Zero-dimensional Symmetry in honour of George Willis

Locally compact groups play a central role in mathematics as they naturally appear in various fields, capturing the symmetry of mathematical objects. The study of locally compact groups naturally splits into two cases: the connected case and the totally disconnected case.

The structure of connected locally compact groups has been determined: by classical results of Gleason-Yamabe and Montgomery-Zippin it is known that connected locally compact groups are inverse limits of Lie groups. On the other hand, the general structure of totally disconnected locally compact (tdlc) groups is still far from being fully understood and the study of tdlc groups is a very active field of research.

For a long time, the only significant result about the structure of tdlc groups was van Dantzig’s theorem from 1936, stating that every tdlc group admits a neighborhood basis of the identity consisting of compact open subgroups. The study of tdlc groups was brought back to the spotlight in 1994 by George Willis by his seminal paper on the scale function and its applications to the structure theory of tdlc groups, now known as Willis theory.

The aim of this workshop is to celebrate George Willis’ work, his numerous contributions to mathematics, and to bring together experts from various fields of research related to the study of tdlc groups, ranging from functional analysis, representation theory, combinatorics, and geometric group theory.

This workshop is supported by AMSI and AustMS through the AMSI-AustMS Workshop Funding.