Workshop description
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
Each invited speaker will deliver a mini-series of talks on selected topic.
- Bettina Eick Technische Universität Braunschweig ``Computation with polycyclic groups''
- Alexander Hulpke Colorado State University ``Finite permutation quotients of infinite groups: algorithmic connection in both directions''
- André Nies University of Auckland ``Computably totally disconnected locally compact groups''
- Katrin Tent Universität Münster ``First-order rigidity of profinite groups''
Registration
Due to limited space for the workshop, we may need to restrict the total number of attendees. If you would like to attend, please complete this form to lodge your expression of interest in the workshop. Allocation of places will be based on merit.
» Registration Expressions of Interest «
The registration fee will cover the welcome reception, catering during the event and the workshop dinner. Fees are as follows:
| Members* | A$250 |
| Non-members | A$350 |
| Students | A$150 |
*AMSI members, and members of AustMS and its affiliates
Dates
The workshop will be held from 24th to 28th October (Monday to Friday), 2022.
Venue
The workshop will be held at Quest Newcastle West (787 Hunter St, Newcastle West NSW 2302 [Google map]).
(Note that there is another Quest Apartments in Newcastle, also on Hunter Street: the workshop is at the "Newcastle West" one, between Stewart Avenue and Wood Street.)
Schedule 
Abstracts are available by clicking on talk titles (or view all abstracts).
| Monday 24 October | |
| 08:45 - 09:00 | Welcome |
| 09:00 - 09:30 | George Willis How do we talk to a computer about TDLC groups and why do we wish to? |
| 09:30 - 10:00 | Michal Ferov A candidate paradigm for computation and visualisation in TDLC groups |
| 10:00 - 11:00 | Morning tea and introduction |
| 11:00 - 12:00 | Stephan Tornier Two GAP packages relating to groups acting on trees |
| 12:00 - 12:30 | David Allingham Web-based tree-drawing tools |
| 12:30 - 13:30 | Lunch |
| 13:30 - 14:00 | Breakout |
| 14:00 - 15:00 | George Willis Introduction to TDLC groups |
| 15:00 - 15:30 | Afternoon tea |
| 15:30 - 16:30 | André Nies Computably t.d.l.c. groups (part 1)
 |
| 16:30 - 17:00 | Summary session |
| Tuesday 25 October | |
| 09:00 - 10:00 | Alexander Hulpke Finite permutation quotients of infinite groups: Algorithmic connection in both directions (part 1) |
| 10:00 - 10:30 | Morning tea |
| 10:30 - 11:30 | André Nies |
| 11:30 - 12:30 | Bettina Eick |
| 12:30 - 14:00 | Lunch |
| 14:00 - 15:00 | Breakout |
| 15:00 - 15:30 | Afternoon tea |
| 15:30 - 16:00 | Breakout |
| 16:00 - 17:00 | Katrin Tent |
| Wednesday 26 October | |
| 09:00 - 10:00 | Alexander Hulpke Finite permutation quotients of infinite groups: Algorithmic connection in both directions (part 2) |
| 10:00 - 10:30 | Morning tea |
| 10:30 - 11:30 | Breakout |
| 11:30 - 12:30 | Bettina Eick |
| 12:30 - 14:00 | Lunch |
| 14:00 - 15:00 | Breakout: Colin Reid and Stephan Tornier - Groups acting on trees |
| 15:00 - 15:30 | Afternoon tea |
| 15:30 - 16:00 | Breakout |
| 16:00 - 17:00 | Katrin Tent |
| Thursday 27 October | |
| 09:30 - 10:00 | Ari Markowitz Title tba |
| 10:00 - 10:30 | Morning tea |
| 10:30 - 12:30 | Breakout: André Nies |
| 12:30 - 14:00 | Lunch |
| Free afternoon | |
| 18:00 - 22:00 | Workshop dinner |
| Friday 28 October | |
| 09:00 - 09:30 | João Vitor Pinto e Silva Title tba |
| 09:30 - 10:00 | Max Carter Title tba |
| 10:00 - 10:30 | Morning tea |
| 10:30 - 12:30 | Breakout |
| 12:30 - 14:00 | Lunch |
| 14:00 - 15:00 | Wrap-up session |
| Departure | |
Organisers
The workshop organisers are:
- Heiko Dietrich Monash University
- Michal Ferov The University of Newcastle
- Melissa Lee The University of Auckland
- George Willis The University of Newcastle
Sponsors
