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, mathematical structure, structure, space, Mathematica ...

. He works at Duke University and specializes in differential geometry.

Education and career

Bryant grew up in a farming family in

Harnett County Harnett County is a county located in the U.S. state of North Carolina. As of the 2020 census, the population was 133,568. Its county seat is Lillington; its largest city is Dunn. Harnett County is part of the Fayetteville Metropolitan Stati ...

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. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which r ...

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 research university in Houston, Texas. It is on a 300-acre campus near the Houston Museum District and adjacent to the Texas Medical Center. Rice is ranked among the top universit ...

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 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 u ...

, 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, Califo ...

(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 Nevanlinna Prize (to be rename ...

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, ...

, 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, 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 an American international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsi ...

. 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 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 b ...

, 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 ...

Shiing-Shen Chern Shiing-Shen Chern (; , ; October 28, 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 geom ...

, 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 Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to po ...

, geometry of PDEs,

Finsler geometry In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold where a (possibly asymmetric) Minkowski functional is provided on each tangent space , that enables one to define the length of any smooth curve ...

and

mathematical physics Mathematical physics refers to 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 t ...

. 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. T ...

hyperbolic space In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal to -1. It is homogeneous, and satisfies the stronger property of being a symmetric space. ...

, 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-c ...

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 In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which parallel transport around closed loops fails to preserve the geom ...

are G₂ or

Spin(7) In mathematics, a Spin(7)-manifold is an eight-dimensional Riemannian manifold whose holonomy group is contained in Spin(7). Spin(7)-manifolds are Ricci-flat and admit a parallel spinor. They also admit a parallel 4-form, known as the Cayley form ...

); 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. Formerly residing in Le Castera in Las ...

'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

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 viewe ...

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 28, 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 geom ...

, Zhongmin Shen) * ''Exterior Differential Systems'', MSRI Publ. 18, Springer Verlag 1991, (with

Robert Brown Gardner Robert Brown (Robby) Gardner (February 27, 1939 – May 5, 1998) was an American mathematician who worked on differential geometry, a field in which he obtained several novel results. He was the author and co-author of three influential books, pr ...

, H. L. Goldschmidt and

) *''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 working in the field of symplectic geometry, who has also made contributions to the fields of microlocal analysis, spectral theory, and mathematical physics. He is a t ...

, 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 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 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