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{{short description|American mathematician}}
{{Short description|American mathematician (born 1953)}}
{{Use mdy dates|date=May 2015}}
{{Use mdy dates|date=May 2015}}
{{Infobox scientist
{{Infobox scientist
| name = Robert L. Bryant
| name = Robert L. Bryant
| image = Robert Bryant.jpg
| image = Robert Bryant.jpg
| caption = Bryant at [[Mathematical Research Institute of Oberwolfach|Oberwolfach]] in 2007
| caption = Bryant at [[Simons Laufer Mathematical Sciences Institute|MSRI]] in 2007
| birth_name = Robert Leamon Bryant
| birth_name = Robert Leamon Bryant
| birth_date = {{birth date and age|1953|08|30}}
| birth_date = {{birth date and age|1953|08|30}}
| birth_place = [[Kipling, North Carolina]], U.S.
| birth_place = [[Kipling, North Carolina]], U.S.
| nationality = [[United States|American]]
| nationality = [[United States|American]]
| alma_mater = [[North Carolina State University at Raleigh]]<br />[[University of North Carolina at Chapel Hill]]
| alma_mater = [[North Carolina State University at Raleigh]]<br />[[University of North Carolina at Chapel Hill]]
| doctoral_advisor = [[Robert Brown Gardner]]
⚫
| field = Mathematics
| doctoral_advisor = [[Robert Brown Gardner]]
| doctoral_students = [[Jeanne N. Clelland]]
| known_for = [[Bryant surface]]<br />[[Ricci flow#Ricci soliton|Bryant soliton]]
| thesis_title = Some Aspects of the Local and Global Theory of Pfaffian Systems
| thesis_title = Some Aspects of the Local and Global Theory of Pfaffian Systems
| thesis_year = 1979
| thesis_year = 1979
⚫
| workplaces = [[Duke University]]<br />[[University of California at Berkeley]]<br />[[Rice University]]<br />[[Mathematical Sciences Research Institute]]
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| fields = [[Mathematics]]
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| website = {{URL|http://fds.duke.edu/db/aas/math/bryant}}
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| workplaces = [[Duke University]]<br />[[University of California, Berkeley]]<br />[[Rice University]]<br />[[Mathematical Sciences Research Institute]]
| awards = [[Sloan Research Fellowship]], 1982
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| website = {{URL|http://fds.duke.edu/db/aas/math/bryant}}
}}
}}
[[File:BoysSurfaceTopView.PNG|thumb|Robert Bryant, working with R. Kusner, found this [[parameterization]] of [[Boy's surface]] which minimizes the [[Willmore energy]]]]
[[File:BoysSurfaceTopView.PNG|thumb|Robert Bryant, working with R. Kusner, found this [[parameterization]] of [[Boy's surface]] which minimizes the [[Willmore energy]]<ref>{{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}}</ref>]]


'''Robert Leamon Bryant''' (born August 30, 1953, [[Kipling, North Carolina|Kipling]]) is an American [[mathematician]] and Phillip Griffiths Professor of Mathematics at [[Duke University]].<ref name="homepage">http://fds.duke.edu/db/aas/math/faculty/bryant</ref> He specializes in [[differential geometry]].
'''Robert Leamon Bryant''' (born August 30, 1953) is an American mathematician. He works at [[Duke University]] and specializes in [[differential geometry]].<ref name="homepage">{{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}}</ref>


==Education and career==
==Education and career==
Bryant obtained a bachelor's degree at [[North Carolina State University at Raleigh|North Caroline State University at Raleigh]] in 1974 and a PhD at [[University of North Carolina at Chapel Hill]]. His thesis was entitled "''Some Aspects of the Local and Global Theory of Pfaffian Systems''" and was written under the supervision of [[Robert Brown Gardner|Robert Gardner]].<ref name=":0">{{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}}</ref>
Bryant grew up in a farming family in [[Harnett County, North Carolina|Harnett County]] and was a [[First-generation college students in the United States|first-generation college student]].<ref name=":1" /> He obtained a bachelor's degree at [[North Carolina State University at Raleigh|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 Brown Gardner|Robert Gardner]].<ref name=":0">{{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}}</ref>


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. Since 2007 he is professor at [[University of California, Berkeley|University of California at Berkeley]].
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).<ref>{{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}}</ref> In 2013 he returned to Duke University as Phillip Griffiths Professor of Mathematics.
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Bryant was awarded in 1982 a [[Sloan Research Fellowship|Sloan Research Fellowship.]]<ref>{{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}}</ref> In 1986 he was [[List of International Congresses of Mathematicians Plenary and Invited Speakers#1986, Berkeley|invited speaker]] at the [[International Congress of Mathematicians]] in Berkeley.<ref>{{Cite book|url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1986.1/ICM1986.1.ocr.pdf|title=Proceedings of the International Congress of Mathematician 1986|year=1987|editor-last=Gleason|editor-first=Andrew|location=Berkley|pages=505}}</ref>


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Bryant was awarded in 1982 a [[Sloan Research Fellowship]].<ref>{{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}}</ref> In 1986 he was [[List of International Congresses of Mathematicians Plenary and Invited Speakers#1986, Berkeley|invited speaker]] at the [[International Congress of Mathematicians]] in Berkeley.<ref>{{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}}</ref>
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He was elected in 2002 a fellow of the [[American Academy of Arts and Sciences]]<ref>{{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}}</ref>, in 2007 a member of the [[National Academy of Sciences]]<ref>{{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}}</ref> and in 2013 a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref>


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He was elected in 2002 a fellow of the [[American Academy of Arts and Sciences]],<ref>{{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}}</ref> in 2007 a member of the [[National Academy of Sciences]],<ref>{{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}}</ref> in 2013 a fellow of the [[American Mathematical Society]]<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref> and in 2022 a fellow of the [[American Association for the Advancement of Science]].<ref>{{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}}</ref><ref>{{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}}</ref> He is also a member of the [[Association for Women in Mathematics]], the [[National Association of Mathematicians]] and the [[Mathematical Association of America]].<ref>{{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}}</ref>
Bryant served as the director of the [[Mathematical Sciences Research Institute]] (MSRI) from 2007 to 2013<ref>{{cite web |url=http://www.msri.org/about/governance/trustees/TrusteesInfo/200000251/show_trustees |title=Biography: Robert Bryant |publisher=MSRI |year=2008 |url-status=dead |archive-url=https://web.archive.org/web/20090917003521/http://www.msri.org/about/governance/trustees/TrusteesInfo/200000251/show_trustees |archive-date=September 17, 2009 |df=mdy-all }}</ref> and as the president of the American Mathematical Society for the 2-years term 2015-2016.<ref>{{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}}</ref><ref>{{Cite web|title=AMS Presidents: Robert Bryant|url=https://www.ams.org/about-us/presidents/63-bryant|access-date=2021-08-06|website=American Mathematical Society|language=en}}</ref>


He served as the [[American Mathematical Society#Presidents|president of the American Mathematical Society]] for the 2-years term 2015–2016,<ref>{{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}}</ref><ref name=":1" /> for which he was the first openly gay president.<ref name=":1">{{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}}</ref><ref>{{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}}</ref>
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Bryant is on the board of directors of [[EDGE Program|EDGE]], a transition program for women entering graduate studies in the mathematical sciences.<ref>{{Cite web|last=|title=Board of Directors|url=https://www.edgeforwomen.org/support-edge/the-edge-foundation/|url-status=live|access-date=2021-08-06|website=EDGE Foundation|language=en-US}}</ref> He is also a board member of [[Spectra (mathematical association)|Spectra]], an association for LGBT mathematicians.<ref>{{cite web |title=Spectra |url=http://lgbtmath.org/People.html |access-date=30 September 2019}}</ref>

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Bryant is on the board of directors of [[EDGE Program|EDGE]], a transition program for women entering graduate studies in the mathematical sciences.<ref>{{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}}</ref> He is also a board member of [[Spectra (mathematical association)|Spectra]], an association for LGBT mathematicians that he helped to create.<ref>{{cite web |title=Spectra |url=http://lgbtmath.org/People.html |access-date=30 September 2019}}</ref><ref>{{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}}</ref>


== Research ==
== Research ==
Bryant's research interests cover many areas in [[Riemannian geometry]], [[Partial differential equation|geometry of PDEs]] and [[mathematical physics]].
Bryant's research has been influenced by [[Élie Cartan]], [[Shiing-Shen Chern]], and [[Phillip Griffiths]].<ref name=":1" /> His research interests cover many areas in [[Riemannian geometry]], [[Partial differential equation|geometry of PDEs]], [[Finsler geometry]] and [[mathematical physics]].<ref>{{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}}</ref>


In 1987 he proved several properties of surfaces of unit constant [[mean curvature]] in [[hyperbolic space]], which are now called [[Bryant surface]]s in his honour.<ref>{{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}}</ref> In 2001 he contributed many advancements to the theory of Bochner-Kähler metrics, the class of [[Kahler metrics|Kähler metrics]] whose Bochner curvature vanishes.<ref>{{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}}</ref>
In particular, he is known for his works in [[differential system|exterior differential systems]], [[holonomy|special holonomy]], and [[Finsler geometry]]. [[Bryant surface]]s, surfaces of unit constant [[mean curvature]] in [[hyperbolic space]], are named after him.<ref>{{citation|last=Rosenberg|first=Harold|title=The global theory of minimal surfaces in flat spaces (Martina Franca, 1999)|volume=1775|pages=67–111|year=2002|series=Lecture Notes in Math.|contribution=Bryant surfaces|location=Berlin|publisher=Springer|doi=10.1007/978-3-540-45609-4_3|mr=1901614}}.</ref> The [[Ricci flow|Bryant soliton]] is also named after him.<ref name="homepage" />


In 1987 he produced the first examples of [[Riemannian metric|Riemannian metrics]] with exceptional holonomy (i.e. whose [[holonomy groups]] are [[G2 (mathematics)|G<sub>2</sub>]] or [[Spin group|Spin(7)]]); this showed that every group in [[Marcel Berger]]'s classification can arise as a holonomy group.<ref>{{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}}</ref> Later, he also contributed to the classification of exotic holonomy groups of arbitrary (i.e. non-Riemannian) [[Torsion tensor|torsion]]-free [[Affine connection|affine connections]].<ref>{{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}}</ref><ref>{{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}}</ref>
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He is author of 7 books and more than 60 papers,<ref>{{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}}</ref><ref>{{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}}</ref> and he has supervised 26 PhD students.<ref name=":0" />


Together with [[Phillip Griffiths]] and others co-authors, Bryant developed the modern theory of [[Exterior differential system|Exterior Differential Systems]], writing two influential monographs, which have become the standard reference in the topic.<ref>{{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}}</ref><ref>{{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}}</ref> He also worked on their [[cohomology]]<ref>{{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}}</ref><ref>{{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}}</ref> and applications to PDEs.<ref>{{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}}</ref><ref>{{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}}</ref>
==Selected publications==

* editor with David Bao, [[S. S. Chern]], Zhongmin Shen: ''A sampler of Riemann-Finsler Geometry'', Cambridge University Press 2004
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He is author of more than 60 papers,<ref>{{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}}</ref><ref>{{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}}</ref> and he has supervised 26 PhD students.<ref name=":0" />
* ''Bochner-Kähler metrics'', Journal of the American Mathematical Society, vol. 14 no. 3, 2001, pp.&nbsp;623–715 {{arxiv|math/0003099}}

* with Robert Brown Gardner, [[S. S. Chern]], H. L. Goldschmidt, [[Phillip Griffiths]]: ''Exterior Differential Systems'', MSRI Publ. 18, Springer Verlag 1991
==Books==
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* with Phillip Griffiths, Dan Grossmann: ''Exterior Differential Systems and Euler-Lagrange Partial Differential Equations'', Chicago Lectures in Mathematics, University of Chicago Press 2003<ref>{{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 }}</ref>
* ''A sampler of Riemann-Finsler Geometry'', Cambridge University Press 2004 (editor with David Bao, [[S. S. Chern]], Zhongmin Shen)
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* editor with [[Victor Guillemin]], [[Sigurdur Helgason (mathematician)|Sigurdur Helgason]], R. O. Wells: ''Integral Geometry'', Contemporary Mathematics 63, AMS 1987
* ''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]])
* ''Metrics with exceptional holonomy'', Annals of Mathematics, vol. 126, 1987, pp.&nbsp;525–567
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*''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)<ref>{{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 }}</ref>
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* ''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.&nbsp;5–181
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*''Integral Geometry'', Contemporary Mathematics 63, AMS 1987 (editor with [[Victor Guillemin]], [[Sigurdur Helgason (mathematician)|Sigurdur Helgason]], R. O. Wells)
* with Lucas Hsu, Phillip Griffiths: ''Hyperbolic exterior differential systems and their conservation laws'', Parts 1,2, Selecta Mathematica, 1, 1995, 21-112, 265-323
⚫
* ''An introduction to [[Lie group]]s and symplectic geometry'', in ''Geometry and quantum field theory'', IAS/Park City Math. Series 1, American Mathematical Society 1995, pp.&nbsp;5–181
* with Griffiths: ''Characteristic Cohomology of Differential Systems'', Parts 1,2, Journal of the AMS, vol. 8, 1995, pp.&nbsp;507–596, Duke Math. J., vol. 78, 1995, pp.&nbsp;531–676
* with Hsu, Griffiths: ''Toward a Geometry of Differential Equations'', in: ''Geometry, Topology & Physics'', Conf. Proc. Lecture Notes Geom. Topology, VI, International Press, Cambridge, MA, 1995, pp.&nbsp;1–76
* ''Toward a Geometry of Differential Equations'', in: ''Geometry, Topology & Physics'', Conf. Proc. Lecture Notes Geom. Topology, VI, International Press, Cambridge, MA, 1995, pp.&nbsp;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''.
Bryant and [[David R. Morrison (mathematician)|David Morrison]] are the editors of vol. 4 of the ''Selected Works of Phillip Griffiths''.


==References==
==References==
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==External links==
==External links==
* [http://www.msri.org/people/staff/bryant/ Homepage at MSRI]
* [https://www.slmath.org/people/228 Homepage at MSRI]
* [https://scholars.duke.edu/person/bryant Homepage at Duke University]
* [https://scholars.duke.edu/person/bryant Homepage at Duke University]


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[[Category:20th-century American mathematicians]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Differential geometers]]
[[Category:1953 births]]
[[Category:Living people]]
[[Category:Living people]]
[[Category:Differential geometers]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:Fellows of the American Academy of Arts and Sciences]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Presidents of the American Mathematical Society]]
[[Category:Presidents of the American Mathematical Society]]
[[Category:1953 births]]
[[Category:Mathematicians from North Carolina]]
[[Category:Mathematicians from North Carolina]]
[[Category:LGBT scientists from the United States]]
[[Category:American LGBTQ scientists]]
[[Category:LGBT mathematicians]]
[[Category:LGBTQ mathematicians]]
[[Category:University of North Carolina at Chapel Hill alumni]]
[[Category:Sloan Research Fellows]]
[[Category:Rice University faculty]]
[[Category:Duke University faculty]]
[[Category:University of California, Berkeley faculty]]

Latest revision as of 04:01, 15 November 2024

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]

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

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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