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
differential geometry, exterior differential systems, complex geometry
Computational Mathematics
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
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

Bryant, RL. "Minimal surfaces of constant curvature in S^n." Trans. Amer. Math. Soc. 290.1 (1985): 259-271.

Bryant, RL. "Lie groups and twistor spaces." Duke Math. J. 52.1 (1985): 223-261.

Bryant, RL. "A duality theorem for Willmore surfaces." J. Differential Geom. 20.1 (1984): 23-53.

Berger, E, and Griffiths, P. "The Gauss equations and rigidity of isometric embeddings." Duke Math. J. 50.3 (1983): 803-892.

Griffiths, P, and Yang, D. "Characteristics and existence of isometric embeddings." Duke Math. J. 50.4 (1983): 893-994.

Bryant, RL. "Conformal and minimal immersions of compact surfaces into the 4-sphere." J. Differential Geom. 17.3 (1982): 455-473. (Academic Article)

Bryant, RL. "Submanifolds and special structures on the octonians." J. Differential Geom. 17.2 (1982): 185-232.

Bryant, RL. "Holomorphic curves in Lorentzian CR-manifolds." Trans. Amer. Math. Soc. 272.1 (1982): 203-221.

Berger, E, and Griffiths, P. "Some isometric embedding and rigidity results for Riemannian manifolds." Proc. Nat. Acad. Sci. U.S.A. 78.8 (1981): 4657-4660.

Bryant, RL. "Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms." Adv. Stud. Pure Math., 37, Math. Soc. Japan, Tokyo, 2002, 1--44. Open Access Copy