Here you can find some of my projects.

## Publications

Here you will find some of my published documents of several kinds.

### Preprints

• Hitchin map on even very stable upward flows. (With Tamás Hausel) arXiv link

### Posters

• Very Stable $$U(p,q)$$-Higgs bundles. Institute of Science and Technology Austria (ISTA) Summer Internship 2022. Supervised by Tamás Hausel. download pdf

### Talks

• The Hitchin Fibration and Spectral Curves. Hitchin-Ngô Lab Working Group on the Hitchin Fibration, Langlands duality and mirror symmetry, Instituto de Ciencias Matemáticas (ICMAT), February 2022. download talk notes

### Theses

• Invariants for the action of $$\text{Gal}(\overline{ \mathbb Q }/ \mathbb Q)$$ on dessins d’enfants. Mathematics bachelor thesis. Supervised by Ernesto Girondo. download pdf

• Reinforcement learning via dueling bandits. Computer Science bachelor thesis. Supervised by Pablo Castells. download pdf

## ApunTeX - Mathematics Course Notes (in Spanish)

These are my revised class notes (in Spanish) from lectures I attended as part of my Degree in Mathematics at Universidad Autónoma de Madrid (UAM). Before being published here, I revised them individually, adding a cover image, a summary page and short explanatory paragraphs where I felt they were needed.

These documents are:

• A direct an ordered collection of the most important definitions and results from the subject in question, at undergraduate level.
• A collection of full proofs of said results (except in the most basic cases).
• A guide to quickly review previously acquired ideas, or to check specific aspects that might have not been fully understood at first.

These documents are NOT:

• A textbook.
• A collection of exercises to practice your knowledge.
• A list of examples to illustrate the ideas presented. Sometimes, particular examples are included when they can be fruitful or interesting, but they’re not the point of these notes and, as such, they’re very sparse, in favor of the first bullet point of the previous list.

Find the documents here:

• Geometry of Curves and Surfaces (Geometría de Curvas y Superficies): download pdf
• Integration and Measure Theory (Teoría de la Integral y la Medida): download pdf