The notion of asymptotic center (or central sequence algebras) has been incredibly useful for distinguishing II$_1$ factors. As such, there are many named concepts describing the asymptotic center, including the super McDuff property, which says that a II$_1$ factor $M$ has II$_1$ factorial relative commutant in an ultrapower. In this talk, we introduce an (ultrapower-free) uniform version of the super McDuff property. We show the uniform super McDuff property is preserved under elementary equivalence and in some sense generic among II$_1$ factors.

This is joint work with Isaac Goldbring, David Jekel, and Srivatsav Kunnawalkam Elayavalli.

Bio: Jenny Pi is a current graduate student at UC Irvine, under supervision of Isaac Goldbring. Her research has mostly been in model theory of II$_1$ factors and free probability.