Titles and Abstracts of Talks Title: Derivations on Von Neumann Algebras and L 2 -cohomology Title: Maximal Amenable Von Neumann Subalgebras Arising from Amenable Subgroups

Consider a maximal amenable subgroup H in a discrete countable group G. In this talk I will give a general condition implying that the von Neumann subalgebra LH is still maximal amenable inside LG. The condition is expressed in terms of H-invariant measures on some compact G-space. As an example I will show that the subgroup of upper triangular matrices inside SL(n,Z) gives rise to a maximal amenable subalgebra. This talk is based on a joint work with Alessandro Carderi. Lewis Bowen (UT Austin) Title: Equivalence relations acting on bundles of hyperbolic spaces Abstract: Under appropriate properness and local compactness conditions, a measured equivalence relation that acts isometrically on a bundle of hyperbolic spaces has nice properties. For example, every aperiodic hyperfinite subequivalence relation is contained in a unique maximal hyperfinite subequivalence relation and every nonamenable subequivalence relation contains a treeable nonamenable subequivalence relation. I’ll explain this and other nice properties. This is joint work with Sukhpreet Singh. Under appropriate properness and local compactness conditions, a measured equivalence relation that acts isometrically on a bundle of hyperbolic spaces has nice properties. For example, every aperiodic hyperfinite subequivalence relation is contained in a unique maximal hyperfinite subequivalence relation and every nonamenable subequivalence relation contains a treeable nonamenable subequivalence relation. I’ll explain this and other nice properties. This is joint work with Sukhpreet Singh.