This is a series of one-day meetings, with the aim of bringing together geometric group theorists, topologists, and geometers in the North-Rhine Westphalia region of Germany. Sign up to the mailing list here.
6th Meeting - Bonn, Friday 6th November 2026
Local organisers: Sam Hughes and Lawk Mineh.
Registration
No registration is needed to participate in this event.
Location
The event will happen in the "Lipschitz-Saal". This is in the Mathematical Institute, Endenicher Allee 60. This is a 10-to-15 minute walk from the Hauptbahnhof, or a five minute bus ride (604, 605, 606, 607) and a one minute walk.
Schedule
13:00: Arrival
13:30: Talk 1 - Zahra Mohammadi Khagheshlaghi (University of Münster)
On the Model Theory of the Free Factor Complex
The free factor complexes (AFn) and (OFn) encode the structure of free factors of (Fn) and their conjugacy classes. Bestvina and Bridson proved that, for (n≥3), their automorphism groups are precisely Aut(Fn) and Out(Fn), respectively. A key step in their proof is to recognise algebraic relations, such as when free factors give a free product decomposition of (Fn), using only the combinatorics of the complexes. In model theory, this is called definability, and it ensures that automorphisms preserve these relations.
I will explain how this viewpoint leads to a model-theoretic study of these complexes, including how rigidity arguments yield homogeneity and primeness for their first-order theories. The main focus will be stability theory and what it reveals about the complexity of definable relations. In joint work with Katrin Tent, we proved that (AF2), equipped with the complement relation, is (ω)-stable. I will then turn to higher ranks, where (\omega)-stability fails, and describe what we know so far about the model theory of these complexes.
14:30: Break
15:00: Talk 2 - Adrien Abgrall (École Normale Supérieure de Lyon)
Embeddings between square-free right-angled Artin groups
A result of Droms states that two right-angled Artin groups (RAAGs) are isomorphic if and only if their defining graphs are isomorphic. However, deciding whether one RAAG embeds as a subgroup of another is a much harder, and largely open, problem. Substantial progress was made by Kim and Koberda, notably solving the two-dimensional case, relying on their definition of the extension graph of a RAAG, an object somewhat analogous to the curve graph of a surface. Quasi-isometric embedding between RAAGs was also recently studied by Bader–Bensaïd–Petyt. I will present a joint work with Sasha Gurieva and Camille Horbez where we investigate measurable embedding, a measured analogue of coarse embedding. We completely characterize measurable embedding among square-free RAAGs (i.e. RAAGs that do not contain F2 x F2). Interestingly, the characterization is both in terms of subgroup embedding and of extension graphs. It is also algorithmically decidable.
16:00: Break
16:30: Talk 3 - Tara Brendle (University of Glasgow)
The Burau representation
(Joint work with Joan Birman and Vasudha Bharathram.) In 1935 Werner Burau introduced a representation of the braid group Bn into GL(n, ℤ[t, t⁻¹]). This representation is known to be faithful for n = 3 and not to be faithful for n ≥ 5. In this talk, we will give a new proof of faithfulness for n = 3, and describe how to adapt this for the case n = 4.
17:30: Dinner and discussion
Travel funding
We have some funding available to cover train travel for graduate students and early career researchers in the region. If you would like to apply for travel funding, please contact one of the local organizers before 14th October 2026.
Contact
Martina Conte (Bielefeld): mconte(at)math.uni-bielefeld.de
Sam Hughes (Bonn): hughes(at)math.uni-bonn.de
Georges Neaime (Bielefeld): gneaime(at)math.uni-bielefeld.de
Lawk Mineh (Bonn): lawk(at)math.uni-bonn.de
Sam Shepherd (Münster): sam.shepherd(at)uni-muenster.de
Robin J. Sroka (Münster): robinjsroka(at)uni-muenster.de