Eduard Einstein: Relatively Geometric Actions on CAT(0) Cube Complexes

The study of hyperbolic and relatively hyperbolic groups acting on CAT(0) cube complexes has produced exciting recent results in geometric group theory. I will talk about a new kind of action of a relatively hyperbolic group on a CAT(0) cube complex called a relatively geometric action. In joint work with Daniel Groves, we develop analogues of tools used to construct and study geometric actions of hyperbolic and relatively hyperbolic groups on CAT(0) cube complexes, including a relatively geometric version of Agol's Theorem. I will also discuss some of the structural theorems we hope to prove and a potential application to the Relative Cannon Conjecture.