David Kerr: Tower decompositions for free actions of amenable groups

Recently Downarowicz, Huczek, and Zhang proved that every discrete amenable group can be tiled by translates of finitely many Følner sets with prescribed approximate invariance. I will show how this can be used to strengthen the Rokhlin lemma of Ornstein and Weiss, with applications to topological dynamics and the classification program for simple separable nuclear C*-algebras.