Research

Research interests

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.

PhD Thesis

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

  1. Intermediate Jacobian fibration of a cubic fourfold containing a plane and Prym fibrations, to appear, 2022.
  2. On symplectic birational self-maps of projective hyperkähler manifolds of K3[n]-type, with Yajnaseni Dutta and Yulieth Prieto-Montañez, arXiv, 2022.
  3. A Lagrangian fibration on a moduli space of sheaves on a K3 surface, arXiv, 2021.
  4. Categorical vs Topological entropy of autoequivalences of surfaces , Moscow Mathematical Journal, 2021, Vol. 21, No 2, 401–412, doi , arXiv.

Other mathematical writing

  • Notes from the ERC HyperK Seminar (winter 2021): Gushel-Mukai manifolds, with P. Beri, O. Debarre and D. Pirozhkov, pdf
  • PhD thesis (2021): Study of moduli spaces and dynamics of derived categories, pdf
  • Master thesis (M2, 2018): pdf

Some workshops I attended