# Scott Schneider: Commuting endomorphisms and hypersmooth equivalence relations, III

Thursday, October 6, 2016, from 4 to 5:30pm
East Hall, room 3096

Speaker: Scott Schneider (University of Michigan)

Title: Commuting endomorphisms and hypersmooth equivalence relations, III

Abstract:

An equivalence relation E is hypersmooth (hyperfinite) if E is the union of an increasing sequence of smooth (finite) Borel equivalence relations. In the mid 80s, Weiss proved that the equivalence relation generated by a finite family of commuting Borel automorphisms is hyperfinite, and in the mid 90s, Dougherty, Jackson, and Kechris proved that the equivalence relation generated by a single Borel endomorphism is hypersmooth. We will generalize both results to show that the equivalence relation generated by a finite family of commuting Borel endomorphisms is hypersmooth. As is typical in this area, the proof will involve the construction of a suitable family of Borel marker sets. This is the third, and last, of this series of talks.