Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

We will start with classical questions from 70's which ask whether almost commuting matrices have to be close to exactly commuting ones. Of course the notions of "almost" and "close" need clarification and generally can vary with the specific problem in question. There is also a quantifying aspect and an algorithmic issue in searching for the commuting matrices whenever they do exist. Besides being popular in Linear Algebra and Operator Theory, questions of this kind arise also in Quantum Information Theory. A further development of such questions comes from Group Theory and asks whether almost representations of a group have to be close to actual representations. We will present results on that from joint work with Don Hadwin.