# Amitsur seminar: Benjamin Bachner (HUJI), Sprinzak 116

Title:Non-stability of $Z^2$ and group cohomology
Abstract: Given two unitary matrices that almost commute, is it necessarily the case that they are close to two exactly commuting unitary matrices? It turns out that the answer depends on the matrix norm one works with. We introduce the study of the stability of a group with respect to a matrix norm, and the connection of this question with the stability of $Z^2$. We prove that for the $p$-Schetten norm, the answer is negative, and present a newer, conceptual proof using group cohomology.