# Bertram Kostant

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Bertram Kostant
Bertram Kostant at a workshop on “Enveloping Algebras and Geometric Representation Theory” in Oberwolfach, 2009
BornMay 24, 1928
DiedFebruary 2, 2017 (aged 88)
NationalityAmerican
Alma materPurdue University
University of Chicago (PhD)
Known forKostant partition function
Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants
AwardsWigner Medal (2016)
Scientific career
FieldsMathematics
InstitutionsMassachusetts Institute of Technology
University of California, Berkeley
ThesisRepresentations of a Lie algebra and its enveloping algebra on a Hilbert space
Doctoral advisorIrving Segal
Doctoral students

Bertram Kostant (May 24, 1928 – February 2, 2017)[1] 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.[2] 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.[3] 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.[4]

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.[5] He was an Invited Speaker of the ICM with talk Orbits and quantization theory in 1970 at Nice.[6]

## Notes

1. ^ "Bertram Kostant, professor emeritus of mathematics, dies at 88". MIT News. 16 February 2017.
2. ^ "Professor Kostant's Homepage". MIT Math Department. Retrieved 2007-10-31. CS1 maint: discouraged parameter (link)
3. ^ Bertram Kostant (2008-02-12). "On Some Mathematics in Garrett Lisi's 'E8 Theory of Everything'". UC Riverside mathematics colloquium. Retrieved 2008-06-15. CS1 maint: discouraged parameter (link)
4. ^ Porter, Tim (April 8, 2014), "Hochschild-Kostant-Rosenberg theorem", nLab.
5. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
6. ^ Kostant, Bertram. "Orbits and quantization theory." Archived 2015-03-26 at the Wayback Machine In Actes, Congrès intern. Math., Nice, vol. 2, pp. 395–400. 1970.