The next meeting of the North British Geometric Group Theory network will be held on Monday 05 February 2018 in the Newhaven Lecture Theatre of the International Centre for Mathematical Sciences (ICMS), 15 South College Street, Edinburgh.

Lunch

Timetable

1:45 Mark Lawson (Heriot-Watt): Groups from groupoids

Groupoids have come to play an important role in group theory, such as in the work of Matui. The aim of my talk is to provide, what I believe, is the correct framework for understanding this connection and, thereby, connections with other parts of mathematics.

3:00 Rachael Boyd (Aberdeen): Homological stability for Artin monoids

Many sequences of groups satisfy a phenomenon known as homological stability. In my talk, I will report on recent work proving a homological stability result for sequences of Artin monoids, which are monoids related to Artin and Coxeter groups. From this, one can conclude homological stability for the corresponding sequences of Artin groups, assuming a well-known conjecture in called the K(\pi,1)-conjecture. This extends the known cases of homological stability for the braid groups and other classical examples.

4:00 Tea/Coffee Break

4:30 Pavel Tumarkin (Durham): Coxeter groups, quiver mutations and hyperbolic manifolds

Mutations of quivers were introduced by Fomin and Zelevinsky in the beginning of 2000's in the context of cluster algebras. Since then, mutations appear (sometimes completely unexpectedly) in various domains of mathematics and physics. Using mutations of quivers, Barot and Marsh constructed a series of presentations of finite Coxeter groups as quotients of infinite Coxeter groups. I will discuss a generalization of this construction leading to a new invariant of bordered marked surfaces, and a geometric interpretation: it occurs that presentations constructed by Barot and Marsh give rise to a construction of geometric manifolds with large symmetry groups, in particular to some hyperbolic manifolds of small volume with proper actions of Coxeter groups.

Dinner