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Vitaly Bergelson (born 1950 in Kiev〔) is a mathematical researcher and professor at the 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.〔 He gave an invited address at the International Congress of Mathematicians in 2006 in Madrid.〔( ICM 2006, Invited Lectures Abstracts ), ICM2006.org. Accessed January 23, 2010〕 Among Bergelson's best known results is a polynomial generalization of Szemerédi's theorem.〔Szemerédi, E., ''On sets of integers containing no k elements in arithmetic progression''. Collection of articles in memory of Juriĭ Vladimirovič Linnik. Acta Arithmetica, vol. 27 (1975), pp. 199–245〕 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".〔V. Bergelson, A. Leibman, ''Polynomial extensions of van der Waerden's and Szemerédi's theorems.'' Journal of the American Mathematical Society, vol. 9 (1996), no. 3, pp. 725–753〕 The Bergelson-Leibman theorem〔Alexander Soifer, Branko Grünbaum, and Cecil Rousseau, (Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators. ) Springer-Verlag, New York, 2008, ISBN 0-387-74640-4; p. 358〕 and the techniques developed in its proof spurred significant further applications and generalizations, particularly in the recent work of Terence Tao.〔Tao, Terence. ''A quantitative ergodic theory proof of Szemerédi's theorem.'' Electronic Journal of Combinatorics, vol. 13 (2006), no. 1〕〔Tao, Terence, and Ziegler, Tamar. ''The primes contain arbitrarily long polynomial progressions.'' Acta Mathematica, vol. 201 (2008), no. 2, pp. 213–305〕 In 2012 he became a fellow of the American Mathematical Society.〔(List of Fellows of the American Mathematical Society ), retrieved 2012-11-10.〕 ==References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Vitaly Bergelson」の詳細全文を読む スポンサード リンク
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