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Robert Bryant (mathematician)

Robert Leamon Bryant (born August 30, 1953) is an American mathematician. He works at Duke University and specializes in differential geometry.[2]

Robert L. Bryant
Bryant at MSRI in 2007
Born
Robert Leamon Bryant

(1953-08-30) August 30, 1953 (age 71)
Kipling, North Carolina, U.S.
NationalityAmerican
Alma materNorth Carolina State University at Raleigh
University of North Carolina at Chapel Hill
Known forBryant surface
Bryant soliton
AwardsSloan Research Fellowship, 1982
Scientific career
FieldsMathematics
InstitutionsDuke University
University of California, Berkeley
Rice University
Mathematical Sciences Research Institute
Thesis Some Aspects of the Local and Global Theory of Pfaffian Systems  (1979)
Doctoral advisorRobert Brown Gardner
Doctoral studentsJeanne N. Clelland
Websitefds.duke.edu/db/aas/math/bryant
Robert Bryant, working with R. Kusner, found this parameterization of Boy's surface which minimizes the Willmore energy[1]

Education and career

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Bryant grew up in a farming family in Harnett County and was a first-generation college student.[3] He obtained a bachelor's degree at North Caroline State University at Raleigh in 1974 and a PhD at University of North Carolina at Chapel Hill in 1979. His thesis was entitled "Some Aspects of the Local and Global Theory of Pfaffian Systems" and was written under the supervision of Robert Gardner.[4]

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.

Between 2007 and 2013 he worked as full professor at University of California, Berkeley, where he served as the director of the Mathematical Sciences Research Institute (MSRI).[5] In 2013 he returned to Duke University as Phillip Griffiths Professor of Mathematics.

Bryant was awarded in 1982 a Sloan Research Fellowship.[6] In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley.[7]

He was elected in 2002 a fellow of the American Academy of Arts and Sciences,[8] in 2007 a member of the National Academy of Sciences,[9] in 2013 a fellow of the American Mathematical Society[10] and in 2022 a fellow of the American Association for the Advancement of Science.[11][12] He is also a member of the Association for Women in Mathematics, the National Association of Mathematicians and the Mathematical Association of America.[13]

He served as the president of the American Mathematical Society for the 2-years term 2015–2016,[14][3] for which he was the first openly gay president.[3][15]

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]

Research

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Bryant's research has been influenced by Élie Cartan, Shiing-Shen Chern, and Phillip Griffiths.[3] His research interests cover many areas in Riemannian geometry, geometry of PDEs, Finsler geometry and mathematical physics.[19]

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]

Together with Phillip Griffiths and others co-authors, Bryant developed the modern theory of Exterior Differential Systems, writing two influential monographs, which have become the standard reference in the topic.[25][26] He also worked on their cohomology[27][28] and applications to PDEs.[29][30]

He is author of more than 60 papers,[31][32] and he has supervised 26 PhD students.[4]

Books

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  • A sampler of Riemann-Finsler Geometry, Cambridge University Press 2004 (editor with David Bao, S. S. Chern, Zhongmin Shen)
  • Exterior Differential Systems, MSRI Publ. 18, Springer Verlag 1991, ISBN 0-226-07794-2 (with Robert Brown Gardner, S. S. Chern, H. L. Goldschmidt and Phillip Griffiths)
  • 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]
  • Integral Geometry, Contemporary Mathematics 63, AMS 1987 (editor with Victor Guillemin, Sigurdur Helgason, R. O. Wells)
  • 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.

References

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  1. ^ 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.
  2. ^ "Robert Bryant, Phillip Griffiths Professor of Mathematics and Professor of Computer Science and Chair".
  3. ^ a b c d "AMS Presidents: Robert Bryant" (PDF). American Mathematical Society. Retrieved August 6, 2021.
  4. ^ a b "Robert Bryant – The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved August 6, 2021.
  5. ^ "Biography: Robert Bryant". MSRI. 2008. Archived from the original on September 17, 2009.
  6. ^ "Past Fellows | Alfred P. Sloan Foundation". sloan.org. Archived from the original on March 14, 2018. Retrieved August 6, 2021.
  7. ^ 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.
  8. ^ "Robert L. Bryant". American Academy of Arts & Sciences. Retrieved August 6, 2021.
  9. ^ "Robert L. Bryant". www.nasonline.org. Retrieved August 6, 2021.
  10. ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
  11. ^ "Robert Bryant Named AAAS Fellow". Department of Mathematics. January 27, 2022. Retrieved January 30, 2022.
  12. ^ "Five Duke Faculty Named AAAS Fellows for 2021". today.duke.edu. January 26, 2022. Retrieved January 30, 2022.
  13. ^ "Members | Mathematical Association of America". www.maa.org. Retrieved January 30, 2022.
  14. ^ "Bryant Begins Term as AMS President". American Mathematical Society, Homepage. February 3, 2015.
  15. ^ Adriana Salerno (June 28, 2017). "Love simeq love: A celebration of LGBT+ Mathematicians". Retrieved October 25, 2021.
  16. ^ "Board of Directors". EDGE Foundation. Retrieved August 6, 2021.
  17. ^ "Spectra". Retrieved September 30, 2019.
  18. ^ 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.
  19. ^ "Robert Bryant – Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics". Retrieved January 30, 2022.
  20. ^ Bryant, Robert (1987). "Surfaces of mean curvature one in hyperbolic space". Astérisque. 154–155: 27. Zbl 0635.53047.
  21. ^ 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.
  22. ^ Bryant, Robert L. (1987). "Metrics with Exceptional Holonomy". Annals of Mathematics. 126 (3): 525–576. doi:10.2307/1971360. ISSN 0003-486X. JSTOR 1971360.
  23. ^ 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
  24. ^ Bryant, Robert L. (2000). "Recent Advances in the Theory of Holonomy". Astérisque, Séminaire Bourbaki. 266: 351–374. arXiv:math/9910059.
  25. ^ 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.
  26. ^ 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.
  27. ^ 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.
  28. ^ 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.
  29. ^ 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.
  30. ^ 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.
  31. ^ "MR: Bryant, Robert L. - 42675". mathscinet.ams.org. Retrieved August 6, 2021.
  32. ^ "Publications of Robert L. Bryant". www.msri.org. Retrieved August 6, 2021.
  33. ^ 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.
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