# Bertram Kostant

Bertram Kostant
Bertram Kostant at a workshop on “Enveloping Algebras and Geometric Representation Theory” in Oberwolfach, 2009
Born May 24, 1928
Died February 2, 2017 (aged 88)
Nationality American
Alma mater Purdue University
University of Chicago (PhD)
Known for Kostant partition function
Awards Wigner Medal (2016)
Scientific career
Fields Mathematics
Institutions Massachusetts Institute of Technology
University of California, Berkeley
Thesis Representations of a Lie algebra and its enveloping algebra on a Hilbert space
Doctoral students Arlie Petters
James Lepowsky
Stephen Rallis
James Harris Simons
Moss Sweedler
David Vogan
Birgit Speh

Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician.[1]

## 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 many 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]