Quasi-isometries of group pairs


A recent trend in geometric group theory is to understand the large scale geometry of a group with respect to a collection of subgroups. The objects of study are pairs consisting of a finitely generated group and a finite collection of subgroups, and there is a notion of quasi-isometry of pairs inducing an equivalence. This relation captures classical phenomena in the study of quasi-isometric rigidity and brings up natural questions. The talk will introduce some of these topics and discuss recent results obtained in joint work with Sam Hughes and Luis Sánchez Saldaña.