Shlomo Sternberg
| Shlomo Sternberg | |
|---|---|
| Born | 1936 |
| Fields | Mathematics |
| Institutions |
Harvard University New York University University of Chicago |
| Alma mater |
Johns Hopkins University (PhD 1955) |
| Doctoral advisor | Aurel Friedrich Wintner |
| Doctoral students |
Victor Guillemin (Harvard, 1962) Ravindra Kulkarni (Harvard, 1968) Hubert Goldschmidt (Harvard, 1967) Eric Grinberg (Harvard, 1983) Yael Karshon (Harvard, 1993) |
Shlomo Zvi Sternberg (born 1936), is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory.
Sternberg earned his PhD in 1955 from Johns Hopkins University where he wrote a dissertation under Aurel Wintner. This became the basis for his first well-known published result known as the "Sternberg linearization theorem" which asserts that a smooth map near a hyperbolic fixed point can be made linear by a smooth change of coordinates provided that certain non-resonance conditions are satisfied. Also proved were generalizations of the Birkhoff canonical form theorems for volume preserving mappings in n-dimensions and symplectic mappings, all in the smooth case. (An account of these results and of their implications for the theory of dynamical systems can be found in Bruhat's exposition "Travaux de Sternberg", Seminaire Bourbaki, Volume 8. 1961).
After postdoctoral work at New York University (1956-1957) and an instructorship at University of Chicago (1957–1959) Sternberg joined the Mathematics Department at Harvard University in 1959, where he was George Putnam Professor of Pure and Applied Mathematics until 2017. Since 2017, he is Emeritus Professor at the Harvard Mathematics Department.
In the 1960s Sternberg became involved with Isadore Singer in the project of revisiting Élie Cartan's papers from the early 1900s on the classification of the simple transitive infinite Lie pseudogroups, and of relating Cartan's results to recent results in the theory of G-structures and supplying rigorous (by present-day standards) proofs of his main theorems. Also, in a sequel to this paper written jointly with Victor Guillemin and Daniel Quillen, he extended this classification to a larger class of pseudogroups: the primitive infinite pseudogroups. (One important by-product of the GQS paper was the " integrability of characteristics" theorem for over-determined systems of partial differential equations. This figures in GQS as an analytical detail in their classification proof but is nowadays the most cited result of the paper.)
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