Noncommutative Geometry Seminar

A II_1 factor is an infinite dimensional von Neumann algebra which has infinite center and admits a trace. As I will recall, examples of II_1 factors arise naturally from countable groups (with infinite conjugacy classes), and their measure preserving actions on probability spaces. I will present a recent result showing the existence of uncountably many separable II_1 factors whose ultrapowers, with respect to arbitrary ultrafilters, are pairwise non-isomorphic. More precisely, the families of non-isomorphic II_1 factors originally introduced by McDuff (1969) are such examples. This is joint work with Remi Boutonnet and Ionut Chifan.