# 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

##### Analysis

##### Computational Mathematics

##### Geometry: Differential & Algebraic

##### Mathematical Physics

##### PDE & Dynamical Systems

##### Topology

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.

### 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)

Bryant, RL. "Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor." Open Access Copy

Bryant, RL. "Some remarks on G_2-structures." Open Access Copy

## 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, RL. "Real hypersurfaces in unimodular complex surfaces." (July 27, 2004). 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. "Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces." (March 5, 2001). Open Access Copy

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

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