Titlebook: An Irregular Mind; Szemerédi is 70 Imre Bárány,József Solymosi,Gábor Sági Book 2010 János Bolyai Mathematical Society and Springer-Verlag 2

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Squares In Sumsets,A finite set A of integers is square-sum-free if there is no subset of A sums up to a square. In 1986, Erdős posed the problem of determining the largest cardinality of a square-sum-free subset of .. Answering this question, we show that this maximum cardinality is of order n1/3+0(1).

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Are There Arbitrarily Long Arithmetic Progressions In The Sequence of Twin Primes?,The problem in the title seemed to be out of reach of any methods before 2004. We have still no answer for it, and it is no surprise that we will not answer it in the present work either. However, in the last few years the following developments arose in connection with the above problem. Supported by OTKA Grants K72731, K67676 and ERC-AdG.228005.

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,Towards A Noncommutative Plünnecke-Type Inequality,We relax the assumption of commutativity in certain Plünnecke-type inequalities.

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Imre Bárány,József Solymosi,Gábor SágiSpecial volume on the occasion of Endre Szemeredi‘s 70th birthday - A collection of exceptional papers by world-leading mathematicians, among them several Fields-Medailists - For the first time a poly

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978-3-662-50641-7János Bolyai Mathematical Society and Springer-Verlag 2010

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Book 2010 volume is a celebration of Szemerédi‘s achievements and personality, on the occasion of his seventieth birthday. It exemplifies his extraordinary vision and unique way of thinking. A number of colleagues and friends, all top authorities in their fields, have contributed their latest research papers

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Book 2010sets of the integers, extremal problems in hypergraphs theory, and random graphs, all of them beautiful, Szemerédi type mathematics. It also contains published accounts of the first two, very original and highly successful Polymath projects, one led by Tim Gowers and the other by  Terry Tao.

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https://doi.org/10.1007/978-3-322-83834-6tates of the bonds need not be independent; furthermore, increasing events need not be positively correlated, so new techniques are needed in the analysis. The main new ingredients are a generalization of Harris’s Lemma to products of partially ordered sets, and a new proof of a type of Russo-Seymour- Welsh Lemma with minimal symmetry assumptions.