Vitaly Bergelson
Encyclopedia
Vitaly Bergelson is a mathematical researcher and professor at the Ohio State University in Columbus, Ohio
. His research focuses on Ergodic theory
and Combinatorics
. He received his Ph.D in 1984 under Hillel Furstenberg at the Hebrew University of Jerusalem
.
Bergelson 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 progression
s. 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
.
Columbus, Ohio
Columbus is the capital of and the largest city in the U.S. state of Ohio. The broader metropolitan area encompasses several counties and is the third largest in Ohio behind those of Cleveland and Cincinnati. Columbus is the third largest city in the American Midwest, and the fifteenth largest city...
. His research focuses on Ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
and Combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
. He received his Ph.D in 1984 under Hillel Furstenberg at the Hebrew University of Jerusalem
Hebrew University of Jerusalem
The Hebrew University of Jerusalem ; ; abbreviated HUJI) is Israel's second-oldest university, after the Technion – Israel Institute of Technology. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J...
.
Bergelson gave an Invited Address at the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in 2006 in Madrid.
Among Bergelson's best-known results is a polynomial generalization of Szemerédi's theorem
Szemerédi's theorem
In number theory, Szemerédi's theorem is a result that was formerly the Erdős–Turán conjecture...
. 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 progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...
s. 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
Terence Tao
Terence Chi-Shen Tao FRS is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory...
.
External links
- Bergelson's web page at OSU
- Vitaly Bergelson, Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...