File:BoysSurfaceTopView.PNG of Boy's surface which minimizes the Willmore energy{{Cite journal|last=Kusner|first=Rob|date=1987|title=Conformal geometry and complete minimal surfaces|url=https://www.ams.org/bull/1987-17-02/S0273-0979-1987-15564-9/|journal=Bulletin of the American Mathematical Society|language=en|volume=17|issue=2|pages=291–295|doi=10.1090/S0273-0979-1987-15564-9|issn=0273-0979|doi-access=free}}]]

Robert Leamon Bryant (born August 30, 1953) is an American mathematician. He works at Duke University and specializes in differential geometry.{{Cite web|title=Robert Bryant, Phillip Griffiths Professor of Mathematics and Professor of Computer Science and Chair|url=http://fds.duke.edu/db/aas/math/faculty/bryant}}

Education and career

Bryant grew up in a farming family in Harnett County and was a first-generation college student. 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.{{Cite web|title=Robert Bryant – The Mathematics Genealogy Project|url=https://www.mathgenealogy.org/id.php?id=22429|access-date=2021-08-06|website=www.mathgenealogy.org}}

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).{{cite web|year=2008|title=Biography: Robert Bryant|url=http://www.msri.org/about/governance/trustees/TrusteesInfo/200000251/show_trustees|archive-url=https://web.archive.org/web/20090917003521/http://www.msri.org/about/governance/trustees/TrusteesInfo/200000251/show_trustees|archive-date=September 17, 2009|publisher=MSRI|df=mdy-all}} In 2013 he returned to Duke University as Phillip Griffiths Professor of Mathematics.

Bryant was awarded in 1982 a Sloan Research Fellowship.{{Cite web|title=Past Fellows {{!}} Alfred P. Sloan Foundation|url=https://sloan.org/past-fellows|access-date=2021-08-06|website=sloan.org|language=en|archive-date=March 14, 2018|archive-url=https://web.archive.org/web/20180314000756/https://sloan.org/past-fellows}} In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley.{{Cite conference |url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1986.1/ICM1986.1.ocr.pdf |author=Robert L. Bryant |title=A Survey of Riemannian Metrics with Special Holonomy Groups |book-title=Proceedings of the International Congress of Mathematicians 1986 |date=1987 |editor-last=Gleason|editor-first=Andrew|location=Berkley |publisher=American Mathematical Society |isbn=|page=505}}

He was elected in 2002 a fellow of the American Academy of Arts and Sciences,{{Cite web|title=Robert L. Bryant|url=https://www.amacad.org/person/robert-l-bryant|access-date=2021-08-06|website=American Academy of Arts & Sciences|language=en}} in 2007 a member of the National Academy of Sciences,{{Cite web|title=Robert L. Bryant|url=http://www.nasonline.org/member-directory/members/61518.html|access-date=2021-08-06|website=www.nasonline.org}} in 2013 a fellow of the American Mathematical Society[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10. and in 2022 a fellow of the American Association for the Advancement of Science.{{Cite web|title=Robert Bryant Named AAAS Fellow|url=https://math.duke.edu/news/robert-bryant-named-aaas-fellow|access-date=2022-01-30|website=Department of Mathematics|date=January 27, 2022 |language=en}}{{Cite web|title=Five Duke Faculty Named AAAS Fellows for 2021|url=https://today.duke.edu/2022/01/five-duke-faculty-named-aaas-fellows-2021|access-date=2022-01-30|website=today.duke.edu|date=January 26, 2022 |language=en}} He is also a member of the Association for Women in Mathematics, the National Association of Mathematicians and the Mathematical Association of America.{{Cite web|title=Members {{!}} Mathematical Association of America|url=https://www.maa.org/programs/faculty-and-departments/common-vision/members|access-date=2022-01-30|website=www.maa.org}}

He served as the president of the American Mathematical Society for the 2-years term 2015–2016,{{cite web|date=February 3, 2015|title=Bryant Begins Term as AMS President|url=https://www.ams.org/news?news_id=2558|website=American Mathematical Society, Homepage}} for which he was the first openly gay president.{{Cite web|title=AMS Presidents: Robert Bryant|url=https://www.ams.org/journals/notices/201606/rnoti-p614.pdf|access-date=2021-08-06|website=American Mathematical Society|language=en}}{{Cite web|title=Love simeq love: A celebration of LGBT+ Mathematicians|url=https://blogs.ams.org/inclusionexclusion/2017/06/28/love-simeq-love-a-celebration-of-lgbt-mathematicians/|access-date=2021-10-25|author=Adriana Salerno|author-link=Adriana Salerno|date=June 28, 2017|language=en}}

Bryant is on the board of directors of EDGE, a transition program for women entering graduate studies in the mathematical sciences.{{Cite web|last=|title=Board of Directors|url=https://www.edgeforwomen.org/support-edge/the-edge-foundation/|access-date=2021-08-06|website=EDGE Foundation|language=en-US}} He is also a board member of Spectra, an association for LGBT mathematicians that he helped to create.{{cite web |title=Spectra |url=http://lgbtmath.org/People.html |access-date=30 September 2019}}{{cite news |author=Robert Bryant |author2=Ron Buckmire |author3=Lily Khadjavi |author4=Douglas Lind |date=June–July 2019 |title=The Origins of Spectra, an Organization for LGBT Mathematicians |journal=Notices of the American Mathematical Society |volume=66 |issue=6 |pages=678–685| url=http://www.lgbtmath.org/NoticesArticle/Article.pdf |via=LGBT Math}}

Research

Bryant's research has been influenced by Élie Cartan, Shiing-Shen Chern, and Phillip Griffiths. His research interests cover many areas in Riemannian geometry, geometry of PDEs, Finsler geometry and mathematical physics.{{Cite web|title=Robert Bryant – Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics|url=https://sites.duke.edu/scshgap/robert-bryant/|access-date=2022-01-30|language=en-US}}

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.{{Cite journal|last=Bryant|first=Robert|date=1987|title=Surfaces of mean curvature one in hyperbolic space|url=http://www.numdam.org/item/?id=AST_1987__154-155__321_0|journal=Astérisque|volume=154–155|page=27|zbl=0635.53047}} In 2001 he contributed many advancements to the theory of Bochner-Kähler metrics, the class of Kähler metrics whose Bochner curvature vanishes.{{Cite journal|last=Bryant|first=Robert|date=2001|title=Bochner-Kähler Metrics|journal=Journal of the American Mathematical Society|volume=14|issue=3|pages=623–715|doi=10.1090/S0894-0347-01-00366-6|jstor=827103|arxiv=math/0003099|s2cid=119625517}}

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.{{Cite journal|last=Bryant|first=Robert L.|date=1987|title=Metrics with Exceptional Holonomy|journal=Annals of Mathematics|volume=126|issue=3|pages=525–576|doi=10.2307/1971360|jstor=1971360|issn=0003-486X}} Later, he also contributed to the classification of exotic holonomy groups of arbitrary (i.e. non-Riemannian) torsion-free affine connections.{{Citation|last=Bryant|first=Robert L.|title=Complex Geometry and Lie Theory|chapter=Two exotic holonomies in dimension four, path geometries, and twistor theory|date=1991|chapter-url=http://www.ams.org/pspum/053|series=Proceedings of Symposia in Pure Mathematics|volume=53|pages=33–88|editor-last=|editor-first=|place=Providence, Rhode Island|publisher=American Mathematical Society|language=en|doi=10.1090/pspum/053/1141197|isbn=978-0-8218-1492-5|access-date=2021-08-08|editor2-last=|editor2-first=|editor3-last=|editor3-first=|doi-access=free}}{{Cite journal|last=Bryant|first=Robert L.|date=2000|title=Recent Advances in the Theory of Holonomy|journal=Astérisque, Séminaire Bourbaki|volume=266|pages=351–374|arxiv=math/9910059}}

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.{{Cite book|last1=Bryant|first1=Robert L.|url=http://link.springer.com/10.1007/978-1-4613-9714-4|title=Exterior Differential Systems|last2=Chern|first2=S. S.|last3=Gardner|first3=Robert B.|last4=Goldschmidt|first4=Hubert L.|last5=Griffiths|first5=P. A.|date=1991|publisher=Springer New York|isbn=978-1-4613-9716-8|series=Mathematical Sciences Research Institute Publications|volume=18|location=New York, NY|doi=10.1007/978-1-4613-9714-4}}{{Cite book|last=Bryant|first=Robert L.|title=Exterior differential systems and Euler-Lagrange partial differential equations|date=2003|publisher=University of Chicago Press|others=Phillip Griffiths, Daniel Andrew Grossman|isbn=0-226-07793-4|location=Chicago|oclc=51804819}} He also worked on their cohomology{{Cite journal|last1=Bryant|first1=Robert L.|last2=Griffiths|first2=Phillip A.|date=1995|title=Characteristic Cohomology of Differential Systems (I): General Theory|journal=Journal of the American Mathematical Society|volume=8|issue=3|pages=507–596|doi=10.2307/2152923|jstor=2152923|issn=0894-0347}}{{Cite journal|last1=Bryant|first1=Robert L.|last2=Griffiths|first2=Phillip A.|date=1995-06-01|title=Characteristic cohomology of differential systems II: Conservation laws for a class of parabolic equations|url=https://projecteuclid.org/journals/duke-mathematical-journal/volume-78/issue-3/Characteristic-cohomology-of-differential-systems-II--Conservation-laws-for/10.1215/S0012-7094-95-07824-7.full|journal=Duke Mathematical Journal|volume=78|issue=3|doi=10.1215/S0012-7094-95-07824-7|issn=0012-7094}} and applications to PDEs.{{Cite journal|last1=Bryant|first1=Robert|last2=Griffiths|first2=Phillip|last3=Hsu|first3=Lucas|date=1995-03-01|title=Hyperbolic exterior differential systems and their conservation laws, part I|journal=Selecta Mathematica|language=en|volume=1|issue=1|pages=21–112|doi=10.1007/BF01614073|s2cid=195271133|issn=1420-9020}}{{Cite journal|last1=Bryant|first1=R.|last2=Griffiths|first2=P.|last3=Hsu|first3=L.|date=1995-09-01|title=Hyperbolic exterior differential systems and their conservation laws, part II|journal=Selecta Mathematica|language=en|volume=1|issue=2|pages=265–323|doi=10.1007/BF01671567|s2cid=15812302|issn=1420-9020}}

He is author of more than 60 papers,{{Cite web|title=MR: Bryant, Robert L. - 42675|url=https://mathscinet.ams.org/mathscinet/MRAuthorID/42675|access-date=2021-08-06|website=mathscinet.ams.org}}{{Cite web|title=Publications of Robert L. Bryant|url=https://www.msri.org/people/staff/bryant/RLBpubs.html|access-date=2021-08-06|website=www.msri.org}} and he has supervised 26 PhD students.

Books

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){{cite journal |author=Olver, Peter J. |author-link=Peter J. Olver |title=Review: Exterior differential systems and Euler-Lagrange partial differential equations, by R. L. Bryant, P. A Griffiths, and D. A. Grossman |journal=Bull. Amer. Math. Soc. (N.S.) |year=2005 |volume=42 |issue=3 |pages=407–412 |url=https://www.ams.org/journals/bull/2005-42-03/S0273-0979-05-01062-1/S0273-0979-05-01062-1.pdf |doi=10.1090/s0273-0979-05-01062-1|doi-access=free }}
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)