On the higher categorical side, I'm working on a paper with my thesis work for general (∞,n) - categories using complete Segal Θn-spaces. I am also working on a project that explores the definition of the Bordism category as an (∞,∞) - category using complicial spaces.
I'm also interested in the topic of homotopical combinatorics, which has in its center the objects of transfer systems. Here is a wonderful introductory document to learn more about what transfer systems are. Within this field, I'm currently working on a project that studies left and right Bousfield localizations for different posets using transfer systems.
Characterizing model structures on finite posets - with Kristen Mazur, Angélica Osorno, Constanze Roitzheim, Rekha Santhanam and Danika Van Niel. Preprint, 2025. To be found soon in Math Z.
On minimal bases in homotopical combinatorics - with Katharine Adamyk, Scott Balchin, Miguel Barrero, Steven Scheirer, Noah Wisdom. Preprint, 2025. To be found soon in Glasgow Math Journal.
Uniquely compatible transfer systems for cyclic groups of order prqs - with Kristen Mazur, Angélica Osorno, Constanze Roitzheim, Rekha Santhanam and Danika Van Niel. Topology and its applications, 376, 2025.
My PhD thesis project consisted of looking at monoidal (∞,1) - categories as (∞, 2) - categories with one object. I mainly used the perspective of Segal Θ2-spaces with varying conditions of completeness and discreteness.
Segal Θ2-monoids as monoidal (∞,1) - categories - UVA thesis repository, 2025.
My Master's thesis was on the Atiyah-Segal completion theorem. This project was completed at Universidad Nacional de Colombia, sede Medellín and received the award: tésis meritoria (thesis cum laude).
Atiyah-Segal’s completion theorem - Universidad Nacional de Colombia thesis repository, 2020.