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
On minimal bases in homotopical combinatorics - with Katharine Adamyk, Scott Balchin, Miguel Barrero, Steven Scheirer, Noah Wisdom. Preprint, 2025
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.