From combinatorics to ergodic theory and back again

Bryna R Kra*

*Corresponding author for this work

Research output: Contribution to conferencePaper

10 Scopus citations

Abstract

Multiple ergodic averages, such as the average of expressions like f 1(Tnx) f2(T2nx). .. f k(Tknx), were first studied in the ergodic theoretic proof of Szemerédi's Theorem on arithmetic progressions. It turns out that all constraints on such averages (in a sense that we describe) have an algebraic character, arising from identities in nilpotent groups. We discuss these averages, several generalizations, and combinatorial implications of the results.

Original languageEnglish (US)
Pages57-76
Number of pages20
Publication statusPublished - Dec 1 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006

Other

Other25th International Congress of Mathematicians, ICM 2006
CountrySpain
CityMadrid
Period8/22/068/30/06

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Keywords

  • Arithmetic progressions
  • Multiple ergodic theorem
  • Multiple recurrence
  • Nilsystems

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Kra, B. R. (2006). From combinatorics to ergodic theory and back again. 57-76. Paper presented at 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain.