
Recent Posts
 Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
 Distal systems and Expansive systems
 Structure of multicorrelation sequences with integer part polynomial iterates along primes
 Tao’s Proof of (logarithmically averaged) Chowla’s conjecture for two point correlations
 A viewpoint on Katai’s orthogonality criterion
Tag Archives: Bergelson
Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications
Vitaly Bergelson, Florian Richter and I have recently uploaded to the arXiv our new paper entitled “Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications”. We establish a new multiple recurrence result (and consequentially a … Continue reading
Posted in Combinatorics, Ergodic Theory, paper, Ramsey Theory
Tagged Bergelson, Hardy fields, nonconventional ergodic averages, Richter
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Optimal intersectivity
In ergodic Ramsey theory, one often wants to prove that certain dynamically defined sets in a probability space intersect (or “recur”) in nontrivial ways. Typically, this is achieved by studying the long term behavior of the sets as the dynamics … Continue reading
Posted in Combinatorics, Probability, Ramsey Theory, Tool
Tagged Bergelson, Dodos, Kanallopoulos, Poincare, Tyros
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Single and multiple recurrence along nonpolynomial sequences
Vitaly Bergelson, Florian Richter and I have recently uploaded to the arXiv our new paper “Single and multiple recurrence along nonpolynomial sequences”. In this paper we address the question of what combinatorial structure is present in the set of return … Continue reading
Posted in Ergodic Theory, paper
Tagged Bergelson, Haland, Nonpolynomial sequences, Richter, Syndetic sets, Thick sets
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An arithmetic van der Corput trick and the polynomial van der Waerden theorem
The van der Corput difference theorem (or trick) was develop (unsurprisingly) by van der Corput, and deals with uniform distribution of sequences in the torus. Theorem 1 (van der Corput trick) Let be a sequence in a torus . If … Continue reading
Measure preserving actions of affine semigroups and {x+y,xy} patterns
Vitaly Bergelson and I have recently submitted to the arXiv our paper entitled `Measure preserving actions of affine semigroups and patterns’. The main purpose of this paper is to extend the results of our previous paper, establishing some partial progress … Continue reading
New polynomial and multidimensional extensions of classical partition results
Vitaly Bergelson, John Johnson and I recently uploaded to the arXiv a paper entitled “New polynomial and multidimensional extensions of classical partition results“. In this post I will give some motivating examples for the results in the paper. To keep … Continue reading
Posted in Combinatorics, paper, Ramsey Theory
Tagged Bergelson, Deuber, Johnson, monochromatic configurations, polynomials, Rado
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Convergence and Recurrence of Z actions
Ergodic Ramsey Theory started with Furstenberg’s proof of Szemeredi’s theorem in arithmetic progressions in 1977. Through a correspondence principle, Furstenberg realized that Szemeredi’s theorem follows from a dynamical statement: for every invertible, ergodic measure preserving transformation of a probability space … Continue reading
Posted in Ergodic Theory, State of the art
Tagged Austin, Bergelson, convergence, Conze, ergodic theorem, Furstenberg, Host, Katznelson, Kra, Leibman, Lesigne, Poincare, recurrence, Tao, Walsh
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On {x+y,xy} patterns in large sets of countable fields
Vitaly Bergelson and I have recently uploaded to the arXiv our joint paper `On patterns in large sets of countable fields‘. We prove a result concerning certain monochromatic structures in countable fields and a corresponding density version. Schur’s Theorem, proved … Continue reading
Brauer’s theorem and a coloring trick of Bergelson
— 1. Introduction — Ramsey theory concerns essentially two types of results: coloring and density results. Coloring results state that given a finite partition of some structured set (usually ) one of the cells in the partition still has some … Continue reading
Posted in Combinatorics, Ergodic Theory, Ramsey Theory, Tool
Tagged Bergelson, coloring, coloring trick, density, ramsey theory, Szemeredi's theorem, van der waerden
3 Comments