[Turkmath:5637] Galatasaray Üniversitesi Genel Seminerleri

[özge ülkem]

Merhabalar,

25 Mayıs Çarşamba günü saat 15.00'de Koç Üniversitesi'nden Asgar Jamneshan Galatasaray Üniversitesi'nde bir konuşma verecektir. Konuşma Microsoft Teams üzerinden online olarak yapılacaktır. İlgilenenler konuşma linki için ozgeulkem at gmail.com adresine mail atabilirler. Konuşmanın detaylarını aşağıda bulabilirsiniz.

Sevgiler,
Özge Ülkem

Title: The structure of arbitrary Conze-Lesigne systems

Abstract: Conze-Lesigne systems are abelian measure-preserving dynamical systems which are isomorphic to their second Host-Kra-Ziegler factors. These factors (and their versions of higher order) are relevant ​in multiple recurrence and related topics in additive combinatorics (e.g. Szemeredi's theorem). In this talk, we present a structure theorem for Conze-Lesigne systems for actions of an arbitrary countable discrete abelian group, describing such systems as an inverse limit of translational systems G/L, where G is a locally compact nilpotent group of nilpotency class 2 and L is a lattice in G. Such structure theorems were previously known in the important special cases of finitely generated abelian groups by work of Conze and Lesigne and direct sums of finite fields by work of Bergelson, Tao, and Ziegler. We will review some of this literature by way of illustrating examples. If time permits, we present an application of our structure theorem to give a qualitative proof of the inverse theorem for the Gowers U^3-uniformity norm of an arbitrary finite abelian group via a correspondence principle. This talk is based on work jointly with Shalom and Tao. I will introduce and motivate the topic to a general mathematical audience in the first half of my talk.



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