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

Bryant, RL. "Recent advances in the theory of holonomy." Asterisque 266.5 (2000): 351-374. Open Access Copy

Bryant, RL. "Calibrated Embeddings in the Special Lagrangian and Coassociative Cases." Annals of Global Analysis and Geometry 18.3-4 (2000): 405-435. Open Access Copy

Bryant, R. "Élie Cartan and geometric duality." Journées Élie Cartan 1998 et 1999 16 (2000): 5-20. Open Access Copy

Sharpe, E, and Bryant, RL. "D-branes and Spin^c-structures." Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 450.4 (1999): 353-357. Open Access Copy

Bryant, RL. "Some examples of special Lagrangian tori." Adv. Theor. Math. Phys. 3.1 (1999): 83-90. Open Access Copy

Bryant, RL. "Projectively flat Finsler 2-spheres of constant curvature." Selecta Math. (N.S.) 3.2 (1997): 161-203. Open Access Copy

Bryant, RL, and Griffiths, PA. "Characteristic cohomology of differential systems. I. General theory." Journal of the American Mathematical Society 8.3 (September 1, 1995): 507-507. Full Text

Bryant, RL, and Griffiths, PA. "Characteristic cohomology of differential systems, II: Conservation laws for a class of parabolic equations." Duke Math. Journal 78.3 (1995): 531-676.

Griffiths, PA, Hsu, L, and Bryant, RL. "Hyperbolic exterior differential systems and their conservation laws, Part I." Selecta Math. (N.S.) 1.1 (1995): 21-112.