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Eleventh Barcelona Weekend in Group Theory (2016)

Speakers: Javier Aramayona (ICMAT - Universidad Autónoma de Madrid), Albert Garreta (Stevens Institute of Technology), Alejandra Garrido (Université de Genève), Alexey Talambutsa (Steklov Institute of Mathematics), Alexander Zakharov (Euskal Herriko Unibertsitatea, Universidad del País Vasco)

The Eleventh Barcelona Weekend in Group Theory will take place on May 20th and 21st, 2016. The Barcelona Weekend is a short but intense meeting, with three talks on Friday and two talks on Saturday.

All talks will take place at the Facultat de Matemàtiques i Estadística, in the UPC campus. The address is Pau Gargallo, 5, room TBA.

The program will be as follows:

Friday, May 20th, 2016

    • 15:00 Javier Aramayona (ICMAT - Universidad Autónoma de Madrid, Spain).


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.



    • 16:15 Albert Garreta Fontelles (Stevens Institute of Technology, Hoboken, NJ, USA)


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.



    • 17:30 Alejandra Garrido (Université de Genève, Switzerland).


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.

Saturday, May 21st, 2016

    • 10:30 Alexey Talambutsa (Steklov Institute of Mathematics, Moscow, Russia).


Growth of Baumslag-Solitar groups and lamplighter groups

      Abstract: TBA



    • 11:45 Alexander Zakharov (Euskal Herriko Unibertsitatea, Universidad del País Vasco, Bilbao, Spain).


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.
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