Undergraduate Math Club Seminar

Start with a finitely presented group G. Suppose we have an assignment of linear operators to the generators which "almost" form a group representation, in the sense that they satisfy the group relations up to some small error. One way to get such an assignment is to start with a group representation and then add small error terms to the image. Is this the only possibility?

If G is finite, the answer is yes! We'll sketch a proof of this "stability" theorem and then discuss applications to robust self-testing in pseudotelepathy games. For the application, we'll introduce a graphical calculus for proving equations in finitely presented groups, sometimes called "group pictures" or "van Kampen diagrams". Based on joint work with Andrea Coladangelo and Thomas Vidick.