Title: A Recipe for Almost Representations of Groups that are Far from Genuine Representations

 

Abstract: A discrete group is said to be "stable" if every map from the group to unitary matrices that is "almost multiplicative" is "close" to a genuinely multiplicative map. Different notions differ on how to make "almost multiplicative" and "close" more formal. My talk will focus on matricial stability where these notions are defined in terms of the point-operator norm topology, and Frobenius stability, where they are defined in terms of the point-Frobenius topology. I will explain how one can get an "almost multiplicative map" from a 2-cohomology class in operator norm, and use a similar technique to show that finitely generated nilpotent groups are Frobenius stable if and only if they are virtually cyclic.