In modern geometric group theory, knowing whether a group is amenable or not is a crucial distinction. This has for example in the case of finitely generated groups an impact on how the growth of balls in the group's Cayley graph (a graph isometric to the group) behave. A key indicator of amenability are Følner sequences: by constructing an explicit sequence of subsets of the group, one is able to prove amenability.
However, amenability is not a notion limited to the finitely generated/discrete world: it is also an interesting notion to study groups acting over riemannian manifolds (the mathematical object used in geometry to describe curved spaces). In this talk, we will discuss how a particular riemannian manifold, the Sol geometry, can be equiped with a group structure and how to prove its amenability using Følner sequences.
No prior knowledge of geometric group theory or riemannian geometry is required to attend this talk.
