Bertram Kostant | |
|---|---|
 Bertram Kostant at a workshop on “Enveloping Algebras and Geometric Representation Theory” inOberwolfach, 2009 | |
| Born | (1928-05-24)May 24, 1928 |
| Died | February 2, 2017(2017-02-02) (aged 88) Roslindale,Massachusetts, U.S. |
| Nationality | American |
| Alma mater | Purdue University (BS) University of Chicago (PhD) |
| Known for | Kostant's convexity theorem Kostant partition function Kostant polynomial Geometric quantization Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants Hochschild-Kostant-Rosenberg theorem |
| 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 advisor | Irving Segal |
| Doctoral students | |
Bertram Kostant (May 24, 1928 – February 2, 2017)[1] was an Americanmathematician who worked inrepresentation theory,differential geometry, andmathematical physics.
Kostant grew up inNew York City, where he graduated fromStuyvesant High School in 1945.[2] He went on to obtain an undergraduate degree in mathematics fromPurdue University in 1950. He earned his Ph.D. from theUniversity of Chicago in 1954, under the direction ofIrving Segal, where he wrote a dissertation on representations of Lie groups.
After time at theInstitute for Advanced Study,Princeton University, and theUniversity of California, Berkeley, he joined the faculty at theMassachusetts Institute of Technology, where he remained until his retirement in 1993. Kostant's work has involvedrepresentation theory,Lie groups,Lie algebras,homogeneous spaces,differential geometry andmathematical physics, particularlysymplectic geometry. He has given several lectures on the Lie groupE8.[3] He has been one of the principal developers of the theory ofgeometric quantization. His introduction of the theory ofprequantization has led to the theory of quantumToda lattices. TheKostant partition function is named after him. WithGerhard Hochschild andAlex F. T. W. Rosenberg, he is one of the namesakes of the Hochschild–Kostant–Rosenberg theorem which describes theHochschild homology of somealgebras.[4]
His students includeJames Harris Simons,James Lepowsky,Moss Sweedler,David Vogan, andBirgit Speh. At present he has more than 100 mathematical descendants.
Kostant was a Guggenheim Fellow in 1959-60 (in Paris), and a Sloan Fellow in 1961-63. In 1962 he was elected to the American Academy of Arts and Sciences, and in 1978 to the National Academy of Sciences. In 1982 he was a fellow of the Sackler Institute for Advanced Studies at Tel Aviv University. In 1990 he was awarded the Steele Prize of the American Mathematical Society, in recognition of his 1975 paper, “On the existence and irreducibility of certain series of representations.”
In 2001, Kostant was a Chern Lecturer and Chern Visiting Professor at Berkeley. He received honorary degrees from the University of Córdoba in Argentina in 1989, the University of Salamanca in Spain in 1992, and Purdue University in 1997. The latter, from his alma mater, was an honorary Doctor of Science degree, citing his fundamental contributions to mathematics and the inspiration he and his work provided to generations of researchers.
In May 2008, the Pacific Institute for Mathematical Sciences hosted a conference: “Lie Theory and Geometry: the Mathematical Legacy of Bertram Kostant,” at the University of British Columbia, celebrating the life and work of Kostant in his 80th year. In 2012, he was elected to the inaugural class of fellows of the American Mathematical Society. In the last year of his life, Kostant traveled to Rio de Janeiro for the Colloquium on Group Theoretical Methods in Physics, where he received the prestigious Wigner Medal, “for his fundamental contributions to representation theory that led to new branches of mathematics and physics.”
