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 …

" C*-approximation theory has provided the foundation for many of the most important
conceptual breakthroughs and applications of operator algebras. This book systematically …

Around 1990 George Elliott proposed a bold conjecture that a certain subcategory c of
separable nuclear C∗-algebras could be classified by K-theoretic invariants Ell which …

Probably the most famous of Grothendieck's contributions to Banach space theory is the
result that he himself described as “the fundamental theorem in the metric theory of tensor …

" These notes are centered around the equivalence of two major open problems: one
formulated by Connes (1976), about traces and ultraproducts of von Neumann algebras, the …

This is an introductory survey of the emerging theory of two new classes of (discrete,
countable) groups, called hyperlinear and sofic groups. They can be characterized as …

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 …

In his celebrated paper in 1976, A. Connes casually remarked that any finite von Neumann
algebra ought to be embedded into an ultraproduct of matrix algebras, which is now known …

We prove that Connes' Embedding Conjecture holds for the von Neumann algebras of sofic
groups, that is sofic groups are hyperlinear. Hence we provide some new examples of …

We study factorization and dilation properties of Markov maps between von Neumann
algebras equipped with normal faithful states, ie, completely positive unital maps which …