Dr Alejandra Garrido Angulo

Dr Alejandra Garrido Angulo

Postdoctoral Research Associate

School of Mathematical and Physical Sciences

Career Summary

Biography

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

I joined UON in October 2018, where I am a Postdoctoral Research Associate in George Willis' growing research group

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!



Qualifications

  • Doctor of Philosophy, University of Oxford - UK

Keywords

  • group theory
  • groups acting on trees
  • profinite groups
  • self-similar groups
  • symmetry
  • topological groups
  • totally disconnected locally compact groups

Languages

  • French (Fluent)
  • Spanish (Mother)
  • German (Fluent)

Fields of Research

Code Description Percentage
010106 Lie Groups, Harmonic and Fourier Analysis 5
010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) 10
010105 Group Theory and Generalisations 85

Professional Experience

UON Appointment

Title Organisation / Department
Postdoctoral Research Associate University of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/09/2016 - 1/09/2018 Alexander von Humboldt Postdoctoral Research Fellow University of Düsseldorf
Germany
1/08/2015 - 30/06/2016 Postdoctoral assistant University of Geneva
Switzerland

Invitations

Organiser

Year Title / Rationale
2018 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/
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Chapter (1 outputs)

Year Citation Altmetrics Link
2018 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)
DOI 10.1017/9781108332675
Citations Scopus - 1
Co-authors Alejandra Garrido, Stephan Tornier

Journal article (6 outputs)

Year Citation Altmetrics Link
2018 Francoeur D, Garrido A, 'Maximal subgroups of groups of intermediate growth', Advances in Mathematics, 340 1067-1107 (2018) [C1]
DOI 10.1016/j.aim.2018.10.026
Co-authors Alejandra Garrido
2018 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.

DOI 10.1007/s00013-018-1278-6
Co-authors Alejandra Garrido
2017 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.

DOI 10.1090/proc/13499
Citations Scopus - 5Web of Science - 2
Co-authors Alejandra Garrido
2016 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.

DOI 10.1007/s11856-016-1402-x
Citations Scopus - 5Web of Science - 3
Co-authors Alejandra Garrido
2016 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.

DOI 10.4171/GGD/355
Citations Scopus - 2Web of Science - 1
Co-authors Alejandra Garrido
2014 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.

DOI 10.1016/j.jalgebra.2013.08.025
Citations Scopus - 2Web of Science - 2
Co-authors Alejandra Garrido
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Grants and Funding

Summary

Number of grants 1
Total funding $150,000

Click on a grant title below to expand the full details for that specific grant.


20161 grants / $150,000

Alexander von Humboldt Postdoctoral Research Fellowship$150,000

Prestigious competitive fellowship for researchers from outside Germany with above average qualifications, within four years of PhD. A Humboldt Research Fellowship for postdoctoral researchers allows researchers to carry out long-term research (6-24 months) in Germany. Applicants choose their own topic of research and their academic host.

Funding body: Alexander Von Humboldt Foundation

Funding body Alexander Von Humboldt Foundation
Project Team

Alejandra Garrido, Benjamin Klopsch

Scheme Postdoctoral Research Fellowship
Role Lead
Funding Start 2016
Funding Finish 2018
GNo
Type Of Funding International - Competitive
Category 3IFA
UON N
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Dr Alejandra Garrido Angulo

Position

Postdoctoral Research Associate
School of Mathematical and Physical Sciences
Faculty of Science

Contact Details

Email alejandra.garridoangulo@newcastle.edu.au

Office

Room SR118
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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