Appears in collection : XVIII International Workshop in Set Theory / XVIII Atelier International de Théorie des Ensembles

The characterization of hyperfinite equivalence relations is a major open problem of descriptive set theory. A similarly notorious open problem is whether every hyper-hyperfinite equivalence relation is hyperfinite. In this talk, I will show that, perhaps surprisingly, a negative answer to the latter implies a negative answer to the former. I will also discuss a recent development connecting Borel amenability to complexity.