SDU Operator Algebras Seminar

Title: Cantor correlations

Abstract: A non-local game is one where two players play cooperatively against a referee, trying to convince the latter of the joint possession of a certain predescribed knowledge, without any ingame communication allowed. When considering the infinite repetition of G, Cantor spaces arise naturally as infinite cartesian products of finite sets. In this talk, we introduce no-signalling correlations and subclasses thereof over a quadruple of Cantor spaces and describe them as states on tensor products of inductive limits of operator systems. En route, we establish a natural approximation scheme for Cantor correlations using finite correlations acting on the finite components. We introduce Cantor games, canonically associate one to a sequence of finite input/output games and show that the numerical sequence of values of the games converges to the value of the Cantor game. Time permitted, we will discuss synchronous and bisynchronous Cantor correlations and their applications to quantum symmetries of Cantor graphs and factorizable maps on the C*-algebra of compact operators. Based on joint work with Alexandros Chatzinikolaou, Ivan Todorov and Lyudmila Turowska.