Centre de Rescherches Mathématiques, Montreal, CA [php]    
  4. The idea of Holonomy, October 14, 2010, MAA Carriage House, Washington, DC [the-idea-of-holonomy]    
  5. On the life and work of S.-S. Chern, August 19, 2010, ICM in Hyderabad, India [player.php]    
Recent Grant Support

  • The Geometry of Partial Differential Equations, National Science Foundation, DMS-1359583, 2013/09-2014/06.      
Conferences Organized

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320