## North British Geometric Group Theory Seminar

### Friday 6th September, University of Newcastle

The schedule will be
- 1130-1220 Montserrat Casals-Ruiz (Oxford)
Title: Embeddability and universal equivalence of partially commutative groups

Abstract: In this talk we will present counter-examples to the extension graph and weakly chordal conjectures of Kim and Koberda. If time permits, we will further discuss a sufficient condition for embeddability between partially commutative groups which we then use to establish a criterion for their universal equivalence.

- 1230-1340: Lunch, on campus or in a sandwich shop.

- 1340-1430 Armando Martino (Southampton)
Title: The conjugacy problem for Houghton's group

Abstract: Joint work with Yago Antolin and Jose Burillo. Houghton's groups are examples of finitely presented groups which do not belong to any of the classes which are known to have solvable conjugacy problem; they are neither hyperbolic, nor bi-automatic nor conjugacy separable. I will outline a solution to the conjugacy problem for these groups which relies on an understanding of the action on the set of "branches", as well as some elementary facts about permutation groups.

- 1440-1530 Ian Chiswell (QMUL)
Title: Ordering free products and graph products.

Abstract:
A proof will be outlined that a graph product of (two-sided) orderable groups is orderable. To do this, a canonical method is needed to order the free product of a family of groups, given a total order on the index set of the family. The corresponding result for graph products of right-orderable groups and for graph products of locally indicable groups is much easier to prove. Another similar method for defining orders on free products will be discussed briefly.

- 1540-1600 Tea

- 1600-1650 Peter Kropholler (Southampton)
Title: Homological dimension of discrete soluble groups revisited

Lectures will be in room TR4 on the fourth floor of the Herschel
buildings (home of the School of Mathematics and Statistics) at Newcastle University.

Afterwards we'll go straight to dinner, which I shall book for 1745 (details to be confirmed)
Avanti's in Jesmond
(close to West Jesmond metro, which 2 stops from Newcastle Haymarket and the
University, 4 stops from Newcastle Central Station, 9 stops from Newcastle airport).

The meeting is funded by grants from the London Mathematical
Society, the Edinburgh Mathematical Society and the Glasgow Mathematical Journal.

Organiser: Sarah Rees (SarahDOTReesATnclDOTacDOTuk), Tel: 0191 222 7236