From combinatorics to ergodic theory and back again

Bryna Kra

From combinatorics to ergodic theory and back again

Bryna Kra^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to conference › Paper › peer-review

11 Scopus citations

Abstract

Multiple ergodic averages, such as the average of expressions like f ₁(Tⁿx) f₂(T²ⁿx). .. f _k(T^knx), 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 language	English (US)
Pages	57-76
Number of pages	20
State	Published - 2006
Event	25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain Duration: Aug 22 2006 → Aug 30 2006

Other

Other	25th International Congress of Mathematicians, ICM 2006
Country/Territory	Spain
City	Madrid
Period	8/22/06 → 8/30/06

Keywords

Arithmetic progressions
Multiple ergodic theorem
Multiple recurrence
Nilsystems

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "From combinatorics to ergodic theory and back again",

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 Szemer{\'e}di'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.",

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author = "Bryna Kra",

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AB - 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.

KW - Arithmetic progressions

KW - Multiple ergodic theorem

KW - Multiple recurrence

KW - Nilsystems

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T2 - 25th International Congress of Mathematicians, ICM 2006

Y2 - 22 August 2006 through 30 August 2006

ER -

From combinatorics to ergodic theory and back again

Abstract

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Keywords

ASJC Scopus subject areas

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