Analysis Seminar

Aareyan Manzoor, University of Waterloo

There is a non-Connes embeddable equivalence relation

Connes embeddability of a group is a finite dimensional approximation property. It turns out this property depends only on the so-called group von Neumann algebra. The property can be extended to all von Neumann algebras. The fact that there is a von Neumann algebra without this property was proved in 2020 using the quantum complexity result MIP*=RE. It is still open for group von Neumann algebras. I will discuss the best-known partial result, which is that there is a group action without this property. In particular, this implies the negation to the Aldous-Lyons conjecture, a big problem in probability theory

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