North British Geometric Group Theory Network 2019-2020

The next meeting of the North British Geometric Group Theory network will be held on Wednesday 13 November 2019 in the main lecture theatre of the International Centre for Mathematical Sciences (ICMS), Bayes Centre, 47 Potterrow, Edinburgh.


Lunch

Some of us will informally meet at the restaurant Spoon around 12:15.

Timetable

1:45 Ashot Minasyan (Southampton): CAT(0) groups need not be biautomatic

A group G, generated by a finite set X, is said to be biautomatic, if there is a regular language L over X, representing elements of G, such that paths in the Cayley graph \Gamma(G,X), labelled by words from L, satisfy a certain fellow traveler property. Many groups acting on non-positively curved spaces are known to be biautomatic: e.g., word hyperbolic groups and CAT(0) cubical groups. In the talk I will give examples of CAT(0) groups which are not biautomatic. I will also discuss further properties of such groups and remaining questions. This is based on a joint work with Ian Leary.

3:00 María Cumplido Cabello (Heriot-Watt): Links between two complexes for spherical Artin groups

In this talk we will focus on how parabolic subgroups of Artin groups of spherical type act on the additional length complex, CAL-- a flag complex of infinite diameter introduced by Calvez and Wiest in 2017. We prove that the elements that stabilise a parabolic subgroup act elliptically on CAL. This result provide us links between CAL and the new complex of irreducible parabolic subgroups, P, and allows us to prove that P has also infinite diameter. On the other hand, we can also use this result to prove that the sequence of exponential growth rates of braid groups with respect to the Garside generating set, goes to infinity. This is a joint work with Yago Antolín

4:00 Tea/Coffee Break

4:30 Martin Edjvet (Nottingham): Relative Asphericity

We discuss relative group presentations,asphericity and consequences. We will then consider some recent applications to deciding finiteness for certain families of groups and to equations over torsion-free groups.


Dinner

There will be an early evening dinner at 18:00 at Beirut Restaurant, 24 Nicholson Square, for those able to stay.

Coming to ICMS

Click here for directions to ICMS. On the map, Waverley Station is towards the top, adjacent to Waverley Bridge. It is about 10 minutes walk from the station to ICMS.


This meeting is partially supported by a Scheme 3 grant from the London Mathematical Society, and by a grant from the Glasgow Mathematical Journal Learning and Research Support Fund.

The Mastermind is Sarah Rees.

The local organisers for this meeting are Laura Ciobanu (Heriot-Watt) and Alexandre Martin (Heriot-Watt).

Webpage designed by Nick Gilbert