Robert Bryant

  • Philip Griffiths Professor of Mathematics
  • Professor in the Department of Mathematics
External address: 103 Physics Bldg, West Campus, Durham, NC 27708
Internal office address: Box 90320, Durham, NC 27708-0320
Phone: (919) 660-2817
Office Hours: 

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

Research Areas and Keywords

Algebra & Combinatorics
integrability, symplectic geometry
Analysis
differential geometry, exterior differential systems, complex geometry
Computational Mathematics
integrability
Geometry: Differential & Algebraic
differential geometry, holonomy, exterior differential systems, integrability, curvature, Lie groups, symplectic geometry, complex geometry, homology
Mathematical Physics
holonomy, exterior differential systems, symplectic geometry
PDE & Dynamical Systems
differential geometry, holonomy, exterior differential systems, integrability, symplectic geometry
Topology
curvature, Lie groups, homology

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.

Education & Training
  • Ph.D., University of North Carolina at Chapel Hill 1979

  • B.A., North Carolina State University 1974

Selected Grants

(90-0718) Mathematical Sciences: Differential Geometry awarded by National Science Foundation (Principal Investigator). 1989 to 1992

(89-0300) Differential Geometry awarded by National Science Foundation (Principal Investigator). 1989 to 1990

Pages

Bryant, R. "Metrics with holonomy G2 or Spin(7)." Workshop Bonn 1984 (Bonn, 1984). Ed. F Hirzebruch, J Schwermer, and S Suter. Berlin, Germany: Springer, 1985. 269-277. (Chapter)

Bryant, R, and Griffiths, PA. "Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle." Arithmetic and geometry, Vol. II. Ed. M Artin and J Tate. Boston, MA: Birkhäuser Boston, 1983. 77-102. (Chapter)

Bryant, R, Chern, SS, and Griffiths, PA. "Exterior Differential Systems." Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations (Beijing, 1980). Ed. SS Chern and WT Wu. Beijing, PRC; New York, NY: Science Press; Gordon & Breach Science Publishers, 1982. 219-338. (Chapter)

Pages

Bryant, RL. "On the geometry of almost complex 6-manifolds." The Asian Journal of Mathematics 10.3 (September 2006): 561-606.

BRYANT, RL. "Conformal geometry and 3-plane fields on 6-manifolds." RIMS Kokyuroku 1502 (Developments of Cartan Geometry and Related Mathematical Problems) (July 2006): 1-15. Open Access Copy

Bryant, R, and Freed, D. "Shiing-Shen Chern - Obituary." PHYSICS TODAY 59.1 (January 2006): 70-72. Full Text

Bryant, RL. "SO(n)-invariant special Lagrangian submanifolds of C^{n+1} with fixed loci." Chinese Annals of Mathematics, Series B 27.1 (January 2006): 95-112. Open Access Copy

Bryant, R, Edelsbrunner, H, Koehl, P, and Levitt, M. "The area derivative of a space-filling diagram." Discrete and Computanional Geometry 32.3 (2004): 293-308. Full Text

Bryant, RL. "Some remarks on Finsler manifolds with constant flag curvature." Houston Journal of Mathematics 28.2 (2002): 221-262. (Academic Article) Open Access Copy

Bryant, RL. "Bochner-Kähler metrics." Journal of the AMS 14.3 (2001): 623-715. Open Access Copy

Bryant, RL. "Harmonic morphisms with fibers of dimension one." Communications in Analysis and Geometry 8.2 (2000): 219-265. (Academic Article) Open Access Copy

Pages

Pages