Robert Bryant, Philip Griffiths Professor of Mathematics and Professor of Computer Science

Robert Bryant

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.

Most recently, I have been named as the Director of the Simons Collaboration "Special Holonomy in Geometry, Analysis, and Physics", and so most of my research lately and in the near future will be directed towards problems in this area.

Office Location:  103 Physics
Office Phone:  (919) 660-2800, (919) 660-2817
Email Address: send me a message
Web Pages:  https://fds.duke.edu/db/aas/math/faculty/bryant
http://math.duke.edu/people/robert-bryant

Teaching (Fall 2017):  (typical courses)

Teaching (Spring 2018):

Office Hours:

Tuesdays and Thursdays, 10:30-12:00PM, and by appointment
Education:

Ph.D.University of North Carolina at Chapel Hill1979
BSNorth Carolina State University at Raleigh1974
B.A.North Carolina State University1974
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:

Almost complex manifolds • calibrations • CR hypersurfaces • exterior differential systems • Finsler • Geometry, Differential • Global differential geometry • solitons

Duties:

Currently serving as President of the American Mathematical Society (2015-2017)
Current Ph.D. Students  

Recent Publications   (search)

  1. Bryant, RL; Huang, L; Mo, X, On Finsler surfaces of constant flag curvature with a Killing field, Journal of Geometry and Physics, vol. 116 (June, 2017), pp. 345-357 [doi]
  2. Bryant, RL, On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg (Preprint, December 22, 2015) [arXiv:1512.07100]  [abs]
  3. Bryant, RL, On the conformal volume of 2-tori (Preprint, July 6, 2015) [arXiv:1507.01485]  [abs]
  4. Bryant, RL, S.-S. Chern's study of almost-complex structures on the six-sphere (Preprint, May, 2014) [arXiv:1405.3405]  [abs]
  5. Bryant, RL, Notes on exterior differential systems (Preprint, May, 2014) [arXiv:1405.3116]  [abs] [author's comments]
Selected Invited Lectures

  1. Parking Cars, Rolling Balls, and Falling Cats: The Concept of Holonomy, May 22, 2013, Simons Foundation in New York City    
  2. Geometry Old and New: From Euclid to String Theory, November 1, 2012, Humboldt State University, Arcata, CA [title.]    
  3. Applications of Cartan's generalization of Lie's Third Theorem, June 13, 2011, Centre de Rescherches Mathématiques, Montreal, CA [various]    
  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 [Ch]    
Recent Grant Support

Conferences Organized