Tue, 12 May 2026
15:00
15:00
L6
Median metric groups
Pénélope Azuelos
(Dept of Maths University of Bristol)
Abstract
Median spaces form a broad and increasingly important class of metric spaces, encompassing both CAT(0) cube complexes and real trees. Finitely generated groups which admit free transitive (or proper cocompact) actions on discrete median spaces — equivalently, on the 0-skeletons of CAT(0) cube complexes — are reasonably well understood. In contrast, much less is known about their continuous analogue: groups acting freely and transitively on connected median spaces. I will present some methods for constructing such actions, focusing on actions on real trees and their products, and discuss some of the surprising behaviours that show up. Even when considering real trees, the class of groups acting on such spaces is vastly more diverse than in the discrete setting: while any simplicial tree admits at most one free vertex transitive action, we will see that there are 2^{2^{\aleph_0}} pairwise non-isomorphic groups which admit a free transitive action on the universal real tree with continuum valence.