From local to global structure  24 - 28 August 2020

08:00 - 17:00
Room : GA 3 21

Organisers

Pierre-Emmanuel Caprace, Université Catholique de Louvain, Institut de Recherche en Mathématiques et Physique (IRMP)

Michael Giudici, The University of Western Australia

Colin Reid, The University of Newcastle, Australia

Stephan Tornier, The University of Newcastle, Australia

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.

Name University Dates of visit
Pierre-Emmanuel Caprace Université Catholique de Louvain, Institut de Recherche en Mathématiques et Physique (IRMP) 24/08/2020 - 28/08/2020
Michael Giudici The University of Western Australia 24/08/2020 - 28/08/2020
Colin Reid The University of Newcastle, Australia 24/08/2020 - 28/08/2020
Stephan Tornier The University of Newcastle, Australia 24/08/2020 - 28/08/2020
Total Guests : 4
Name University Dates of visit
Total Guests : 0