Math Graduate Student Seminar

Connes' embedding conjecture asserts that a wide class of von Neumann algebras have a certain finite approximation property. It has numerous implications in operator algebras, noncommutative geometry and quantum information theory. We will discuss emerging connections between Connes' embedding conjecture and the ergodic theory of direct products of free groups. These connections are interesting on an abstract level because they relate the 'static' embedding conjecture to dynamics, and on a more practical level because the ergodic theoretic reformulations of the embedding conjecture seem closer to current techniques than the operator algebraic statement.