
Recent Posts
 An arithmetic van der Corput trick and the polynomial van der Waerden theorem
 Piecewise syndetic sets, topological dynamics and ultrafilters
 Measure preserving actions of affine semigroups and {x+y,xy} patterns
 Szemerédi Theorem Part VI – Dichotomy between weak mixing and compact extension
 Gaussian systems
Category Archives: Ramsey Theory
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
Szemerédi Theorem Part VI – Dichotomy between weak mixing and compact extension
This is the sixth and final post in a series about Szemerédi’s theorem. In this post I complete the proof of the Multiple Recurrence Theorem, which I showed in a previous post of this series to be equivalent to Szemerédi’s … Continue reading
Posted in Ergodic Theory, Ramsey Theory
Tagged Compact extensions, joinings, Szemeredi's theorem, weak mixing
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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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A proof of Deuber’s theorem using HalesJewett’s theorem
In my previous post I explained how Rado’s theorem follows from Deuber’s theorem (which in turn gives a little more than Rado’s theorem, in one direction). The main purpose of this post is to give a full proof of Deuber’s … Continue reading
Rado’s theorem and Deuber’s theorem
In this post I talk about (and prove) a fundamental theorem of Rado in Ramsey’s theory. I will prove “half” of the theorem and will postpone the second part of the proof to a future post. To better appreciate Rado’s … Continue reading
HalesJewett and a generalized van der Warden Theorems
The HalesJewett theorem is one of the most fundamental results in Ramsey theory, implying the celebrated van der Waerden theorem on arithmetic progressions, as well an its multidimensional and IP versions. One interesting property of the HalesJewett’s theorem is that … Continue reading