My main research field are hyperKähler varieties. I'm interested in their links with Fano varieties, particularly cubic threefolds and fourfolds. On the otherhand, I study the geometry of Lagrangian fibrations on such varieties. I like to use derived tools, as derived categories, homological projective duality, Bridgeland stability conditions.
My PhD topic splits into two parts. On the one hand, I study autoequivalences of the derived categories of smooth projective complex surfaces. I'm interested in the action on cohomology they induce and in their categorical entropy. On the other hand, I study moduli spaces of sheaves on Fano threefold, K3 surfaces and I'm interested in stability conditions on K3 surfaces and hyperKähler varieties.
Publications and preprints
- Intermediate Jacobian fibration of a cubic fourfold containing a plane and Prym fibrations, to appear, 2022.
- On symplectic birational self-maps of projective hyperkähler manifolds of K3[n]-type, with Yajnaseni Dutta and Yulieth Prieto-Montañez, arXiv, 2022.
- A Lagrangian fibration on a moduli space of sheaves on a K3 surface, arXiv, 2021.
- Categorical vs Topological entropy of autoequivalences of surfaces , Moscow Mathematical Journal, 2021, Vol. 21, No 2, 401–412, doi , arXiv.
Other mathematical writing
Some workshops I attended
- September 2022: Hyperkähler varieties and related topics, Sapienza Università di Roma.
- June 2022: CATS60 (in honor of Carlos Simpson), Toulouse, IMT.
- May 2022: Géométrie algébrique en l'honneur de Claire Voisin, Paris, IHP.
- November 2019: Géométrie Algébrique, Géométrie Complexe, Marseille, CIRM.
- September 2019: The Geometry of Derived Categories, Liverpool University.
- June 2019: Workshop on Derived Categories, Moduli Spaces and Deformation Theory, Cetraro, Italy.
- December 2018: Géométrie Algébrique, Géométrie Complexe, Marseille, CIRM.