Francesco Genovese bio photo

Francesco Genovese

Postdoc researcher in Mathematics

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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

Preprints

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)