My thesis project involves looking at monoidal (∞ ,1) - categories as (∞, 2) - categories with one object. I'm mainly using the perspective of complete Segal Θn-spaces. One of the advantages of this perspective is that it can be generalized for models of (∞, n) - categories and is a perspective that I'm interested in exploring in the future.
I'm also interested in the topic of homotopical combinatorics, more specifically, transfer systems. Here is a wonderful introductory document to learn more about transfer systems. I'm currently part of two separate research projects in homotopical combinatorics:
As a follow-up on our collaboration in the WIT workshop, our team is exploring model category structures on n - dimensional finite grids using the tools of transfer systems in cyclic groups.
As part of the MRC event, our team is focusing on minimal generating sets for transfer systems for various families of groups.
Uniquely compatible transfer systems for cyclic groups of order prqs - with Kristen Mazur, Angélica Osorno, Constanze Roitzheim, Rekha Santhanam and Danika Van Niel. To be found soon in Topology and its applications, 2025.
On minimal bases in homotopical combinatorics - with Katharine Adamyk, Scott Balchin, Miguel Barrero, Steven Scheirer, Noah Wisdom. Preprint, 2025
You can also find my Master's thesis on the Atiyah-Segal completion theorem here. This project was completed at Universidad Nacional de Colombia, sede Medellínn and received the award: tésis meritoria (thesis cum laude).