Alessandro Sisto

Mapping class groups mod powers of Dehn twists

Quotients of mapping class groups by large powers of Dehn twists have shown up naturally in rather different contexts, from topological quantum field theories to small-cancellation theory. I will give an overview of what we know and don't know about these quotients, what they have been used for, and their connections with famous open problems, including residual finiteness of hyperbolic groups and the congruence subgroup property for mapping class groups.