Welcome to my personal website. You can find about my projects below these lines, learn more about me in the about section or read some of my blog posts in the posts section.


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


  • Cyclic Higgs bundles and the Toledo invariant. (With Oscar García-Prada) arXiv link

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


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


  • 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


  • Cyclic Higgs bundles and Vinberg theory. Mathematics master’s thesis. Supervised by Oscar García-Prada. download pdf

  • 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:

  • Real Analysis I (Cálculo I): download pdf
  • Set and number theory (Conjuntos y Números): download pdf
  • Linear Algebra (Álgebra Lineal): download pdf
  • Real Analysis II (multivariable) (Cálculo II): download pdf
  • Algebra and euclidean geometry (Álgebra Lineal y Geometría): download pdf
  • Numerical analysis (Cálculo numérico): download pdf
  • Probability I (Probabilidad I): download pdf
  • Algebraic Structures and Group Theory (Estructuras Algebraicas): download pdf
  • Mathematical Analysis (Análisis matemático): download pdf
  • Geometry of Curves and Surfaces (Geometría de Curvas y Superficies): download pdf
  • Ordinary Differential Equations (Ecuaciones diferenciales): download pdf
  • Topology (Topología): download pdf
  • Galois Theory (Teoría de Galois): download pdf
  • Integration and Measure Theory (Teoría de la Integral y la Medida): download pdf
  • Mathematical Models (Modelización): download pdf
  • Complex Analysis (Variable Compleja I): download pdf
  • Differential Geometry (Geometría Diferencial): download pdf
  • Algebraic Number Theory (Teoría Algebraica de Números): download pdf
  • Commutative Algebra (Álgebra Conmutativa): download pdf
  • Geometry and Topology (Geometría y Topología): download pdf

Found any typos or improvements, or have any general feedback? Please let me know via mail.

These documents are completely free to download and use, and subject to a creative commons license. If you found them helpful, consider donating via PayPal.

Other projects

Some of my other minor projects can be found at my my github.

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