Bertram Kostant

Bertram Kostant
230px Bertram Kostant at a workshop on “Enveloping Algebras and Geometric Representation Theory” in Oberwolfach, 2009
Born	(1928-05-24)May 24, 1928 Brooklyn, New York
Died	Roslindale, Massachusetts
Nationality	American
Fields	Mathematics
Institutions	Massachusetts Institute of Technology University of California, Berkeley
Alma mater	Purdue University University of Chicago (PhD)
Thesis	Representations of a Lie algebra and its enveloping algebra on a Hilbert space
Doctoral advisor	Irving Segal
Doctoral students	Marjorie Batchelor James Lepowsky Arlie Petters Stephen Rallis James Harris Simons Birgit Speh Moss Sweedler David Vogan
Known for	Kostant's convexity theorem Kostant partition function Kostant polynomial Geometric quantization Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants Hochschild-Kostant-Rosenberg theorem
Notable awards	Wigner Medal (2016)

Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics.

Early life and education

Kostant grew up in New York City, where he graduated from Stuyvesant 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, 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 groups, Lie algebras, homogeneous spaces, differential geometry and mathematical physics, particularly symplectic geometry. 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 and Alex F. T. W. Rosenberg, 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, Moss Sweedler, David Vogan, 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 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.

Selected publications

• with Louis Auslander:
• with Stephen Rallis:
• with David Kazhdan and Shlomo Sternberg:
• with Shrawan Kumar:
• with Shlomo Sternberg:
• with Gerhard Hochschild and Alex Rosenberg: (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)

See also

• Chern's conjecture (affine geometry)
• Supermanifold
• Symplectic spinor bundle

References

• Kostant's home page at MIT
• Bertram Kostant at the Mathematics Genealogy Project