From combinatorics to ergodic theory and back again

Autores: Bryna Kra
Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 57-76
Idioma: inglés
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Resumen
- Multiple ergodic averages, such as the average of expressions like f1(T nx) f2(T 2nx) . . . fk(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.