
Recent Posts
 Affine Images of Infinite sets
 Additive transversality of fractal sets in the reals and the integers
 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
Category Archives: paper
Additive transversality of fractal sets in the reals and the integers
Daniel Glasscock, Florian Richter and I have just uploaded to the arXiv our new paper entitled “Additive transversality of fractal sets in the reals and the integers”. In this paper we introduce a new notion of fractal sets of natural … Continue reading
Posted in Combinatorics, Number Theory, paper
Tagged Furstenberg, Glasscock, Hochman, integer dimension, integer fractal, Lindenstrauss, Meiri, Peres, Richter, Shmerkin, transversality, Wu
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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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Structure of multicorrelation sequences with integer part polynomial iterates along primes
Andreas Koutsogiannis, Anh Le, Florian Richter and I have just uploaded to the arXiv a new paper entitled “Structure of multicorrelation sequences with integer part polynomial iterates along primes”. This short paper establishes a natural common extension of our earlier … Continue reading
Posted in Ergodic Theory, paper, State of the art
Tagged Koutsogiannis, Le, multicorrelation sequences, nilsequences, Richter
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A proof a sumset conjecture of Erdős
Florian Richter, Donald Robertson and I have uploaded to the arXiv our paper entitled A proof a sumset conjecture of Erdős. The main goal of the paper is to prove the following theorem, which verifies a conjecture of Erdős discussed … Continue reading
Posted in Combinatorics, paper
Tagged density, erdos, Richter, Robertson, StoneCech compactification, sumset, Ultrafilters, weak mixing
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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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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
Large subsets of discrete hypersurfaces in Z^d contain arbitrarily many collinear points
— 1. Introduction — Recently, Florian Richter and I uploaded to the arXiv our paper titled `Large subsets of discrete hypersurfaces in contain arbitrarily many collinear points’. This was the outcome of a fun project which started when we learned … Continue reading
Posted in Analysis, Combinatorics, paper
Tagged Banach density, collinear points, Lipschitz, Pomerance, Rademacher's theorem, Richter
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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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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