Totally Disconnected Locally Compact Groups via Group Actions (Online) (21w5151)

The Banff International Research Station will host the "Totally Disconnected Locally Compact Groups via Group Actions" workshop in Banff from August 15 to August 20, 2021.

Group actions are a mathematical approach to analysing structures by studying the rearrangements of the elements of the structure that preserve the defining properties of the structure. Indeed, historically, group theory developed primarily as a technique for handling questions concerning the resolution of algebraic equations (the group introduced here by Galois permutes the roots of the equation), and has since become a standard language for formalising
and solving various natural questions from a wide range of mathematics.

Finite permutation groups are understood through combinatorial methods, with a large role played by representation theory, while concepts from logic and topology come to the fore when studying infinite permutation groups. This workshop will bring together researchers on both finite and infinite permutation groups to share techniques and recent advances, but with the main focus being on infinite groups, in particular totally disconnected locally compact groups. These infinite permutation groups have finite sub-degrees and so the theory is intrinsically related to that of finite permutation groups. The subject is advancing on many fronts due to several recent developments, in model theory, in analysis and topology, in number theory and combinatorics, in geometry, and via the numerous applications of the classification of finite simple groups. The timing of this workshop is ideal for a diverse group of researchers to gather and discuss these advances and the future directions.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).