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Title: Von Neumann equivalence rigidity

Abstract: The notion of measure equivalence of discrete groups has been introduced by Gromov as a measurable variant of the topological notion of quasi-isometry. Measure equivalence of groups is tightly related to the theory of II_1 factors: if G and H are measure equivalent, then they admit free ergodic probability measure preserving action for which their von Neumann algebras are stably isomorphic. Also, two groups G and H are called W*-equivalent if their group von Neumann algebras are stably isomorphic.

A few years ago, it was discovered that there is an even coarser notion of equivalence of groups, coined von Neumann equivalence, which is implied by both measure equivalence and W*-equivalence. In a work in progress with Stefaan Vaes we prove a unique factorization for products of hyperbolic groups up to von Neumann equivalence.

Zoom link to live sessions: https://uiowa.zoom.us/j/95316149275

UICapture link to recordings:

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