Groups and topology

Friday 28th April 2023, A54 Postgraduate Statistics Centre (TBC), Lancaster University (hybrid). Local organiser: Nadia Mazza.

Topological methods have long been used in group theory, often referring to the link with the fundamental group. Such methods have led to very powerful results with applications beyond the realm of pure mathematics, e.g. in neuroscience (cf. EPFL’s Blue Brain Project). The purpose of the meeting is to gather group theorists whose topological methods have found interesting applications opening new directions for research in pure mathematics.


All talks will be held in person and online. The room for in person participants is A54 Lecture Theatre, Postgraduate Statistics Centre (campus MazeMap).

The timetable is as follows, where all times are given in Greenwich Mean Time:

  • 13:15-14:15: Markus Szymik (Sheffield), Spaces of involutions in absolute Galois groups
  • 14:20-15:20: Lewis Molyneux (RHUL), BNSR-invariants and finite index subgroups
  • 15:20-16:00: Refreshments
  • 16:00-17:00: Jim Belk (Glasgow)

To register for the event or to receive the talk links, please email the organiser Nadia Mazza (

The FCG Research Group is supported by an LMS Joint Research Groups in the UK Scheme 3 grant. This meeting is also supported by the EPSRC. Limited funding is available for PhD students, allocated on a first come first served basis.

For UK-based mathematicians with caring duties the LMS has a Caring Supplementary Grant scheme which allows participants of meetings like ours to apply for help covering caring costs.


  • Markus Szymik (Sheffield), Spaces of involutions in absolute Galois groups
    Motivated by attempts to extend analogies between primes and knots to infinite places, I will give a new description of spaces of involutions in absolute Galois groups. The result has a topological and an algebraic component. While the topological aspect is relatively standard, the algebraic part involves a refinement of the theory of groups, namely quandles. The talk shall also be an advertisement for the latter and discuss the subtle relationship between quandles and groups.
  • Lewis Molyneux (RHUL), BNSR-invariants and finite index subgroups
    The Bieri-Neumann-Strebel-Renz invariant for discrete groups is a powerful tool for documenting and understanding finiteness properties of groups. However, it is often difficult to calculate. In this talk, I will present a sufficient condition for a useful definition of equality between the BNSR-invariant of a group and its subgroup, allowing for these invariants to be calculated on the same topological space. We will then see how this relation between invariants is applied to the calculation of the BNSR-invariant for the irrational slope Thompson group Fτ, as defined by Cleary and further described by Burillo, Nucinkis and Reeves.