Thu, 11 Jun 2026
15:00
15:00
L4
Von Neumann Equivalence Rigidity
Daniel Drimbe
(University of Iowa)
Abstract
The notion of measure equivalence for discrete groups was introduced by Gromov as a measurable counterpart to the geometric notion of quasi-isometry. Measure equivalence is closely connected to the theory of II_1 factors: if groups G and H are measure equivalent, then they admit free ergodic probability measure preserving actions whose associated von Neumann algebras are stably isomorphic. Also, two groups G and H are said to be W*-equivalent if their group von Neumann algebras are stably isomorphic.
More recently, an even coarser equivalence relation between groups, termed von Neumann equivalence, was introduced by Ishan, Peterson, and Ruth; it is implied by both measure equivalence and W*-equivalence. In joint work with Stefaan Vaes, we established a unique factorization theorem for direct products of hyperbolic groups up to von Neumann equivalence.
Looking for a graduate job or internship this summer?
JPMorgan will be running two events in the Mathematical Institute on Wednesday 3rd June. One event is aimed at Prelims and Part A students, the other at Part B and Part C/OMMS students.
If you weren't able to make it to the event in London for Sophie Germain's 250th birthday, the videos from the event are now available online!