It is a classical theorem of Hulanicki from the 60s that a group is amenable if and only if its maximal and reduced C*-algebras are the same.  Similarly, if a groupoid is amenable, Renault showed around 1980 then its maximal and reduced C*-algebras are the same.
In this talk I'll discuss all this, and show that the converse to Renault's theorem is false.  I won't assume any background in amenability or groupoids (or groupoid C*-algebras).

海报