Dynamical systems and Ramsey theory – Ramsey DocCourse Prague 2016

The following notes are from the Ramsey DocCourse in Prague 2016. The notes are taken by me and I have edited them. In the process I may have introduced some errors; email me or comment below and I will happily fix them.

Title: Ergodic theory and amenable groups

Lecturer: Benjamin Weiss

Date: October 31, 2016.

Main Topics: Three equivalent notions of amenability, Basic concepts in ergodic actions, Furstenberg’s Ergodic proof of Szemerédi’s theorem

Definitions: Ergodic action, weak mixing, mixing, Banach limit, amenable group, left invariant mean, paradoxical decomposition, Følner sequence

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