An equation is stable if an almost-solution (or a solution of the corresponding inequality) is close to an exact solution. For example, xyx-1y-1=1 is stable if almost commuting matrices are, in the given norm and independently of the matrix size, close to matrices that commute. Over the past few years, the topic has flourished rapidly, expanding in many exciting directions. Focusing on permutation matrices, we give an introduction to the topic, outline recent developments, and suggest a few open problems.
Based on joint works with Liviu Paunescu (Bucharest).
