Corpus ID: 237940159

The Connes Embedding Problem: A guided tour

@article{Goldbring2021TheCE,
  title={The Connes Embedding Problem: A guided tour},
  author={Isaac Goldbring},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.12682}
}
  • Isaac Goldbring
  • Published 26 September 2021
  • Computer Science, Mathematics, Physics
  • ArXiv
The Connes Embedding Problem (CEP) is a problem in the theory of tracial vonNeumann algebras and askswhether or not every tracial vonNeumann algebra embeds into an ultrapower of the hyperfinite II1 factor. The CEP has had interactions with a wide variety of areas of mathematics, including C-algebra theory, geometric group theory, free probability, and noncommutative real algebraic geometry (to name a few). After remaining open for over 40 years, a negative solution was recently obtained as a… Expand

References

SHOWING 1-10 OF 57 REFERENCES
Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of manyExpand
On Ultraproduct Embeddings and Amenability for Tracial von Neumann Algebras
We define the notion of self-tracial stability for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes Embedding Problem is self-tracially stable if andExpand
Connes' embedding problem and Tsirelson's problem
We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEPExpand
Ultraproducts, QWEP von Neumann Algebras, and the Effros-Mar\'echal Topology
Based on the analysis on the Ocneanu/Groh-Raynaud ultraproducts and the Effros-Mar\'echal topology on the space vN(H) of von Neumann algebras acting on a separable Hilbert space H, we show that for aExpand
Generic orbits and type isolation in the Gurarij space
We study the question of when the space of embeddings of a separable Banach space $E$ into the separable Gurarij space $\mathbf G$ admits a generic orbit under the action of the linear isometry groupExpand
A computability-theoretic reformulation of the Connes Embedding Problem
The Connes Embedding Problem (CEP) asks whether every separable II_1 factor embeds into an ultrapower of the hyperfinite II_1 factor. We show that the CEP is equivalent to the computability of theExpand
Connes' embedding conjecture and sums of hermitian squares
We show that Connes' embedding conjecture on von Neumann algebras is equivalent to the existence of certain algebraic certificates for a polynomial in noncommuting variables to satisfy the followingExpand
TSIRELSON'S PROBLEM AND KIRCHBERG'S CONJECTURE
Tsirelson's problem asks whether the set of nonlocal quantum correlations with a tensor product structure for the Hilbert space coincides with the one where only commutativity between observablesExpand
Building Models by Games
TLDR
A general method for building infinite mathematical structures, and its applications in algebra and model theory are introduced, and a wide variety of algebraic applications are studied. Expand
About the Connes Embedding Conjecture---Algebraic approaches---
This is an expanded lecture note for "Masterclass on sofic groups and applications to operator algebras" (University of Copenhagen, 5-9 November 2012). It is about algebraic aspects of the ConnesExpand
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