Vitaly Bergelson
Vitaly Bergelson | |
|---|---|
 Vitaly Bergelson | |
| Born | 1950 Kiev |
| Alma mater | Hebrew University of Jerusalem |
| Known for | Polynomial generalization of Szemerédi's theorem |
| Awards | Fellow of the American Mathematical Society (2012) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Ohio State University |
| Doctoral advisor | Hillel Furstenberg |
Vitaly Bergelson (born 1950 in Kiev[1]) is a mathematical researcher and professor at Ohio State University in Columbus, Ohio. His research focuses on ergodic theory and combinatorics.
Bergelson received his Ph.D. in 1984 under Hillel Furstenberg at the Hebrew University of Jerusalem.[1] He gave an invited address at the International Congress of Mathematicians in 2006 in Madrid.[2] Among Bergelson's best known results is a polynomial generalization of Szemerédi's theorem.[3] 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".[4] The Bergelson-Leibman theorem[1] and the techniques developed in its proof spurred significant further applications and generalizations, particularly in the recent work of Terence Tao.[5][6]
In 2012, he became a fellow of the American Mathematical Society.[7]
References
- ^ a b c Soifer, Alexander (2008). The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators. Forewords by Branko Grünbaum, Peter D. Johnson Jr., and Cecil C. Rousseau. New York: Springer. p. 358. ISBN 0-387-74640-4.
- ^ Bergelson, Vitaly (2007). "Ergodic Ramsey theory: a dynamical approach to static theorems". Proceedings of the International Congress of Mathematicians, Madrid, Spain, August 2006, Volume II, Invited Lectures (PDF). p. 1655–1678. doi:10.4171/022-2/79. Retrieved 2025-08-06.
- ^ Szemerédi, E. (1975). "On sets of integers containing k elements in arithmetic progression". Acta Arithmetica. 27 (1): 199–245. ISSN 0065-1036. Retrieved 2025-08-06.Collection of articles in memory of Juriĭ Vladimirovič Linnik.
- ^ Bergelson, V.; Leibman, A. (1996). "Polynomial extensions of van der Waerden's and Szemerédi's theorems" (PDF). Journal of the American Mathematical Society. 9 (3). American Mathematical Society (AMS): 725–753. doi:10.1090/s0894-0347-96-00194-4. ISSN 0894-0347. Retrieved 2025-08-06.
- ^ Tao, Terence (2006). "A Quantitative Ergodic Theory Proof of Szemerédi's Theorem". The Electronic Journal of Combinatorics. 13 (1). doi:10.37236/1125. ISSN 1077-8926. Retrieved 2025-08-06.
- ^ Tao, Terence; Ziegler, Tamar (2008). "The primes contain arbitrarily long polynomial progressions" (PDF). Acta Mathematica. 201 (2): 213–305. doi:10.1007/s11511-008-0032-5. ISSN 0001-5962. Retrieved 2025-08-06.
- ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.