Elek Gábor: Uniform Hyperfiniteness

Előadó: Elek Gábor:

Cím: Uniform Hyperfiniteness

Absztrakt: In 1981, Connes, Feldman and Weiss proved that for measure preserving actions (or measured graphs) amenability and hyperfiniteness are equivalent. It is still open whether the equivalence holds for Borel graphs.

I will talk about two recent results of mine. The first is the solution of the  Uniform Local Amenability Conjecture of Brodzki, Niblo, Spakula, Willett and Wright. The second is the equivalence of amenability and hyperfiniteness in the uniform category. It turns out that the results are strongly related.