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Shlomo Zvi Sternberg is a mathematician known for his work in geometry, particularly symplectic geometry and Lie theory.
Sternberg earned his Ph.D 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 lineralization 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..
After postdoctoral work at New York University and an instructorship at University of Chicago Sternberg joined the Mathematics Department at Harvard University in 1959, where he is currently George Putnam Professor of Pure and Applied Mathematics.
In the 1960’s Sternberg became involved with Isadore Singer in the project of revisiting Élie Cartan’s papers from the early 1900’s 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 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.
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