Title: Von Neumann Equivalence
Speaker: Jesse Peterson - Vanderbilt University
Abstract: Two groups are measure equivalent if they have commuting measure-preserving actions on a sigma-finite measure space, such that each group has a finite-measure fundamental domain. We introduce a coarser equivalence, which we call von Neumann equivalence, by allowing the measure space on which the groups act to be non-commutative, i.e., we allow it to be a von Neumann algebra with a semi-finite normal faithful trace. We will show that many "approximation type" properties, (e.g., amenability, property (T)) which are known to be preserved by measure equivalence, are also preserved by von Neumann equivalence. We will also discuss a number of open problems related to this new notion. This is based on joint work with Ishan Ishan and Lauren Ruth.