 ZERODIMENSIONAL SYMMETRY SEMINAR
 Speaker: Alejandra Garrido, The University of Newcastle
 Title: Hausdorff dimension and normal subgroups of freelike prop groups
 Location: Room LG 17, McMullin (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Tue, 27^{th} Nov 2018
 Abstract:
Hausdorff dimension has become a standard tool to measure the "size" of fractals in real space. However, it can be defined on any metric space and therefore can be used to measure the "size" of subgroups of, say, prop groups (with respect to a chosen metric). This line of investigation was started 20 years ago by Barnea and Shalev, who showed that padic analytic groups do not have any "fractal" subgroups, and asked whether this characterises them among finitely generated prop groups.
I will explain what all of this means and report on joint work with Oihana Garaialde and Benjamin Klopsch in which, while trying to solve this problem, we ended up showing an analogue of a theorem of Schreier in the context of prop groups of positive rank gradient: any finitely generated infinite normal subgroup of a prop group of positive rank gradient is of finite index. I will also explain what "positive rank gradient" means, and why prop groups with such a property are "freelike".
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 ZERODIMENSIONAL SYMMETRY SEMINAR
 Speaker: Alejandra Garrido, The University of Newcastle
 Title: Maximal subgroups of some groups of intermediate growth
 Location: Room LG 17, McMullin (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Tue, 16^{th} Oct 2018
 Abstract:
Given a group one of the most natural things one can study about it is its subgroup lattice, and the maximal subgroups take a prominent role. If the group is infinite, one can ask whether all maximal subgroups have finite index or whether there are some (and how many) of infinite index. After telling some historical developments on this question, I will motivate the study of maximal subgroups of groups of intermediate growth and report on joint work with Dominik Francoeur where we give a complete description of all maximal subgroups of some "siblings" of Grigorchuk's group.
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 CARMA SEMINAR
 Speaker: Alejandra Garrido, The University of Newcastle
 Title: Profinite completions of groups acting on rooted trees
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 22^{nd} Feb 2018
 Abstract:
Groups of rooted tree automorphisms, and (weakly) branch groups in particular, have received considerable attention in the last few decades, due to the examples with unexpected properties that they provide, and their connections to dynamics and automata theory. These groups also showcase interesting phenomena in profinite group theory. I will discuss some of these and other profinite completions that one can use to study these groups, and how to find them. All these concepts will be defined in the talk.
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