Department of

September 2018 October 2018November 2018Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We ThFrSa 1 1 2 3 4 5 6 1 2 3 2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10 9 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 151617 16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 23 24 25 26 27 28 29 28 29 30 31 25 26 27 28 29 30 30

Friday, October 12, 2018

**Abstract:** We read through "Følner tilings of actions of amenable groups" by C. Conley et al [arXiv]. In this third talk, I will introduce the notion of Banach density and prove the main theorem about the existence of Følner tilings a.e. using the Banach density version of the Rokhlin lemma (to be proven) and the Lyons–Nazarov matching theorem (proven last time).