Spectral gap and definability

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.

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