T.d.l.c. groups can generally be realised as groups of isometries of locally finite connected graphs, and this viewpoint brings geometry to the investigation of t.d.l.c. groups. Not only are isometry groups of trees and buildings key examples of t.d.l.c. groups, but general results about group structure are related to global metric properties of graphs such as shortest paths, flatness and growth. A critical question is to determine when the isometry group of a vertex-transitive graph is not discrete.
Similarly, natural actions of t.d.l.c. groups on compact spaces, such as the space of closed subgroups or the boundary of a graph, bring ideas from dynamics to the investigation of the groups. Dynamical notions such as invariant random subgroups have a role to play in this investigation.
At this workshop experts on geometry, dynamics and group theory will pool their knowledge to address problems of shared interest.