Schedule
All times are in British Summer Time. All talks take place in Room 2.04 of the Fry Building and on Zoom.
9.00 a.m.–9.05 a.m.
Registration
9.05 a.m.–9.45 a.m.
Thomas Ng (Technion)
What is an HHG?
We will introduce hierarchically hyperbolic groups with an emphasis on examples. In particular, we will see natural operations which preserve hierarchical hyperbolicity as well as more exotic examples that still share the same structure. By focusing on these examples we hope to motivate key aspects in the axiomatic definition of HHG.
9.50 a.m.–10.30 a.m.
Alexander Rasmussen (University of Utah)
Hyperbolic actions of metabelian groups
Classifying the actions of a fixed group on different hyperbolic metric spaces is a natural but typically very difficult problem. Recently, several authors have classified the hyperbolic actions of several families of classically-studied metabelian groups. In this talk we will describe how commutative algebra may be used as a tool to approach these classification problems in a uniform way, and extend the classifications to larger families of metabelian groups.
Break 10.30 a.m.–11.00 a.m.
11.00 a.m.–11.40 p.m.
Sam Hughes (University of Oxford)
Hierarchical hyperbolicity vs biautomaticity
In this talk we will settle the question of whether hierarchically hyperbolic groups are biautomatic.
11.45 a.m.–12.25 p.m.
Harry Petyt (University of Bristol)
The top of an HHG structure
In this talk we'll discuss what possible shapes an HHG structure can have and what this tells us about groups that admit one. Based on joint work with Davide Spriano.
Lunch 12.30 p.m.–1.30 p.m.
1.30 p.m.–2.30 p.m.
Mark Hagen (University of Bristol)
What is combinatorial hierarchical hyperbolicity?
The notion of hierarchical hyperbolicity is a useful tool for understanding the geometry of many groups, but the definition is long --- hence often difficult to verify for examples --- and often quite technical to use. Combinatorial hierarchical hyperbolicity is designed to be a more user-friendly interface with hierarchical hyperbolicity. The idea is, roughly, that naturally-occurring hyperbolic simplicial complexes on which a given group acts can often encode a hierarchically hyperbolic structure when one looks at links of the simplices. I will explain the definition of a "combinatorial HHS" and how constructing a combinatorial HHS structure for a space/group verifies hierarchical hyperbolicity (and hence its consequences), discuss a general template for building combinatorial HHS structures, illustrate it with a concrete example, and mention a few recent cases where this viewpoint was used.
2.40 p.m.–3.40 p.m.
Alexandre Martin (Heriot-Watt University)
Where to find combinatorial HHSs? The case of Artin groups
Combinatorial hierarchical hyperbolicity provides a new way to show that a group is hierarchically hyperbolic, by means of the existence of a suitable hyperbolic complex associated to that group. But given our favourite group, how do we find such a complex? In this talk, I will present a template for constructing such HHSs, and I will illustrate it with the case of right-angled Artin groups and extra-large type Artin groups. This is joint work with Mark Hagen and Alessandro Sisto.
Break 3.45 p.m.–4.15 p.m.
4.15 p.m.–5.15 p.m.
Alessandro Sisto (Heriot-Watt University)
(Hierarchically) hyperbolic quotients of mapping class groups
I will explain how to use the combinatorial HHS machinery to prove that quotients of mapping class groups by suitable powers of Dehn twists are hierarchically hyperbolic. I will also discuss (potential) further quotients.