Bergelson received his Ph.D in 1984 under Hillel Furstenberg at the Hebrew University of Jerusalem. He gave an invited address at the International Congress of Mathematicians in 2006 in Madrid. Among Bergelson's best known results is a polynomial generalization of Szemerédi's theorem. The latter provided a positive solution to the famous Erdős–Turán conjecture from 1936 stating that any set of integers of positive upper density contains arbitrarily long arithmetic progressions. In a 1996 paper Bergelson and Leibman obtained an analogous statement for "polynomial progressions". The Bergelson-Leibman theorem and the techniques developed in its proof spurred significant further applications and generalizations, particularly in the recent work of Terence Tao.
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- Tao, Terence. A quantitative ergodic theory proof of Szemerédi's theorem. Electronic Journal of Combinatorics, vol. 13 (2006), no. 1
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- List of Fellows of the American Mathematical Society, retrieved 2012-11-10.