Group Theory Seminar

Monday, January 29, 2018 11:30 am - 11:30 am EST

Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo

"Problems on sofic and hyperlinear groups"

A sofic group is one that can be locally approximated by finite groups; it is equivalent to embed into a "metric ultraproduct'' of finite groups. A hyperlinear group is the same thing except with unitary matrix groups instead of finite ones. So every sofic group is hyperlinear, but it is still standing whether these classes are the same. In fact nobody knows even one example of a group that is not sofic or hyperlinear!

Sofic/hyperlinear groups are amongst the largest classes of groups for which various famous problems have been verified: Connes's embedding problem, Gottschalk surjunctivity, and Kaplansky's group rings problems, amongst others --- so the problems in soficity can give solutions for even some of the biggest conjectures in other subjects. I'll learn about these and let you know what I find, and as the semester progresses, let's try to get our hands dirty with these groups and see what the field is like.

MC 5479