Vitaly Bergelson

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Vitaly Bergelson is affiliated with the following schools: Ohio State University, Hebrew University of Jerusalem

Vitaly Bergelson's AcademicInfluence.com Rankings

Vitaly Bergelson

Mathematics

#2457

World Rank

#3793

Historical Rank

Measure Theory

#2996

World Rank

#3558

Historical Rank

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Mathematics

Why Is Vitaly Bergelson Influential?

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According to Wikipedia, Vitaly Bergelson 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. 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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Vitaly Bergelson's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Polynomial extensions of van der Waerden’s and Szemerédi’s theorems (1996) (376)
Multiple recurrence and nilsequences (2005) (178)
Weakly mixing PET (1987) (173)
Ergodic Ramsey Theory–an Update (1996) (123)
Nonmetrizable topological dynamics and Ramsey theory (1990) (116)
Distribution of values of bounded generalized polynomials (2007) (88)
Set-polynomials and polynomial extension of the Hales-Jewett Theorem (1999) (83)
Convergence in ergodic theory and probability (1996) (78)
Notions of Size and Combinatorial Properties of Quotient Sets in Semigroups (1998) (77)
An Ergodic IP Polynomial Szemerédi Theorem (2000) (75)
Partition Theorems for Spaces of Variable Words (1994) (74)
Intersective polynomials and the polynomial Szemerédi theorem (2007) (71)
Mixing actions of groups (1988) (70)
Sumset phenomenon in countable amenable groups (2009) (68)
Topics in Dynamics and Ergodic Theory: Minimal idempotents and ergodic Ramsey theory (2003) (65)
IP-sets and polynomial recurrence (1996) (61)
Encyclopaedia of Mathematics, Supplement III (2002) (59)
Ultrafilters, IP sets, Dynamics, and Combinatorial Number Theory (2010) (59)
A nilpotent Roth theorem (2002) (58)
Partition Regular Structures Contained in Large Sets Are Abundant (2001) (58)
An Inverse Theorem for the Uniformity Seminorms Associated with the Action of $${{\mathbb {F}^{\infty}_{p}}}$$ (2009) (57)
Multiplicative structures in additively large sets (2006) (56)
Large sets of integers and hierarchy of mixing properties of measure preserving systems (2008) (55)
AN INVERSE THEOREM FOR THE UNIFORMITY SEMINORMS ASSOCIATED WITH THE ACTION OF Fp (2010) (52)
Rigidity and non-recurrence along sequences (2011) (48)
The Multifarious Poincaré Recurrence Theorem (2000) (48)
A Roth theorem for amenable groups (1997) (47)
Piecewise-Bohr Sets of Integers and Combinatorial Number Theory (2006) (42)
Chapter 12 – Combinatorial and Diophantine Applications of Ergodic Theory (2006) (42)
Sets of Recurrence of Zm-Actions and Properties of Sets of Differences in Zm (1985) (38)
Multiplicatively large sets and ergodic Ramsey theory (2005) (37)
On IP* sets and central sets (1994) (37)
VAN DER CORPUT SETS IN Z d (2007) (36)
Weak mixing implies weak mixing of higher orders along tempered functions (2009) (32)
Idempotent ultrafilters, multipleweak mixing and Szemerédi’s theorem for generalized polynomials (2010) (32)
Multiple Recurrence in Quasirandom Groups (2012) (32)
Polynomial Szemerédi theorems for countable modules over integral domains and finite fields (2005) (31)
Central sets and a non-commutative Roth theorem (2007) (31)
Sets of Recurrence and Generalized Polynomials (1996) (30)
Weakly mixing group actions: a brief survey and an example (2005) (29)
A density statement generalizing Schur's theorem (1986) (29)
SETS OF RECURRENCE OF Z-ACTIONS AND PROPERTIES OF SETS OF DIFFERENCES IN Z (2006) (29)
Ergodic Ramsey Theory (2013) (29)
Multiplicative subgroups of finite index in a ring (1992) (28)
Some new results in multiplicative and additive Ramsey theory (2008) (28)
Additive and Multiplicative Ramsey Theorems in ℕ – Some Elementary Results (1993) (28)
Affine actions of a free semigroup on the real line (2006) (27)
Ergodic and mixing sequences of transformations (1984) (25)
Some results on non-linear recurrence (1994) (25)
From discrete- to continuous-time ergodic theorems (2011) (24)
IP-systems, generalized polynomials and recurrence (2006) (24)
Topological multiple recurrence for polynomial configurations in nilpotent groups (2003) (23)
New polynomial and multidimensional extensions of classical partition results (2015) (23)
Failure of the Roth theorem for solvable groups of exponential growth (2004) (22)
Jointly ergodic measure-preserving transformations (1984) (21)
The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems (2010) (20)
Rado's Theorem for Commutative Rings (1994) (19)
Van der Corput's Difference Theorem: some modern developments (2015) (19)
Mixing sequences in Hilbert spaces (1986) (18)
Additive and Multiplicative Ramsey Theory in the Reals and the Rationals (1999) (18)
Some Topological Semicommutative Van Der Waerden Type Theorems and their Combinatorial Consequences (1992) (18)
On the interplay between additive and multiplicative largeness and its combinatorial applications (2020) (18)
Solvability of Rado systems in D-sets (2008) (17)
Iterated Spectra of Numbers—Elementary, Dynamical, and Algebraic Approaches (1996) (17)
Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤk (2013) (17)
Cubic averages and large intersections (2018) (16)
Sumsets in difference sets (2009) (16)
WM groups and Ramsey theory (2009) (16)
Joint ergodicity for group actions (1988) (15)
Ultrafilters across Mathematics (2010) (15)
Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory (2007) (14)
A combinatorially large cell of a partition of N (1988) (14)
Ergodic theorem involving additive and multiplicative groups of a field and $\{x+y,xy\}$ patterns (2013) (14)
ASPECTS OF UNIFORMITY IN RECURRENCE (2000) (13)
Ramsey theory in noncommutative semigroups (1992) (13)
Ultrafilters and multidimensional Ramsey Theorems (1989) (13)
Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics (2016) (12)
Finite products sets and minimally almost periodic groups (2014) (12)
Polynomial extensions of the Milliken-Taylor Theorem (2014) (11)
Simultaneous dense and nondense orbits for commuting maps (2013) (11)
Ergodic Theory of ℤ d Actions: Ergodic Ramsey Theory (1996) (11)
Ergodicity and mixing of non‐commuting epimorphisms (2005) (11)
Strongly central sets and sets of polynomial returns mod 1 (2012) (11)
Ledrappier’s system is almost mixing of all orders (2008) (10)
Multiple recurrence and large intersections for abelian group actions (2021) (10)
Joint ergodicity along generalized linear functions (2014) (10)
An ergodic correspondence principle, invariant means and applications (2020) (10)
Quotient sets and density recurrent sets (2012) (10)
Uniform distribution of subpolynomial functions along primes and applications (2015) (10)
Ergodic Ramsey theory: a dynamical approach to static theorems (2006) (10)
Polynomial recurrence with large intersection over countable fields (2014) (10)
Measure preserving actions of affine semigroups and $\{x+y,xy\}$ patterns (2015) (10)
Single and multiple recurrence along non-polynomial sequences (2017) (9)
Characterization of joint ergodicity for non-commuting transformations (1986) (9)
Sets Partition Regular for n Equations Need not Solve n + 1 (1996) (9)
A Central Limit Theorem for Conditional Distributions (1996) (9)
Density versions of two generalizations of Schur's theorem (1988) (9)
Ergodic Theory of ℤ d Actions: Uniformity in the polynomial Szemérdi theorem (1996) (8)
All-sum sets in (0,1]—Category and measure (1997) (8)
Dense Difference Sets and Their Combinatorial Structure (2013) (8)
IPr⁎-recurrence and nilsystems (2016) (8)
Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications (2020) (8)
Interplay between notions of additive and multiplicative largeness (2016) (8)
A Krengel-type theorem for finitely-generated nilpotent groups (2001) (7)
Polynomial multiple recurrence over rings of integers (2014) (7)
Sets of large values of correlation functions for polynomial cubic configurations (2016) (7)
A Weyl-type equidistribution theorem in finite characteristic (2016) (7)
Weakly Wandering Vectors for Unitary Actions of Commutative Groups (1994) (7)
Triangles in Cartesian Squares of Quasirandom Groups (2014) (6)
Multiplicative richness of additively large sets in Zd (2018) (6)
A fresh look at the notion of normality (2020) (5)
Unitary ^{}-actions with continuous spectrum (1993) (5)
Multiple recurrence and convergence results associated to $${\text{F}}_P^\omega $$-actions (2015) (5)
New examples of complete sets, with connections to a Diophantine theorem of Furstenberg (2015) (5)
On the interplay between notions of additive and multiplicative largeness and its combinatorial applications (2016) (5)
A structure theorem for level sets of multiplicative functions and applications (2017) (5)
Dynamical generalizations of the prime number theorem and disjointness of additive and multiplicative semigroup actions (2020) (4)
A selection of open problems (2009) (4)
Weakly mixing actions of F ∞ have infinite subgroup actions which are Bernoulli (1988) (4)
An almost mixing of all orders property of algebraic dynamical systems (2017) (3)
POLYNOMIAL EXTENSIONS OF VAN DER WAERDEN'S (1991) (3)
Sums of Powers in Large Finite Fields: A Mix of Methods (2020) (3)
Simultaneous Diophantine approximation and VIP systems (2005) (3)
An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications (2019) (3)
Translation properties of sets of positive upper density (1985) (3)
Khintchine-type recurrence for 3-point configurations (2022) (3)
Title : An Inverse Theorem for the Uniformity Seminorms Associated with the Action of (2010) (3)
Deterministic functions on amenable semigroups and a generalization of the Kamae-Weiss theorem on normality preservation (2020) (3)
A generalization of Kátai's orthogonality criterion with applications (2017) (2)
Some Historical Remarks and Modern Questions Around the Ergodic Theorem (Dynamics of Complex Systems) (2004) (2)
Iterated differences sets, Diophantine approximations and applications (2020) (2)
Polynomial actions of unitary operators and idempotent ultrafilters (2014) (2)
Characterization of Host-Kra factors through a structural theorem for dynamical nilspaces (2015) (2)
A Hot Spot Proof of the Generalized Wall Theorem (2019) (2)
REACTION-DIFFUSION-ADVECTION MODELS FOR SINGLE AND MULTIPLE SPECIES (2009) (2)
On the density of coprime tuples of the form $(n,\lfloor f_1(n)\rfloor,\ldots,\lfloor f_k(n)\rfloor)$, where $f_1,\ldots,f_k$ are functions from a Hardy field (2016) (2)
Polynomial patterns in subsets of large finite fields of low characteristic (2023) (1)
Popular differences for polynomial patterns in rings of integers (2021) (1)
The Furstenberg–Sárközy Theorem and Asymptotic Total Ergodicity Phenomena in Modular Rings (2020) (1)
IP* Sets in Product Spaces (1996) (1)
Uniqueness of a Furstenberg system (2020) (1)
Ultrafilters across mathematics : international congress, Ultramath 2008: Applications of Ultrafilters and Ultraproducts in Mathematics, June 1-7, 2008, Pisa, Italy (2010) (1)
On the density of coprime tuples of the form (n, [f1(n)],...,[fk(n)]), where f1,...,fk are functions from a hardy field (2017) (1)
On the Polynomial Szemer\'edi Theorem in Finite Commutative Rings (2023) (1)
Joint ergodicity of piecewise monotone interval maps (2022) (1)
On $\{x+y,xy\}$ patterns in large sets of countable fields (2013) (1)
Asymptotic total ergodicity for actions of $F[t]$ and Furstenberg--S\'{a}rk\"{o}zy-type theorems over finite fields and rings (2023) (1)
Polynomials at iterated spectra near zero (2011) (1)
Multiple recurrence and convergence results associated to $\mathbb{F}_{p}^ω$-actions (2013) (1)
Strongly mixing systems are almost strongly mixing of all orders (2020) (0)
Multiple Recurrence in Quasirandom Groups (2014) (0)
Applications of multiplicative number theory to uniform distribution and ergodic Ramsey theory (2017) (0)
Uniform distribution of subpolynomial functions along primes and applications (2019) (0)
Discordant sets and ergodic Ramsey theory. (2020) (0)
Joint normality of representations of numbers: an ergodic approach (2022) (0)
Multiplicative richness of additively large sets in $\mathbb{Z}^d$ (2016) (0)
Juxtaposing $d^*$ and $\bar{d}$ (2020) (0)
V.9 Ergodic Theorems (2010) (0)
Some new multi-cell Ramsey theoretic results (2021) (0)
Juxtaposing combinatorial and ergodic properties of large sets of integers (2022) (0)
S ep 2 01 1 From discrete-to continuous-time ergodic theorems In memory of (2011) (0)
Under- and over-independence in measure preserving systems (2020) (0)
Multiple recurrence and convergence results associated to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{F}}_P (2015) (0)
Simultaneous dense and nondense orbits for commuting maps (2015) (0)
Polynomial recurrence with large intersection over countable fields (2016) (0)
Semi-annual Workshop in Dynamical Systems and Related Topics (2020) (0)
The Distribution of the Particles of a Branching Random Walk (1996) (0)
Multiple recurrence and convergence results associated to $\mathbb{F}_{p}^{\omega}$-actions (2013) (0)
Under- and over-independence in measure preserving systems (2018) (0)
Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory (2012) (0)
Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤk (2014) (0)
A Central Limit Theorem for B–free dynamical systems (2016) (0)

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What Schools Are Affiliated With Vitaly Bergelson?

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