Groups' approximation and (non) sofic groups

Alex Lubotzky, Minerva Distinguished Visitor, & Weizmann Institute
Fine Hall Common Room

An interesting subarea of group theory deals with the possible approximations of groups by (almost) representations to the finite symmetric groups or finite dimensional unitary groups. A major (still open) problem is whether every group can be approximated by almost homomorphisms to the symmetric groups.

Group stability offers a way to attack such problems. We will observe that this is a form of property testing and will show some success (and some work in progress) to apply ideas from the previous lectures to this problem.