Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory,

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 multili ...

, and mathematical physics.

Early life and education

Kostant grew up in New York City, where he graduated from

Stuyvesant High School Stuyvesant High School (pronounced ), commonly referred to among its students as Stuy (pronounced ), is a State school, public university-preparatory school, college-preparatory, Specialized high schools in New York City, specialized high school ...

in 1945. He went on to obtain an undergraduate degree in mathematics from Purdue University in 1950. He earned his Ph.D. from the University of Chicago in 1954, under the direction of

Irving Segal Irving Ezra Segal (1918–1998) was an American mathematician known for work on theoretical quantum mechanics. He shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career Segal became known for h ...

, where he wrote a dissertation on representations of Lie groups.

Career in mathematics

After time at the Institute for Advanced Study, Princeton University, and the University of California, Berkeley, he joined the faculty at the Massachusetts Institute of Technology, where he remained until his retirement in 1993. Kostant's work has involved representation theory,

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...

homogeneous space In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group ''G'' is a non-empty manifold or topological space ''X'' on which ''G'' acts transitively. The elements of ' ...

and mathematical physics, particularly

symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed differential form, closed, nondegenerate form, nondegenerate different ...

. He has given several lectures on the Lie group E8. He has been one of the principal developers of the theory of geometric quantization. His introduction of the theory of ''prequantization'' has led to the theory of quantum Toda lattices. The Kostant partition function is named after him. With

Gerhard Hochschild Gerhard Paul Hochschild (April 29, 1915 in Berlin – July 8, 2010 in El Cerrito, California) was a German-born American mathematician who worked on Lie groups, algebraic groups, homological algebra and algebraic number theory. Early life ...

and

Alex F. T. W. Rosenberg Alex F. T. W. Rosenberg (1926–2007) was a German-American mathematician who served as the editor of the '' Proceedings of the American Mathematical Society'' from 1960 to 1965, and of the '' American Mathematical Monthly'' from 1974 to 1976.. ...

, he is one of the namesakes of the Hochschild–Kostant–Rosenberg theorem which describes the Hochschild homology of some algebras. His students include James Harris Simons,

James Lepowsky James "Jim" Lepowsky (born July 5, 1944, in New York City) is a professor of mathematics at Rutgers University, New Jersey. Previously he taught at Yale University. He received his Ph.D. from M.I.T. in 1970 where his advisors were Bertram Kostant ...

, Moss Sweedler,

David Vogan David Alexander Vogan, Jr. (born September 8, 1954) is a mathematician at the Massachusetts Institute of Technology who works on unitary representations of simple Lie groups. While studying at the University of Chicago, he became a Putnam Fellow ...

, and Birgit Speh. At present he has more than 100 mathematical descendants.

Awards and honors

Kostant's honors include election to 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 Nati ...

in 1978. In 2012 he became a fellow of the American Mathematical Society. He was an Invited Speaker of the ICM with talk ''Orbits and quantization theory'' in 1970 at Nice.Kostant, Bertram
"Orbits and quantization theory."
In ''Actes, Congrès intern. Math.'', Nice, vol. 2, pp. 395–400. 1970.

Selected publications

* * * * * * * with Louis Auslander: * with

Stephen Rallis Stephen James Rallis (May 17, 1942 – April 17, 2012) was an American mathematician who worked on group representations, automorphic forms, the Siegel–Weil formula, and Langlands L-functions. Career Rallis received a B.A. in 1964 from Harvard ...

: * * * * with

David Kazhdan David Kazhdan ( he, דוד קשדן), born Dmitry Aleksandrovich Kazhdan (russian: Дми́трий Александро́вич Кажда́н), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 Ma ...

and

Shlomo Sternberg Shlomo Zvi Sternberg (born 1936), is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. Education and career Sternberg earned his PhD in 1955 from Johns Hopkins University, with a thesis en ...

: * * with

Shrawan Kumar Shrawan Kumar may refer to: * Shrawan Kumar (mathematician) Shrawan Kumar is the John R. and Louise S. Parker distinguished professor of mathematics at the University of North Carolina at Chapel Hill. He has written two books: ''Kac-Moody g ...

: *with Shlomo Sternberg: * * with

and

Alex Rosenberg Alex Rosenberg may refer to: * Alexander Rosenberg (born 1946), American philosopher and novelist * Alex F. T. W. Rosenberg (1926–2007), German-American mathematician * Alexander L. Rosenberg (1946–2012), Russian-American mathematician * Alex R ...

: (Reprinted from Trans. Amer. Math. Soc., vol. 102, no. 3, March 1962, pp. 383–408) * (Reprinted from the Amer. J. Math., vol. 81, no. 4, Oct. 1959)

Notes

References

Kostant's home page at MIT
* * {{DEFAULTSORT:Kostant, Bertram 1928 births 2017 deaths 20th-century American mathematicians 21st-century American mathematicians Members of the United States National Academy of Sciences Fellows of the American Mathematical Society Institute for Advanced Study visiting scholars Stuyvesant High School alumni Purdue University alumni University of Chicago alumni Princeton University faculty University of California, Berkeley faculty Massachusetts Institute of Technology faculty People from Brooklyn Mathematicians from New York (state)