## About me

I am a research mathematician based in Madrid; currently Profesora Contratada Doctora (Lecturer / Associate professor) at Universidad Complutense de Madrid, and also member of the Instituto de Ciencias MATemáticas (Mathematical Sciences Institute).

My research is mostly in infinite group theory, particularly groups acting on trees or Cantor sets. I am interested in self-similar groups, profinite groups and more general totally disconnected locally compact groups.

Previously, I have worked as Profesora Ayudante Doctora at the Universidad Autónoma de Madrid and at the Universidad Carlos III de Madrid. Between 2018 and early 2020, I was Postdoctoral Research Associate in the Zero-Dimensional Symmetry Group , led by George Willis, at the University of Newcastle, Australia. From 2016 to 2018, I was Alexander von Humboldt postdoctoral research fellow at the University of Düsseldorf, Germany, hosted by Benjamin Klopsch. Before that, I was Assistante Postdoctorale in Tatiana Nagnibeda's team at the University of Geneva. I completed my DPhil at the University of Oxford in July 2015, under the supervision of John Wilson and supported by Fundación "la Caixa". My undergraduate degree is from the University of St Andrews, Scotland.

### Contact

## Papers

All my papers and pre-prints are available on arXiv.- (with A. Jaikin Zapirain)
**Free factors and profinite completions**,*IMRN, 2022;,rnac309*( arxiv ) -
(with C. Reid)
**Discrete locally finite full groups of Cantor set homeomorphisms**,*Bull. London Math. Soc. Vol 53:4 (Aug 2021) pp.1228-1248*(arxiv) -
(with O. Garaialde Ocaña and B. Klopsch)
**Pro-p groups of positive rank gradient and Hausdorff dimension***Journal of the London Mathematical Society Vol 101: (2020) pp. 1008-1040.*(arxiv) -
(with J. Uria Albizuri)
**Pro-C congruence properties for groups of rooted tree automorphisms.***Archiv der Mathematik Vol.112 (2019) pp.123–137.*(arxiv) -
(with J. Uria Albizuri)
**Multi-GGS-groups have the congruence subgroup property.***Proceedings of the Edinburgh Mathematical Society Vol.62: 3 , August 2019 , pp. 889 - 894*(arxiv) -
(with D. Francoeur)
**Maximal subgroups of groups of intermediate growth.***Advances in Mathematics Volume 340, 15 December 2018, pp. 1067-1107*(arxiv) - (with Y. Glasner and S. Tornier)
**Automorphism groups of trees: generalities and prescribed local actions.**Chapter 6 in*New Directions in Locally Compact Groups, Eds. P.E. Caprace and N. Monod, Cambridge University Press, 2018*. (arxiv) -
(with G.A. Fernández Alcober and J. Uria Albizuri)
**On the congruence subgroup property for GGS-groups.***Proceedings of the American Mathematical Society Vol. 145 (2017), pp. 3311-3322. (arxiv)* **On the congruence subgroup problem for branch groups.***Israel Journal of Mathematics (2016) 216: 1, pp. 1--13.*(arxiv)**Abstract commensurability and the Gupta--Sidki group.***Groups Geometry Dynamics 10 (2016), 523-543*(arxiv)- (with J.S. Wilson)
**On subgroups of finite index in branch groups.***Journal of Algebra Vol. 397 (2014), pp. 32--38.*(arxiv)

### Spring 2021: Reading group on

## Teaching

### 2022-23: Universidad Autónoma de Madrid

- Matemáticas (Bioquímica)
- Matemáticas (Ciencias Ambientales)

### Past Teaching

- 2020-21, 2021-22: Teoría de Galois (UAM)
- 2020-21, 2021-22: Matemáticas para Biología (UAM)
- Semestre 2, 2019-20: Calculus/Cálculo II (UC3M)
- January 2020: Geometric group theory [co-taught with Murray Elder and Lawrence Reeves] (AMSI Summer School)
- 2019: MATH1210 Mathematical Discovery (Newcastle)
- Winter 2017-18: Undergraduate reading seminar Seminar Charaktertheorie endlicher Gruppen (Düsseldorf)
- July 2017: Introduction to branch groups and groups of intermediate growth [Advanced course] ( Groups of Intermediate growth in Sevilla )
- Spring 2015-16: Méthodes géométriques et asymptotiques en théorie des groupes (Genève)
- Spring 2015-16: Travaux Pratiques en Analyse I, Algèbre I, Géométrie I (Genève)
- Autumn 2015-16: Analyse I (Genève)
- Trinity 2014: Groups and actions (New College, Oxford)
- Hilary 2014: Integration (New College and Somerville College, Oxford)
- Hilary 2012, 2013: Group Theory and an Introduction to Character Theory (Oxford)
- Michaelmas 2012, 2013: Galois Theory (Oxford)

## Seminars/Reading groups

### Spring 2021: Reading group on *Groups, Trees and Projective modules*

We read Dicks' book with the same name. Summary and schedule.

## Miscellanea

#### Member of the Executive Committee of the Severo Ochoa Center of Excellence Grant awarded to ICMAT.

In charge of PhD scholars and other introduction to research programs.