Math @ Duke

Robert L Bryant, Phillip Griffiths Professor of Mathematics
 Contact Info:
Office Location:  103 Physics  Office Phone:  (919) 6602800, (919) 6602817  Email Address:   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 DarbouxWeinstein 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: pseudoholomorphic
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:
PhD  University of North Carolina at Chapel Hill  1979 
BS  North Carolina State University at Raleigh  1974 
 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 SeibergWitten 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)
 Recent Publications
(More Publications)
(search)
 R.L. Bryant, Notes on Exterior Differential Systems
(Preprint, May, 2014) [arXiv:1405.3116] [abs] [author's comments]
 R.L. Bryant, S.s. Chern's study of almostcomplex structures on the sixsphere
(Preprint, May, 2014) [arXiv:1405.3405] [abs]
 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]
 R.L. Bryant and Feng Xu, Laplacian flow for closed G_{2}structures: short time behavior
(Preprint, January, 2011) [arXiv:1101.2004] [abs]
 Nonembedding and nonextension results in special holonomy,
in The many facets of geometry, edited by JeanPierre Bourguignon, Simon Salamon, and Oscar Garcia Prada
(Fall, 2010),
pp. 346367, Oxford University Press, Oxford [MR2681703]
 Selected Invited Lectures
 Parking Cars, Rolling Balls, and Falling Cats: The Concept of Holonomy, May 22, 2013, Simons Foundation in New York City [available here]
 Geometry Old and New: From Euclid to String Theory, November 1, 2012, Humboldt State University, Arcata, CA [1433]
 Applications of Cartan's generalization of Lie's Third Theorem, June 13, 2011, Centre de Rescherches MathÃ©matiques, Montreal, CA [php]
 The idea of Holonomy, October 14, 2010, MAA Carriage House, Washington, DC [theideaofholonomy]
 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, DMS1359583, 2013/092014/06.
 Conferences Organized
 Annual East Coast Geometry Festival, Member of Organizing Board, 1 January 1990
 Bay Area Differential Geometry Seminar, Member, Organizing Committee, 2008  2013
 Chern Centennial Conference, CoOrganizer, October 24, 2011  November 04, 2011
 AIM Workshop on Calibrations, Conference Organizer, June 26, 2006  June 30, 2006
 Singularities in Analysis, Geometry, and Topology: A Conference Honoring the Retirements of F. Reese Harvey and John Polking, Scientific Advisor on Organizing Committee, November 11, 2005  November 13, 2005
 International Symposium on Finsler Geometry, Member of organizing committee, August 10, 2004  August 14, 2004
 Oberwolfach BiAnnual Differential Geometry in the Large, coOrganizer, June 15, 2001  May 31, 2004
 MSRI YearLong Program in Geometry (20032004), coOrganizer, 200104


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

