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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.

N.B.:  I am still not fully competent to manage this Scholars@Duke page, and I have not yet had the opportunity to go through and fix the various errors and omissions that were generated in the 'automatic' importation of items from my FDS page (which is much easier to maintain).  In the meantime, please visit my original web page at https://fds.duke.edu/db/aas/math/faculty/bryant  if you can't find something here that you expect to see.

Contact Info:
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 2016):  (typical courses)

  • MATH 323S.01, GEOMETRY Synopsis
    Gross Hall 104, TuTh 03:05 PM-04:20 PM
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)
Curriculum Vitae
Current Ph.D. Students   (Former Students)

Recent Publications   (More Publications)   (search)

  1. Bryant, RL, On the convex Pfaff-Darboux Theorem of Ekeland and Nirenberg (Preprint, December 22, 2015) [arXiv:1512.07100]  [abs]
  2. Bryant, RL, On the conformal volume of 2-tori (Preprint, July 6, 2015) [arXiv:1507.01485]  [abs]
  3. Bryant, RL, S.-S. Chern's study of almost-complex structures on the six-sphere (Preprint, May, 2014) [arXiv:1405.3405]  [abs]
  4. Bryant, RL, Notes on exterior differential systems (Preprint, May, 2014) [arXiv:1405.3116]  [abs] [author's comments]
  5. Bryant, RL; Eastwood, MG; Gover, AR; Neusser, K, Some differential complexes within and beyond parabolic geometry (March, 2012)  [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    
  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

  • Special Holonomy In Geometry, Analysis and Physics, Simons Foundation, 2016/07-2020/06.      
  • The Geometry of Partial Differential Equations, National Science Foundation, DMS-1359583, 2013/09-2015/06.      
  • The Geometry of Partial Differential Equations and Applications, National Science Foundation, DMS-1359583, 2013/07-2015/06.      
Conferences Organized

 

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

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