Totally disconnected locally compact (TDLC) groups naturally appear in various branches of mathematics, as they capture the structure of symmetries of various mathematical objects, and 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 the approximation of real numbers 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.
Invited speakers will be listed here.
Registration details will be provided at a later date.
We hope to run the conference around Easter, 2022, perhaps with people arriving on Sunday 10th (along with a welcome function). The final dates will be decided later.
Thre conference schedule will be provided at a later date.
Details regarding the conference location will be provided at a later date.
The conference organisers are:
- Heikro Dietrich (Monash University)
- Michal Ferov (The University of Newcastle)
- Melissa Lee (The University of Auckland)
- George Willis (The University of Newcastle)