Uniformity norms on L^{infty} and applications

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• Bernard Host, Marne-le-Vallee
• Tuesday 12 February 2008, 16:00-17:00
• MR13, CMS.

If you have a question about this talk, please contact Ben Green.

A key tool in recent advances in understanding patterns like arithmetic progressions in subsets of the integers is certain norms or seminorms. One example is the norms on Z/NZ introduced by Gowers, and another example is seminorms on bounded functions on a meaure preserving system. We introduce similar seminorms on L^\infty(Z) and study their relation with a class of sequences (the nilsequences) arising from homogeneous spaces of nilpotent Lie groups. We give several application to ergodic theory.

This talk is part of the Discrete Analysis Seminar series.

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