Dr Alejandra Garrido Angulo
Postdoctoral Research Associate
School of Mathematical and Physical Sciences
I was born and raised in Spain, but left at the age of 17 to study Mathematics at the University of St Andrews, Scotland. While I initially leaned towards Physics, I was gradually drawn towards Pure Mathematics and Group Theory in particular, partly thanks to some great lecturers in the subject. By the end of my degree, I was hooked. Keen to learn and discover more, I went on to do a DPhil in Mathematics at the University of Oxford, where I was supervised by John S. Wilson.
My graduate studies were made possible by the generosity of two Spanish foundations, La Caixa and Caja Madrid, that offer scholarships to outstanding students, across all disciplines, on a competitive basis. Sadly, I had to turn down the latter as I couldn't hold both scholarships simultaneously.
After spending a year as a postdoc in the University of Geneva, Switzerland, working in Tatiana Nagnibeda's very stimulating research group, I took up an Alexander von Humboldt Postdoctoral Research Fellowship at the University of Düsseldorf, Germany. I spent two years there, hosted by Benjamin Klopsch.
Research-wise, I am interested in group theory, which is the mathematical study of symmetries of objects and structures. I am particularly interested in self-similar (and fractal) groups, in which certain subgroups of finite index map (surjectively), to the whole group. This means that the the group has a particularly nice action on a rooted tree, which is also called self-similar. Many examples are also branch groups, which gives then a very specific subgroup structure. This has led me to a more general study of groups of tree automorphisms, both profinite and locally compact. Amusingly, my groups have been getting bigger as I have moved jobs!
- Doctor of Philosophy, University of Oxford - UK
- group theory
- groups acting on trees
- profinite groups
- self-similar groups
- topological groups
- totally disconnected locally compact groups
- French (Fluent)
- Spanish (Mother)
- German (Fluent)
Fields of Research
|010106||Lie Groups, Harmonic and Fourier Analysis||5|
|010104||Combinatorics and Discrete Mathematics (excl. Physical Combinatorics)||10|
|010105||Group Theory and Generalisations||85|
|Title||Organisation / Department|
|Postdoctoral Research Associate||University of Newcastle
School of Mathematical and Physical Sciences
|Dates||Title||Organisation / Department|
|1/09/2016 - 1/09/2018||Alexander von Humboldt Postdoctoral Research Fellow||University of Düsseldorf
|1/08/2015 - 30/06/2016||Postdoctoral assistant||University of Geneva
|Year||Title / Rationale|
Trees, dynamics and locally compact groups
International workshop bringing together world experts in self-similar groups and locally compact groups. There were mini-courses and invited research talks on both areas, and some contributed talks from young researchers, encouraging communication between experienced and new researchers in two different areas of research that have many potential connections. About 80 participants. Website: http://reh.math.uni-duesseldorf.de/~internet/trees2018/
For publications that are currently unpublished or in-press, details are shown in italics.
Chapter (1 outputs)
Tornier S, Garrido A, Glasner Y, 'Automorphism groups of trees: generalities and prescribed local actions', New Directions in Locally Compact Groups, Cambridge University Press, Cambridge, UK 92-116 (2018)
Journal article (6 outputs)
Francoeur D, Garrido A, 'Maximal subgroups of groups of intermediate growth', Advances in Mathematics, 340 1067-1107 (2018) [C1]
Garrido A, Uria-Albizuri J, 'Pro- C congruence properties for groups of rooted tree automorphisms', Archiv der Mathematik, (2018)
© 2018, Springer Nature Switzerland AG. We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite c... [more]
© 2018, Springer Nature Switzerland AG. We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-C completions of the group, where C is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the C-congruence subgroup property (C-CSP) if its pro-C completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the C-CSP. In the case where C is also closed under extensions (for instance the class of all finite p-groups for some prime p), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the p-CSP.
Fernández-Alcober GA, Garrido A, Uria-Albizuri J, 'On the congruence subgroup property for GGS-groups', Proceedings of the American Mathematical Society, 145 3311-3322 (2017)
© 2017 American Mathematical Society. We show that all GGS-groups with a non-constant defining vector satisfy the congruence subgroup property. This provides, for every odd prime ... [more]
© 2017 American Mathematical Society. We show that all GGS-groups with a non-constant defining vector satisfy the congruence subgroup property. This provides, for every odd prime p, many examples of finitely generated, residually finite, non-torsion groups whose profinite completion is a pro-p group, and among them we find torsion-free groups. This answers a question of Barnea. On the other hand, we prove that the GGS-group with a constant defining vector has an infinite congruence kernel and is not a branch group.
Garrido A, 'On the congruence subgroup problem for branch groups', Israel Journal of Mathematics, 216 (2016)
© 2016, Hebrew University of Jerusalem. We answer a question of Bartholdi, Siegenthaler and Zalesskii, showing that the congruence subgroup problem for branch groups is independen... [more]
© 2016, Hebrew University of Jerusalem. We answer a question of Bartholdi, Siegenthaler and Zalesskii, showing that the congruence subgroup problem for branch groups is independent of the branch action on a tree. We prove that the congruence topology of a branch group is determined by the group, specifically, by its structure graph, an object first introduced by Wilson. We also give a more natural definition of this graph.
Garrido A, 'Abstract commensurability and the Gupta-Sidki group', Groups, Geometry, and Dynamics, 10 523-543 (2016)
© European Mathematical Society. We study the subgroup structure of the infinite torsion p-groups defined by Gupta and Sidki in 1983. In particular, following results of Grigorchu... [more]
© European Mathematical Society. We study the subgroup structure of the infinite torsion p-groups defined by Gupta and Sidki in 1983. In particular, following results of Grigorchuk and Wilson for the first Grigorchuk group, we show that all infinite finitely generated subgroups of the Gupta-Sidki 3-group G are abstractly commensurable with G or G G. As a consequence, we show that G is subgroup separable and from this it follows that its membership problem is solvable. Along the way, we obtain a characterization of finite subgroups of G and establish an analogue for the Grigorchuk group.
Garrido A, Wilson JS, 'On subgroups of finite index in branch groups', Journal of Algebra, 397 32-38 (2014)
We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure... [more]
We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure lattices of branch groups introduced by the second author. We derive a condition concerning abstract commensurability of branch groups acting on the p-ary tree for any prime p. © 2013 Elsevier Inc.
|Show 3 more journal articles|
Grants and Funding
|Number of grants||1|
Click on a grant title below to expand the full details for that specific grant.
20161 grants / $150,000
Funding body: Alexander Von Humboldt Foundation
|Funding body||Alexander Von Humboldt Foundation|
Alejandra Garrido, Benjamin Klopsch
|Scheme||Postdoctoral Research Fellowship|
|Type Of Funding||International - Competitive|