Research

Overview

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.

Caveat: PDF files uploaded here are often more up-to-date than the arXiv versions.

Publications

• T-structures on unbounded twisted complexes, Mathematische Zeitschrift, 2023 (PDF).

• 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)

Preprints

• T-structures on dg-categories and derived deformations, joint with Wendy Lowen and Michel Van den Bergh, 2022 (PDF) (Seminar)

• Uniqueness of dg-lifts via restriction to injective objects, 2022 (PDF)

• T-structures on unbounded twisted complexes, 2022 (PDF), accepted for publication in Mathematische Zeitschrift

In preparation

• 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)

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