Asymptotic freeness in tracial ultraproducts

I will present novel freeness results in ultraproducts of tracial von Neumann algebras. As a particular case, I will show that if a and b are the generators of the free group F_2, then the relative commutants of a and b in the ultraproduct of the free group factor are free with respect to the ultraproduct trace. The proof is based on a surprising application of Lp-boundedness results of Fourier multipliers in free group factors for p > 2. I will describe applications of these results to absorption and model theory of II_1 factors. This is joint work with Adrian Ioana.