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DTSTAMP:20220615T210000Z
DTSTART:20220615T210000Z
DTEND:20220615T210000Z
SUMMARY:Colloquium/Zuchovitzky prize lecture: Or Shalom (HUJI)
DESCRIPTION:*Title:* Structure theorems in ergodic theory and inverse theorems in \nadditive combinatorics.\n*Abstract:* Szemeredi's theorem asserts that in every subset of the natural \nnumbers of positive density one can find an arithmetic progression of \narbitrary length. In 2001, Gowers gave a quantitative proof for this theorem. \nA key definition in his work are the Gowers norms which measure the \nrandomness of subsets of the natural numbers. Inspired by Furstenberg's \nergodic theoretical proof of Szemeredi's theorem, Gowers proved the following \ndichotomy: Either the given set is close to a random set with respect to \nthese norms, or it admits some algebraic structure. Gowers then proved that \nin each of these cases Szemeredi's theorem holds. Later, Host and Kra studied \nthe structure of certain ergodic systems associated with an infinitary \nversion of the Gowers norms. Inspired by their work, Green, Tao and Ziegler \nimproved Gowers' structure theorem showing that a function (or a set) with \nlarge Gowers norm must ...
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