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Robert Leamon Bryant (born August 30, 1953) is an American mathematician. He works at
Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...
and specializes in
differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...
.


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 The University of North Carolina at Chapel Hill (UNC, UNC–Chapel Hill, or simply Carolina) is a public university, public research university in Chapel Hill, North Carolina, United States. Chartered in 1789, the university first began enrolli ...
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. He worked at
Rice University William Marsh Rice University, commonly referred to as Rice University, is a Private university, private research university in Houston, Houston, Texas, United States. Established in 1912, the university spans 300 acres. Rice University comp ...
for seven years, as assistant professor (1979–1981), associate professor (1981–1982) and full professor (1982–1986). He then moved to
Duke University Duke University is a Private university, private research university in Durham, North Carolina, United States. Founded by Methodists and Quakers in the present-day city of Trinity, North Carolina, Trinity in 1838, the school moved to Durham in 1 ...
, 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 The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...
, where he served as the director of the Mathematical Sciences Research Institute (MSRI). In 2013 he returned to Duke University as Phillip Griffiths Professor of Mathematics. Bryant was awarded in 1982 a
Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...
. In 1986 he was invited speaker at the
International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...
in Berkeley. He was elected in 2002 a fellow of the
American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...
, in 2007 a member of the
National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...
, in 2013 a fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
and in 2022 a fellow of the
American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is a United States–based international nonprofit with the stated mission of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsib ...
. He is also a member of the
Association for Women in Mathematics The Association for Women in Mathematics (AWM) is a professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment o ...
, the National Association of Mathematicians and the
Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university A university () is an educational institution, institution of tertiary edu ...
. He served as the president of the American Mathematical Society for the 2-years term 2015–2016, for which he was the first openly gay president. Bryant is on the board of directors of
EDGE Edge or EDGE may refer to: Technology Computing * Edge computing, a network load-balancing system * Edge device, an entry point to a computer network * Adobe Edge, a graphical development application * Microsoft Edge, a web browser developed by ...
, a transition program for women entering graduate studies in the mathematical sciences. He is also a board member of Spectra, an association for LGBT mathematicians that he helped to create.


Research

Bryant's research has been influenced by
Élie Cartan Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. He ...
,
Shiing-Shen Chern Shiing-Shen Chern (; , ; October 26, 1911 – December 3, 2004) was a Chinese American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...
, and
Phillip Griffiths Phillip Augustus Griffiths IV (born October 18, 1938) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He is a major developer in particular ...
. His research interests cover many areas in
Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as manifold, smooth manifolds with a ''Riemannian metric'' (an inner product on the tangent space at each point that varies smooth function, smo ...
, geometry of PDEs, Finsler geometry and
mathematical physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...
. In 1987 he proved several properties of surfaces of unit constant
mean curvature In mathematics, the mean curvature H of a surface S is an ''extrinsic'' measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. The ...
in
hyperbolic space In mathematics, hyperbolic space of dimension ''n'' is the unique simply connected, ''n''-dimensional Riemannian manifold of constant sectional curvature equal to âˆ’1. It is homogeneous, and satisfies the stronger property of being a symme ...
, which are now called
Bryant surface In Riemannian geometry, a Bryant surface is a 2-dimensional surface embedded in 3-dimensional hyperbolic space with constant mean curvature equal to 1. These surfaces take their name from the geometer Robert Bryant, who proved that every simply-co ...
s in his honour. In 2001 he contributed many advancements to the theory of Bochner-Kähler metrics, the class of Kähler metrics whose Bochner curvature vanishes. 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 Marcel Berger (14 April 1927 – 15 October 2016) was a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques (IHÉS), France. Biography After studying from 1948 to 19 ...
's classification can arise as a holonomy group. Later, he also contributed to the classification of exotic holonomy groups of arbitrary (i.e. non-Riemannian) torsion-free affine connections. Together with
Phillip Griffiths Phillip Augustus Griffiths IV (born October 18, 1938) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He is a major developer in particular ...
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. He also worked on their
cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed ...
and applications to PDEs. He is author of more than 60 papers, 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 Shiing-Shen Chern (; , ; October 26, 1911 – December 3, 2004) was a Chinese American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...
, Zhongmin Shen) * ''Exterior Differential Systems'', MSRI Publ. 18, Springer Verlag 1991, (with Robert Brown Gardner,
S. S. Chern Shiing-Shen Chern (; , ; October 26, 1911 – December 3, 2004) was a Chinese American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...
, H. L. Goldschmidt and
Phillip Griffiths Phillip Augustus Griffiths IV (born October 18, 1938) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He is a major developer in particular ...
) *''Exterior Differential Systems and Euler-Lagrange Partial Differential Equations'', Chicago Lectures in Mathematics, University of Chicago Press 2003, (with Phillip Griffiths and Dan Grossman) *''Integral Geometry'', Contemporary Mathematics 63, AMS 1987 (editor with
Victor Guillemin Victor William Guillemin (born 1937 in Boston) is an American mathematician. He works at the Massachusetts Institute of Technology in the field of symplectic geometry, and he has also made contributions to the fields of microlocal analysis, spec ...
, Sigurdur Helgason, R. O. Wells) * ''An introduction to
Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...
s 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


External links


Homepage at MSRI

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