Research & publications

My mathematical research interests are in abstract algebra. Specifically, noncommutative algebra, Hopf algebras (and their generalizations), quantum groups & category theory. 

Publications & Preprints

[2024] Symmetries of algebras captured by actions of weak Hopf algebras (Algebras and Representation Theory )

Joint with Hongdi Huang, Elizabeth Wicks, Robert Won

[Slides Talk 1] [Slides Talk 2] [Talk 2]

[2023] Algebraic properties of face algebras (Journal of Algebra and Its Applications)

Joint with Chelsea Walton

[Talk 1] [Slides Talk 2]

[2022] Some interactions between Hopf Galois extensions and noncommutative rings (Universitas Scientiarum)

Joint with Armando Reyes

[Slides Talk 1] [Talk 2 (Spanish)] [Poster]

Dissertations, Theses & Final Projects

[2023] Doctorate  - Algebraic properties of weak quantum symmetries [Meritorious Mention]

Advisor: Dr. Chelsea Walton

Co-Advisor: Dr. Armando Reyes

[Document] [Slides Thesis Defense]

[Paper 1] [Talk 1.1] [Slides Talk 1.2]

[Paper 2] [Talk 2] [Slides Talk 2.1] [Slides Talk 2.2]

[2019] Master - Hopf Galois extensions and noncommutative rings [Meritorious Mention]

Advisor: Dr. Armando Reyes

[Document] [Slides Thesis Defense]

[Paper] [Slides Talk 1] [Talk 2 (Spanish)] [Poster]

[2016] Undergraduate - Construcción de álgebras de Hopf mediante extensiones de Ore (construction of Hopf algebras through Ore extensions)

Advisor: Dr. Armando Reyes

[Document (Spanish)] [Slides Talk] [Poster (Spanish)]

Others

[2023] Beamer template for Universidad Nacional de Colombia

[Template]

Remark: A Beamer template for presentations in Spanish at the National University of Colombia. Although it is not an official template, it has been created following the University's identity guidelines.

[2021] Notas de clase sobre Álgebras de Hopf (lecture notes -in Spanish- on Hopf algebras)

[Note 1 (Spanish)] [Note 2 (Spanish)] [Note 3 (Spanish)] [Note 4 (Spanish)] [Note 5 (Spanish)] [Note 6 (Spanish)] [Note 7 (Spanish)] [Note 8 (not available)] [Note 9 (Spanish)] [Note 10 (Spanish)] [Note 11 (Spanish)] [Note 12 (Spanish)]

Remark: these are informal notes that were written for a course in fall of 2021 at Universidad Nacional de Colombia. There could be mistakes, imprecisions and  typos. A cleaner LaTeX version (in English) is under construction.

[2019] Una Guía para Escribir Matemáticas por Dr. Kevin P. Lee (translation to Spanish of "A Guide to Writing Mathematics" by Dr. Kevin P. Lee)

Joint with Alexander Leguizamón | [Document (Spanish)] [Original]

Remark: this a (not so word-by-word) translation of the original mentioned document made with the sole purpose of sharing its contents with our local students and colleagues. We were not able to contact the author, so his name appears here and in the document as reference for his original work and not as implication of collaboration or approval.