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This preprint from yesterday claims to prove that Connes Embedding Conjecture fails.

Since the paper is from outside Operator Algebras (Computer Science/Quantum Computing) and they actually work on Tsirelson's Problem, it would be nice to have some feedback from experts from the Operator Algebra side on both the validity and the consequences of this.

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    $\begingroup$ I'm sure it would be nice. This is not the place for it though. If you have a specific question about the preprint, you might get an expert to weigh in on that point. Gerhard "Discussing Preprints Is Off-Topic Here" Paseman, 2020.01.14. $\endgroup$
    – Gerhard Paseman
    Commented Jan 14, 2020 at 20:22
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    $\begingroup$ The authors are certainly very pedigreed and have been working on the problem for a long time and have a history of making partial progress. Alas, I am also an outside but I did find this blog post by one of the authors extremely enjoyable: mycqstate.wordpress.com/2020/01/14/a-masters-project $\endgroup$
    – Asvin
    Commented Jan 14, 2020 at 20:42
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    $\begingroup$ There is some discussion on Scott Aaronson's blog. $\endgroup$
    – Tobias Fritz
    Commented Jan 14, 2020 at 20:51
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    $\begingroup$ Martin: maybe fire off an email to Vern or Taka, as operator algebraists and operator-space experts who have worked on the links between what-I-shall-always-refer-to-as-Kirchberg's-QWEP-conjecture and Tsirelson's problem? $\endgroup$
    – Yemon Choi
    Commented Jan 14, 2020 at 21:53
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    $\begingroup$ there is equivalences proved by Klep and Schweighofer (with later corrections by more people) between Connes Embedding Conj. and existence of certain decompositions of "positive polynomials in matrix variables" (arxiv.org/abs/math/0607615, fmf.uni-lj.si/~klep/rcec-19jul13.pdf), which are sort of "pure algebra". It would also be interesting to know what kind of said "positive polynomials" arise from that preprint that do not admit these decompositions. $\endgroup$
    – Dima Pasechnik
    Commented Jan 17, 2020 at 13:24

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