As you all (may) know, the Connes embedding conjecture was disproven last year. Also, as its Wikipedia page shows, there are multiple reformulations (but it is definitely not an exhaustive list):
- Kirchberg's QWEP conjecture in C*-algebra theory
- Tsirelson's problem in quantum information theory
- The predual of any (separable) von Neumann algebra is finitely representable in the trace class
So, are there any results that depend on the conjecture or any of the above (or any other) reformulation?