Colloquium, Mathematical Sciences

Abstract: For an(n infinite) group G with n generators, a representation consists of a choice of n invertible matrices that satisfy certain relations. An approximate representation is a choice of n matrices that approximately satisfy these relations. An active area of research recently focuses on whether any approximate representation has to be close to an actual representation, i.e. if any approximate solution to the equations can be perturbed to an honest solution.

The answer is ‘sometimes’. More precisely, there are topological invariants that tell you exactly when such a perturbation is possible, at least in well-behaved enough situations. I’ll try to explain how this works, using appropriate invariants of an analytic and topological nature. I’ll also try to give a rough idea of how the Baum-Connes conjecture, which relates all this to index theory of elliptic differential operators, comes into play.

"Fika" is served at 15.00-15.28 in the lunch room.