A group is said to be Frobenius stable if every function from the group to unitaries that is "almost multiplicative" in the point-Frobenius norm topology is "close" to a genuine representation of the group in the same topology. In this talk, I will summarize my proof that finitely generated nilpotent groups are Frobenius stable if and only if they are virtually cyclic. I will also explain what the same techniques say about operator norm. This generalizes explicit counterexamples developed by Voiculescu and Kazhdan.