Isaac Goldbring - University of California, Irvine (UCI) Spectral gap is an important notion in the theory of unitary group representations as well as in the theory of II_1 factors, in particular in Popa’s successful deformation/rigidity theory. In this talk, I’ll briefly explain the connection between spectral gap and the very important model-theoretic notion of definable set. I will also present some applications of this connection. It is my hope that this link is merely the beginning of a fruitful model-theoretic study of the aforementioned deformation/rigidity theory.