A powerful theme in the structure theory of locally compact groups is that ‘local’ properties of the group can have ‘global’ implications for the structure of the group. A classical example is given by Lie groups and their locally defined Lie algebras. In this workshop we explore local-to-global mechanisms for locally compact groups acting on discrete structures in two different yet related senses.
In the context of groups acting on graphs, ‘local’ refers to the finite permutation groups that vertex stabilisers induce on incident edges. This concept has led to a remarkable structure theory of certain groups acting on graphs, featuring an interplay between finite and infinite permutation groups. It also relates to the long-standing Weiss conjecture.
In the context of general t.d.l.c. groups, ‘local’ refers to the compact open, hence profinite, subgroups. The way these are commensurated reflects the global structure of the group, and the theory of profinite groups thus has implications for the structure of t.d.l.c. groups.
This workshop aims to foster the exchange of results, examples and questions, as well as to open and strengthen collaborations.