Robert Leamon Bryant (born August 30, 1953,
Kipling) is an American
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. He works at
Duke University
Duke University is a private research university in Durham, North Carolina. Founded by Methodists and Quakers in the present-day city of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco and electric power industrialist Jam ...
and specializes in
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and mult ...
.
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
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United State ...
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 (Rice University) is a Private university, private research university in Houston, Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranke ...
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 research university in Durham, North Carolina. Founded by Methodists and Quakers in the present-day city of Trinity in 1838, the school moved to Durham in 1892. In 1924, tobacco and electric power industrialist Jam ...
, 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 land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant un ...
, where he served as the director of the
Mathematical Sciences Research Institute
The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Calif ...
(MSRI). In 2013 he returned to Duke University as Phillip Griffiths Professor of Mathematics.
Bryant was awarded in 1982 a
Sloan Research Fellowship. 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 Nevanlinna Prize (to be rena ...
in Berkeley.
He was elected in 2002 a fellow of the
American Academy of Arts and Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) 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, a ...
, in 2007 a member of the
National Academy of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, 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 Nat ...
, 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, meeting ...
and in 2022 a fellow of the
American Association for the Advancement of Science
The American Association for the Advancement of Science (AAAS) is an American international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific respons ...
. 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
The National Association of Mathematicians is a professional association for mathematicians in the US, especially African Americans and other minorities. It was founded in 1969. and the
Mathematical Association of America.
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, 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 geometr ...
,
Shiing-Shen Chern, 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 was a major developer in particula ...
.
His research interests cover many areas in
Riemannian geometry,
geometry of PDEs,
Finsler geometry and
mathematical physics
Mathematical physics refers to the development of 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 developm ...
.
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. 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'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 was a major developer in particula ...
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 view ...
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, Zhongmin Shen)
* ''Exterior Differential Systems'', MSRI Publ. 18, Springer Verlag 1991, (with
Robert Brown Gardner,
S. S. Chern, 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 was a major developer in particula ...
)
*''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,
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
External links
Homepage at MSRIHomepage 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 LGBT scientists
LGBT mathematicians
University of North Carolina at Chapel Hill alumni
Sloan Research Fellows
Rice University faculty
Duke University faculty
University of California, Berkeley faculty