My mathematical research interests are in abstract algebra. Specifically, noncommutative algebra, Hopf algebras (and their generalizations), quantum groups & category theory.
[2024] Symmetries of algebras captured by actions of weak Hopf algebras (Algebras and Representation Theory)
Joint with Hongdi Huang, Elizabeth Wicks, Robert Won
[2023] Algebraic properties of face algebras (Journal of Algebra and Its Applications)
Joint with Chelsea Walton
[2022] Some interactions between Hopf Galois extensions and noncommutative rings (Universitas Scientiarum)
Joint with Armando Reyes
[2023] Doctor of Science - Mathematics
Algebraic properties of weak quantum symmetries [Meritorious Mention]
Advisor: Dr. Chelsea Walton | Co-Advisor: Dr. Armando Reyes
[2019] Master of Science - Mathematics
Hopf Galois extensions and noncommutative rings [Meritorious Mention]
Advisor: Dr. Armando Reyes
[2016] Bachelor in Mathematics
Construcción de álgebras de Hopf mediante extensiones de Ore (construction of Hopf algebras through Ore extensions)
Advisor: Dr. Armando Reyes
[Document] [Slides Defense] [Poster]
[2023] Beamer template for Universidad Nacional de Colombia
[Template]
Remark: A Beamer template for presentations in Spanish at the National University of Colombia. Although not officially endorsed, it follows the university's visual identity guidelines.
[2021] Lecture Notes on Hopf Algebras (in Spanish)
[Lecture 1] [Lecture 2] [Lecture 3] [Lecture 4] [Lecture 5] [Lecture 6] [Lecture 7] [Lecture 8] [Lecture 9] [Lecture 10] [Lecture 11] [Lecture 12]
Remark: These are informal notes from a 2021 course at Universidad Nacional de Colombia. They may contain mistakes or typos.
[2019] Una Guía para Escribir Matemáticas (translation to Spanish of "A Guide to Writing Mathematics" by Dr. Kevin P. Lee)
Joint with Alexander Leguizamón | [Document (Spanish)] [Original]
Remark: This is not a literal translation. It was created for local educational use. The author's name appears only to credit the original, not to imply collaboration or approval.