Free wreath products of quantum groups

• Speaker: Arthur Troupel, CNRS - Université Paris Cité - IMJ-PRG
• Time: 3:10pm to 3:20pm
• Abstract: The free wreath product of quantum groups is a quantum counterpart of the classical wreath product. The definition was made to generalize an isomorphism we have when considering the automorphism groups of finite graphs. In this talk, I will introduce the notion of quantum groups and free wreath products, and talk about the open questions related to them.

On $\ell$-open and $\ell$-closed $C^*$ algebras

• Speaker: Dolapo Oyetunbi, University of Ottawa
• Time: 3:20pm to 3:30pm
• Abstract: A $C^*$ -algebras is $\ell$-open (or $ell$-closed) if the liftable maps from the $C^*$-algebra to any quotient $C^*$ -algebra is a point-norm open (or closed) set. In this talk, we characterize $\ell$-open and $\ell$-closed $C^*$-algebras and deduce that $\ell$-open $C^*$-algebras are $\ell$-closed as conjectured by Blackadar. Moreover, we show that the notion of $\ell$-open $C^*$-algebras and semiprojective $C^*$-algebras coincide for commutative unital $C^*$-algebras.