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 …

We prove that faithful traces on separable and nuclear C^*-algebras in the UCT class are
quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the …

Partial dynamical systems, originally developed as a tool to study algebras of operators in
Hilbert spaces, has recently become an important branch of algebra. Its most powerful …

Ergodic theory in its broadest sense is the study of group actions on measure spaces.
Historically the discipline has tended to concentrate on the framework of integer actions, in …

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 …

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to
have the unique trace property if its reduced C*-algebra has a unique tracial state. A …

A classification theorem is obtained for a class of unital simple separable amenable Z-stable
C*-algebras which exhausts all possible values of the Elliott invariant for unital stably finite …

For a discrete group G, we consider the minimal C*-subalgebra of ℓ∞(G) that arises as the
image of a unital positive G-equivariant projection. This algebra always exists and is unique …

" 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 …