This is an expository survey with two goals. 1) The primary goal is to discuss and highlight
the impact of two recent influential ideas in geometric group theory. The first of which is the …

We show that a quasi-geodesic in an injective metric space is Morse if and only if it is
strongly contracting. Since mapping class groups and, more generally, hierarchically …

We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial
complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of …

Complete topological descriptions of certain Morse boundaries Page 1 Groups Geom. Dyn. 17
(2023), 157–184 DOI 10.4171/GGD/669 © 2023 European Mathematical Society Published by …

We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend
to quasi-isometries of their maximal hyperbolic space. This has two applications, one …

We prove that Morse local‐to‐global groups grow exponentially faster than their infinite‐
index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the context …

We prove several topological and dynamical properties of the boundary of a hierarchically
hyperbolic group are independent of the specific hierarchically hyperbolic structure. This is …

We show that infinite cyclic subgroups of groups acting uniformly metrically properly on
injective metric spaces are uniformly undistorted. In the special case of hierarchically …

We give a general procedure for constructing metric spaces from systems of partitions. This
generalises and provides analogues of Sageev's construction of dual CAT (0) cube …

The aim of this thesis is to obtain a better understanding of the behavior of exponential
growth rates within the class of groups that act acylindrically in a hyperbolic space in the …