## About me

I am currently an adjunct professor at the Center for Mathematical Modeling at Universidad de Chile. In April 2019, I received my Ph.D. from Université de Paris. My advisors were Anton Zorich and Carlos Matheus. In August 2015, I completed a Master's degree at Universidad de Chile under the direction of Alejandro Maass.

## Research interests

I'm interested in geometry and dynamical systems. Currently, I work on Teichmüller dynamics, flat surfaces and dynamically-defined Cantor sets. My Ph.D. thesis was focused on gaining a deeper understanding of the combinatorial models for the Teichmüller flow and the \(\mathrm{SL}(2, \mathbb{R})\)-action on flat surfaces.

## Articles

### Preprints

Fractal dimensions of the Markov and Lagrange spectra near \(3\) (2022).

With Harold Erazo, Carlos Gustavo Moreira and Sergio Romaña.

. Preprint. .

Kontsevich-Zorich monodromy groups of translation covers of some platonic solids (2022).

With Dami Lee and Anthony Sanchez.

. Preprint. . Mathematica files.

Permutation of periodic points of Veech surfaces in \(\mathcal{H}(2)\) (2021).

With Angel Pardo.

. Preprint. .

The flow group of rooted abelian or quadratic differentials (2021).

With Mark Bell, Vincent Delecroix, Vaibhav Gadre and Saul Schleimer.

. Preprint. .

Coding the Teichmüller flow using Veering triangulations (2019).

With Mark Bell, Vincent Delecroix, Vaibhav Gadre and Saul Schleimer.

. Preprint. .

Simplicity of the Lyapunov spectra of certain quadratic differentials (2017).

. Preprint. .

### Published

Lower bounds on the dimension of the Rauzy gasket (2020).

With Carlos Matheus.

Bulletin de la Société Mathématique de France **148**.2, pp. 321–327.

. Journal. Postprint. .

Counting saddle connections in a homology class modulo \(q\) (with an appendix by Rodolfo Gutiérrez-Romo) (2020).

By Michael Magee and Rene Rühr.

Journal of Modern Dynamics **15**, pp. 237–262.

. Journal. Preprint. .

A family of quaternionic monodromy groups of the Kontsevich–Zorich cocycle (2019).

Journal of Modern Dynamics **14**, pp. 227–242.

. Journal. Postprint. Preprint. .

Classification of Rauzy–Veech groups: proof of the Zorich conjecture (2019).

Inventiones Mathematicae **215**.3, pp. 741–778.

. Journal. Postprint. Preprint. .

Characterization of minimal sequences associated with self-similar interval exchange maps (2018).

With Milton Cobo and Alejandro Maass.

Nonlinearity **31**.4, pp. 1121–1154.

. Journal. Postprint. .

Wandering intervals in affine extensions of self-similar interval exchange maps: the cubic Arnoux–Yoccoz map (2018).

With Milton Cobo and Alejandro Maass.

Ergodic Theory and Dynamical Systems **38**.7, pp. 2537–2570.

. Journal. Postprint. Preprint. .

## Talks and poster sessions

Lower bounds on the Hausdorff dimension of the Rauzy gasket (May, 2019).

Groupe de travail « théorie ergodique et systèmes dynamiques ».

Institut de Mathématiques d'Orsay.

Université Paris-Sud.

Veering triangulations and the Teichmüller flow (April, 2019).

Séminaire « Teich : espaces de Teichmüller ».

Institut de Mathématiques de Marseille.

Aix–Marseille Université.

Rauzy–Veech groups of flat surfaces (March, 2019).

Séminaire de l'équipe de Théorie Ergodique et Systèmes Dynamiques.

Institut Galilée.

Université Paris 13.

Rauzy–Veech groups of translation surfaces (December, 2018).

Annual encounter of the Chilean Mathematical Society (SOMACHI).

Universidad de O'Higgins.

Rauzy–Veech groups of flat surfaces (October, 2018).

Séminaire Théorie Spectrale et Géométrie.

Institut Fourier.

Université Grenoble-Alpes.

Combinatorics of Rauzy–Veech groups (September, 2018).

Journées de Géométrie et Combinatoire dans les Espaces des Modules.

Institut Galilée.

Université Paris 13.

Quaternionic monodromies of the Kontsevich–Zorich cocycle (June, 2018).

Teichmüller dynamics, Mapping class groups and Applications Conference.

Institut Fourier.

Université Grenoble-Alpes.

Rauzy–Veech groups of flat surfaces (April, 2018).

Maryland Spring Dynamical Systems Conference (in memory of William Veech).

Department of Mathematics.

University of Maryland.

Rauzy–Veech groups of flat surfaces (March, 2018).

Geometry, Topology and Dynamics in Low Dimensions Symposium.

Warwick Mathematics Institute.

University of Warwick.

Rauzy–Veech groups of flat surfaces (March, 2018).

Geometry and Topology seminar.

Warwick Mathematics Institute.

University of Warwick.

Rauzy–Veech groups of flat surfaces (March, 2018).

Geometry and Topology seminar.

School of Mathematics & Statistics.

University of Glasgow.

Rauzy–Veech groups of flat surfaces (November, 2017).

Séminaire « Teich : espaces de Teichmüller ».

Institut de Mathématiques de Marseille.

Aix–Marseille Université.

Classification of Rauzy–Veech groups (October, 2017).

Mini-recontre surfaces de translation.

Institut de Mathématiques de Toulouse.

Université Paul Sabatier-Toulouse 3.

Classification of Rauzy–Veech groups (September, 2017).

Séminaire « Plat ».

Institut Henri Poincaré.

Clasificación de los grupos de Rauzy–Veech (September, 2017).

Seminario «Dinámica Porteña».

Instituto de Matemáticas.

Pontificia Universidad Católica de Valparaíso.

Clasificación de los grupos de Rauzy–Veech (August, 2017).

Seminario de Sistemas Dinámicos.

Centro de Modelamiento Matemático.

Universidad de Chile.

Zariski-density of some Rauzy–Veech groups (May, 2017).

Séminaire de Dynamique, Théorie Ergodique et Probabilités.

Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA).

Université de Picardie Jules Verne.

Wandering intervals in affine interval exchange maps: nonreal eigenvalues (October, 2016).

Doctoral school “Applications of Ergodic Theory in Number Theory”.

Centre International de Rencontres Mathématiques.

Chaire Jean-Morlet.

Download poster.

## More about me

I'm fluent in Spanish and English. Some people say I speak French.

I contribute to Etilmercurio, a math and science popularization website in Spanish.

My favorite color is purple. I like jazz and music from the (Post-)Romantic era. I'm a fan of retro websites and videogames.

I consider myself to be an antispeciest, an antinatalist and an anarchist.