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Robert L Bryant, Phillip Griffiths Professor of Mathematics

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

Typical Courses Taught:

  • MATH 123S, GEOMETRY Synopsis
  • MATH 267, DIFFERENTIAL GEOMETRY
  • MATH 268, Topics in DIFFERENTIAL GEOMETRY: Symplectic Geometry Synopsis
    The first third of the course is devoted to 'classical' symplectic geometry: Lagrangians, Legendre transformations, Hamiltonians, symplectic manifolds and the Darboux-Weinstein theorem, symmetries and conservation laws and the Arnold- Liouville theorem, momentum mappings, reduction, and convexity. The second third of the course is devoted to developing elliptic methods: pseudo-holomorphic curves, Gromov compactness and moduli, applications to packing and (non)-squeezing theorems, etc. The final third covers related topics and recent developments, such as relations with toric varieties, representation theory, or other topics that depend on the interests of the class.
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. R.L. Bryant, Notes on Exterior Differential Systems (Preprint, May, 2014) [arXiv:1405.3116]  [abs] [author's comments]
  2. R.L. Bryant, S.-s. Chern's study of almost-complex structures on the six-sphere (Preprint, May, 2014) [arXiv:1405.3405]  [abs]
  3. 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]
  4. R.L. Bryant and Feng Xu, Laplacian flow for closed G2-structures: short time behavior (Preprint, January, 2011) [arXiv:1101.2004]  [abs]
  5. 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]
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