Bertram Kostant facts for kids
Quick facts for kids
Bertram Kostant
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Bertram Kostant at a workshop on “Enveloping Algebras and Geometric Representation Theory” in Oberwolfach, 2009
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| Born | May 24, 1928 |
| Died | February 2, 2017 (aged 88) |
| Nationality | American |
| Alma mater | Purdue University 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 |
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Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician. He made big discoveries in areas like representation theory, differential geometry, and mathematical physics. His work helped us understand complex math problems in new ways.
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Early Life and Learning
Bertram Kostant grew up in New York City. He finished high school at Stuyvesant High School in 1945. He then went to Purdue University, where he earned his first degree in mathematics in 1950.
He continued his studies at the University of Chicago. In 1954, he earned his Ph.D. (a high-level degree). His main teacher was Irving Segal. For his Ph.D., he wrote about "representations of Lie groups," which is a special area of math.
A Career in Math
After finishing his studies, Kostant worked at several famous places. These included the Institute for Advanced Study and Princeton University. He also spent time at the University of California, Berkeley.
Later, he joined the Massachusetts Institute of Technology (MIT). He taught there until he retired in 1993. His work at MIT focused on many advanced math topics.
Exploring Complex Math
Kostant's research covered several important fields. These included representation theory, Lie groups, and Lie algebras. He also studied homogeneous spaces and differential geometry.
He was very interested in mathematical physics, especially symplectic geometry. This area connects math with ideas from physics. He gave many talks about a special Lie group called E8.
Big Ideas and Discoveries
Bertram Kostant was a key person in developing "geometric quantization." This is a way to link ideas from classical physics to quantum physics using geometry. He also introduced "prequantization," which led to the theory of quantum Toda lattices.
A math idea called the Kostant partition function is named after him. He also helped create the Hochschild–Kostant–Rosenberg theorem. This theorem is important in a math area called Hochschild homology.
Many students learned from him and became successful mathematicians. Some of his well-known students include James Harris Simons and David Vogan. He has over 100 "mathematical descendants," meaning students of his students and so on.
Awards and Special Honors
Bertram Kostant received many awards and honors for his important work. In 1959-60, he was a Guggenheim Fellow, which allowed him to do research in Paris. He was also a Sloan Fellow from 1961-63.
He was chosen to be a member of important groups. In 1962, he joined the American Academy of Arts and Sciences. In 1978, he became a member of the National Academy of Sciences.
In 1990, he won the Steele Prize from the American Mathematical Society. This award recognized a special paper he wrote in 1975. He also received honorary degrees from universities in Argentina, Spain, and his old school, Purdue University.
In 2008, a conference was held to celebrate his life and work. It was called "Lie Theory and Geometry: the Mathematical Legacy of Bertram Kostant." In 2012, he was chosen as one of the first fellows of the American Mathematical Society.
In 2016, near the end of his life, he received the prestigious Wigner Medal. He earned this award for his "fundamental contributions to representation theory." His work helped create new areas in both mathematics and physics.
See also
- Chern's conjecture (affine geometry)
- Supermanifold
- Symplectic spinor bundle
