Totally disconnected locally compact (TDLC) groups naturally appear in various branches of mathematics as they capture the structure of symmetries of various mathematical objects, so it is natural to ask for a way of computing in such groups. Unfortunately, there is no formal framework for computation in TDLC groups and nor can there be one, as these groups are uncountable. However, one can hope to develop a formal framework of approximations analogous to how real numbers can be approximated by rational numbers with arbitrary precision.
Locally, TDLC groups are profinite, meaning that they can be understood through sequences of finite groups that increase in size. Computing with larger and larger finite groups would provide more and more precise approximations of local structure of TDLC groups, using formalisms from numerical analysis. Computational aspects of finite permutation groups have been well-studied and this is a very active area of research. The way the local structure is composed to form the large-scale picture of a TDLC group is not dissimilar to the structure of countable groups, for which there is also a well-developed theory of computation.
The aim of the proposed workshop is to bring together experts from four fields of mathematics: permutation groups, algorithmic group theory, numerical analysis, and formal systems and logic, to develop a basis for a framework of computation in TDLC groups and approximation thereof.
- Heiko Dietrich (Monash University)
- Michal Ferov (The University of Newcastle)
- Melissa Lee (The University of Auckland)
- George Willis (The University of Newcastle)
This workshop is supported by AMSI and AustMS through the AMSI-AustMS Workshop Funding program.