Geometric Group Theory Seminar
Title: A random walk through hierarchical hyperbolicity, and applications to mapping class group quotients.
Speaker: Giorgio Mangioni
University: Heriot-Watt University
Abstract:
Hierarchically hyperbolic groups (HHG) generalise both mapping class groups of surfaces and cubulated groups, offering a common framework where one can use tools from both worlds. In the first talk we shall give a gentle, handwavy introduction to what an HHG is, highlighting the geometric intuitions. We then show that random quotients of HHGs are still HHGs, which is evidence towards the fact that this class of groups is pretty wide. In the second talk we focus on mapping class groups, which are the motivating examples of HHGs, and show how their fantastic algebraic/geometric/combinatorial features are inherited by their random quotients. The novel material is based on joint works with Abbott- Berlyne-Ng-Rasmussen, and (behind the scenes) Sisto.
