Michael Björklund: The Lindenstrauss maximal inequality

Ever since Wiener’s generalization of Birkhoff’s ergodic theorem to higher rank abelian groups, the question whether an analogous ergodic theorem holds for all amenable groups has attracted a lot of attention.

Many partial results appeared in the literature until E. Lindenstrauss published his extremely clever solution to this problem in 1999. The gist of Lindenstrauss’ proof is a far-reaching generalization of Hardy-Littlewood’s maximal inequality, which is proved using very innovative random covering lemmata. In this talk I hope to cover Lindenstrauss’ proof of this generalization.