## About me

I am currently an assistant professor at the Department of Mathematical Engineering of Universidad the Chile.

## Research interests

I'm interested in geometry and dynamical systems and their connection with geometry. Currently, I work on Teichmüller dynamics, flat and Riemann surfaces, and dynamically-defined Cantor sets.

## Articles

### Accepted

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

With Harold Erazo, Carlos Gustavo Moreira and Sergio Romaña.

Journal of the European Mathematical Society.

. Preprint. .

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

With Dami Lee and Anthony Sanchez.

Groups, Geometry and Dynamics.

. Preprint. . Mathematica files.

### Preprints

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. .

## 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.