Research
Selected works
Cohomological Hall algebras and their representations via torsion pairs
Joint with Emanuel D. Diaconescu and F. Sala
My third work on representation theory. Combining techniques from higher Segal spaces and derived geometry, we show how a torsion pair on the heart of a t-structure on a 2-dimensional stable \infty-category give rise to a cohomological Hall algebra and a left representation. Under some favorable hypotheses we show that a right representation also exists, and that the two representations together give rise to a geometric Yangian, unifying and generalizing several already known constructions in the literature.
ArXiv HAL
Two-dimensional categorified Hall algebras
Joint with Francesco Sala. Journal of the European Mathematical Society (JEMS) 25 (2023), no. 3, pages 1113–1205.
My first work in representation theory. Using the language of derived geometry and the extended functoriality it grants to topological invariants, we unified all the previously known constructions of 2-dimensional cohomological Hall algebras, and we provided new ones. At the same time, we categorified this important invariant and we studied its behaviour under the non-abelian Hodge correspondence.
Non-archimedean quantum K-invariants
Joint with Tony Y. Yu. Accepted for publication in Journal de l'Ecole Normale Supérierure (2023).
It is the culmination of my work on the non-archimedean approach to mirror symmetry. In this paper we establish the existence of derived analytic stacks of stable curves with target a smooth analytic space, and we use it to provide a geometric formulation of Kontsevich-Manin axioms for Gromov-Witten theory.
Representability theorem in derived analytic geometry
Joint with Tony Y. Yu. Journal of the European Mathematical Society (2020), no. 12, 113-1205.
Motivated by Kontsevich-Soibelman's program on the non-archimedean approach to mirror symmetry, we initiated a vast foundational program aiming at exporting all features of derived algebraic geometry to the non-archimedean setting. This paper is a milestone of this program, and establishes all key results of derived deformation theory, including the fundamental Lurie representability theorem.
GAGA theorems in derived complex geometry
Journal of Algebraic Geometry (2019), no. 28, 519-565.
My first work. Starting from the foundations for derived complex geometry sketched by Jacob Lurie in [DAG-IX], I showed that a number of fundamental results carry over from the algebraic to the analytic setting, and as a consequence I extended Serre's GAGA theorem to the derived world.