The following are the original manuscripts presented to fulfill the respective programs.

• Ph.D. dissertation (2021): The relative Künneth theorem. Texas A&M University (TX). Advisor: Sarah Witherspoon.
• Master's dissertation (2016): A reading on "Algebraic coherent sheaves" by J.-P. Serre. Universite Pierre-et-Marie-Curie (France). Advisor: Bruno Kahn.
• Bachelor's dissertation (2015): Triality: a particularity of Spin(8) (with slides). Universitat Autonoma de Barcelona (Spain). Advisor: Jaume Aguade Bover.

The following are notes written with the intention of being useful for leaning the material they cover. They were written for courses, working seminars, summer schools, and similar. If you find mistakes (typographical or other) in these notes, or have comments, please let me know.

• B-infinity structures, monoidal categories, and singularity categories the transcription of Bernhard Keller's GAP XVII minicourse.
• Monoidal categories based on Monoidal Categories by Chelsea Walton.
• Summary on Lie algebras and their representations.
• An isomorphism between cyclic groups of prime power order.
• Invertible matrices with integer entries whose inverse has integer entries.

The following are selected notes and homework from my graduate courses. Use this raw material at your own risk.

• Math 611 (Introduction to Ordinary and Partial Differential Equations).
• Math 617 (Theory of Functions of a Complex Variable I).
• Math 622 (Differential Geometry I).
• Math 636 (Topology I).
• Math 637 (Topology II).
• Math 653 (Algebra I).
• Math 654 (Algebra II).
• Math 662 (Introduction to Commutative and Homological Algebra).
• Math 662 (Representations of Finite Groups).
• Math 689 (Topological Quantum Computation).

• Introduction a la Geometrie Algebrique: class notes from a course by Ilia Itenberg.
• Theorie de Lie et Representations I: skeleton class notes from a course by David Hernandez.

Due to unbearable sentimentalism and nostalgia, I could not resist the temptation of adding what was probably my first attempt at doing Mathematics, as a result of my first contact with working mathematicians during the summer of 2008. I will never be able to thank Angelica Benito Sualdea enough for her patience, support, and help.

• ElGamal article, the document that resulted from the aforementioned patience, support, and help.
• ElGamal worksheet, for the complementary computations.