The Eleventh Barcelona Weekend in Group Theory took place on May 20th and 21st, 2016.

Friday, May 20th, 2016

- 15:00
**Javier Aramayona**(ICMAT - Universidad Autónoma de Madrid, Spain). - 16:15
**Albert Garreta Fontelles**(Stevens Institute of Technology, Hoboken, NJ, USA) - 17:30
**Alejandra Garrido**(Université de Genève, Switzerland).

*On the automorphism group of a right-angled Artin group*

Abstract: Automorphism groups of right-angled Artin groups form an interesting class of groups, as they "interpolate" between the two extremal cases of Aut(Fn) and GL(n,Z). In this talk we will discuss some conditions on a simplicial graph which imply that the automorphism group of the associated right-angled Artin group has (in)finite abelianization. As a direct consequence, we obtain families of such automorphism groups that do not have Kazhdan's property (T). This is joint work with Conchita Martínez-Pérez.

*Systems of equations in random nilpotent groups*

Abstract: We will present and study a model for choosing random nilpotent groups G, and we will discuss two other models that have been introduced recently. After that, we will provide results concerning equations in nilpotent groups, and we will address the following question: when are systems of equations decidable in a generic G? This is joint work with Alexei Miasnikov and Denis Ovchinnikov.

*Maximal subgroups of groups acting on rooted trees*

Abstract: Maximal subgroups are one of the basic things that one can study about a given group, an immediate question being whether or not they all have finite index (when the group is countably infinite). This question has been studied by many authors in several contexts: linear groups, mapping class groups, hyperbolic groups, etc. Groups of automorphisms of rooted trees provide another interesting setting for this question. This class contains groups of intermediate growth, finitely generated infinite torsion groups, and other groups with "exotic" properties. I will talk about the property of having all maximal subgroups of finite index for some of these groups, which is some of my recent joint work with Dominik Francoeur.

- 10:30
**Alexey Talambutsa**(Steklov Institute of Mathematics, Moscow, Russia). - 11:45
**Alexander Zakharov**(Euskal Herriko Unibertsitatea, Universidad del País Vasco, Bilbao, Spain).

*Growth of Baumslag-Solitar groups and lamplighter groups*

Abstract: So far we know not too many values for the minimal exponential growth rates of the groups. The complication is that the set of all generating sets is usually too large. Still, sometimes it is possible to find the exact values of the growth rates. In the talk I will discuss Baumslag-Solitar groups BS(1,p) and lamplighter groups L_p. Accidentally, for any prime p except 2 the growth rate of the group BS(1,p) is the same as for the group L_p. I will try to explain why this happens. (Based on joint work with M.Bucher).

*Intersection of subgroups in fundamental groups of graphs of groups*

Abstract: We prove estimates of the Hanna Neumann type for the (Kurosh) rank of the intersection of subgroups in fundamental groups of graphs of groups, under different conditions on the edge groups and on the subgroups. This is joint work with Sergei Ivanov.