He worked at Rice University for seven years, as assistant professor (1979–1981), associate professor (1981–1982) and full professor (1982–1986). He then moved to Duke University, where he worked for twenty years as J. M. Kreps Professor.
Bryant is on the board of directors of EDGE, a transition program for women entering graduate studies in the mathematical sciences.[16] He is also a board member of Spectra, an association for LGBT mathematicians that he helped to create.[17][18]
In 1987 he proved several properties of surfaces of unit constant mean curvature in hyperbolic space, which are now called Bryant surfaces in his honour.[20] In 2001 he contributed many advancements to the theory of Bochner-Kähler metrics, the class of Kähler metrics whose Bochner curvature vanishes.[21]
In 1987 he produced the first examples of Riemannian metrics with exceptional holonomy (i.e. whose holonomy groups are G2 or Spin(7)); this showed that every group in Marcel Berger's classification can arise as a holonomy group.[22] Later, he also contributed to the classification of exotic holonomy groups of arbitrary (i.e. non-Riemannian) torsion-free affine connections.[23][24]
Exterior Differential Systems and Euler-Lagrange Partial Differential Equations, Chicago Lectures in Mathematics, University of Chicago Press 2003, ISBN 0-226-07793-4 (with Phillip Griffiths and Dan Grossman)[33]
An introduction to Lie groups and symplectic geometry, in Geometry and quantum field theory, IAS/Park City Math. Series 1, American Mathematical Society 1995, pp. 5–181
Toward a Geometry of Differential Equations, in: Geometry, Topology & Physics, Conf. Proc. Lecture Notes Geom. Topology, VI, International Press, Cambridge, MA, 1995, pp. 1–76 (with Lucas Hsu and Phillip Griffiths)
Bryant and David Morrison are the editors of vol. 4 of the Selected Works of Phillip Griffiths.
Referencesedit
^Kusner, Rob (1987). "Conformal geometry and complete minimal surfaces". Bulletin of the American Mathematical Society. 17 (2): 291–295. doi:10.1090/S0273-0979-1987-15564-9. ISSN 0273-0979.
^"Robert Bryant, Phillip Griffiths Professor of Mathematics and Professor of Computer Science and Chair".
^ abcd"AMS Presidents: Robert Bryant" (PDF). American Mathematical Society. Retrieved August 6, 2021.
^ ab"Robert Bryant – The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved August 6, 2021.
^"Biography: Robert Bryant". MSRI. 2008. Archived from the original on September 17, 2009.
^"Past Fellows | Alfred P. Sloan Foundation". sloan.org. Archived from the original on March 14, 2018. Retrieved August 6, 2021.
^Robert L. Bryant (1987). "A Survey of Riemannian Metrics with Special Holonomy Groups" (PDF). In Gleason, Andrew (ed.). Proceedings of the International Congress of Mathematicians 1986. Berkley: American Mathematical Society. p. 505.
^"Robert L. Bryant". American Academy of Arts & Sciences. Retrieved August 6, 2021.
^"Robert L. Bryant". www.nasonline.org. Retrieved August 6, 2021.
^List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
^"Robert Bryant Named AAAS Fellow". Department of Mathematics. Retrieved January 30, 2022.
^"Five Duke Faculty Named AAAS Fellows for 2021". today.duke.edu. Retrieved January 30, 2022.
^"Members | Mathematical Association of America". www.maa.org. Retrieved January 30, 2022.
^"Bryant Begins Term as AMS President". American Mathematical Society, Homepage. February 3, 2015.
^Adriana Salerno (June 28, 2017). "Love simeq love: A celebration of LGBT+ Mathematicians". Retrieved October 25, 2021.
^"Board of Directors". EDGE Foundation. Retrieved August 6, 2021.
^Robert Bryant; Ron Buckmire; Lily Khadjavi; Douglas Lind (June–July 2019). "The Origins of Spectra, an Organization for LGBT Mathematicians" (PDF). Notices of the American Mathematical Society. Vol. 66, no. 6. pp. 678–685 – via LGBT Math.
^"Robert Bryant – Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics". Retrieved January 30, 2022.
^Bryant, Robert (1987). "Surfaces of mean curvature one in hyperbolic space". Astérisque. 154–155: 27. Zbl 0635.53047.
^Bryant, Robert (2001). "Bochner-Kähler Metrics". Journal of the American Mathematical Society. 14 (3): 623–715. arXiv:math/0003099. doi:10.1090/S0894-0347-01-00366-6. JSTOR 827103. S2CID 119625517.
^Bryant, Robert L. (1987). "Metrics with Exceptional Holonomy". Annals of Mathematics. 126 (3): 525–576. doi:10.2307/1971360. ISSN 0003-486X. JSTOR 1971360.
^Bryant, Robert L. (1991), "Two exotic holonomies in dimension four, path geometries, and twistor theory", Complex Geometry and Lie Theory, Proceedings of Symposia in Pure Mathematics, vol. 53, Providence, Rhode Island: American Mathematical Society, pp. 33–88, doi:10.1090/pspum/053/1141197, ISBN 978-0-8218-1492-5, retrieved August 8, 2021
^Bryant, Robert L. (2000). "Recent Advances in the Theory of Holonomy". Astérisque, Séminaire Bourbaki. 266: 351–374. arXiv:math/9910059.
^Bryant, Robert L.; Chern, S. S.; Gardner, Robert B.; Goldschmidt, Hubert L.; Griffiths, P. A. (1991). Exterior Differential Systems. Mathematical Sciences Research Institute Publications. Vol. 18. New York, NY: Springer New York. doi:10.1007/978-1-4613-9714-4. ISBN 978-1-4613-9716-8.
^Bryant, Robert L. (2003). Exterior differential systems and Euler-Lagrange partial differential equations. Phillip Griffiths, Daniel Andrew Grossman. Chicago: University of Chicago Press. ISBN 0-226-07793-4. OCLC 51804819.
^Bryant, Robert L.; Griffiths, Phillip A. (1995). "Characteristic Cohomology of Differential Systems (I): General Theory". Journal of the American Mathematical Society. 8 (3): 507–596. doi:10.2307/2152923. ISSN 0894-0347. JSTOR 2152923.
^Bryant, Robert L.; Griffiths, Phillip A. (June 1, 1995). "Characteristic cohomology of differential systems II: Conservation laws for a class of parabolic equations". Duke Mathematical Journal. 78 (3). doi:10.1215/S0012-7094-95-07824-7. ISSN 0012-7094.
^Bryant, Robert; Griffiths, Phillip; Hsu, Lucas (March 1, 1995). "Hyperbolic exterior differential systems and their conservation laws, part I". Selecta Mathematica. 1 (1): 21–112. doi:10.1007/BF01614073. ISSN 1420-9020. S2CID 195271133.
^Bryant, R.; Griffiths, P.; Hsu, L. (September 1, 1995). "Hyperbolic exterior differential systems and their conservation laws, part II". Selecta Mathematica. 1 (2): 265–323. doi:10.1007/BF01671567. ISSN 1420-9020. S2CID 15812302.
^"MR: Bryant, Robert L. - 42675". mathscinet.ams.org. Retrieved August 6, 2021.
^"Publications of Robert L. Bryant". www.msri.org. Retrieved August 6, 2021.
^Olver, Peter J. (2005). "Review: Exterior differential systems and Euler-Lagrange partial differential equations, by R. L. Bryant, P. A Griffiths, and D. A. Grossman" (PDF). Bull. Amer. Math. Soc. (N.S.). 42 (3): 407–412. doi:10.1090/s0273-0979-05-01062-1.