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. Splitting unramified Brauer classes by abelian torsors and the period-index problem , with Daniel Huybrechts, arXiv, 2023.
  2. The special Brauer group and twisted Picard varieties, with Daniel Huybrechts, arXiv, 2023.
  3. Intermediate Jacobian fibration of a cubic fourfold containing a plane and Prym fibrations, arXiv, 2023.
  4. On symplectic birational self-maps of projective hyperkähler manifolds of K3[n]-type, with Yajnaseni Dutta and Yulieth Prieto-Montañez, arXiv, 2022.
  5. Moduli spaces of sheaves on Fano threefolds and K3 surfaces of genus 9, to appear in Ann. Inst. Fourier, arXiv, 2021.
  6. 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