My work is centered on homological algebra, which is essentially the study of “linearized scaffolds of spaces”: chain complexes, (co)homology and so on. In some sense, homological algebra is “higher dimensional linear algebra”. I’m mostly interested in the theory and applications of differential graded (=dg) categories, which are categories whose hom-sets are themselves chain complexes. Dg-categories are, in fact, part of the world of higher categories, and they serve as enhancements for triangulated categories - a common tool in contemporary algebra and algebraic geometry.
A derived Gabriel-Popescu theorem for t-structures via derived injectives, joint with Julia Ramos González, International Mathematics Research Notices, 2022 (PDF) (Poster)
T-structures and twisted complexes on derived injectives, joint with Wendy Lowen and Michel Van den Bergh, Advances in Mathematics, 2021 (PDF)
Adjunctions of quasi-functors between dg-categories, Applied Categorical Structures, 2017 (PDF)
The uniqueness problem of dg-lifts and Fourier–Mukai kernels, Journal of the London Mathematical Society, 2016 (PDF)
T-structures on dg-categories and derived deformations, joint with Wendy Lowen and Michel Van den Bergh
Tensor products of Grothendieck t-dg-categories, joint with Julia Ramos González
Perfect complexes of twisted sheaves and dg-enhancements, joint with Riccardo Moschetti and Giorgio Scattareggia (poster)