My main research topics are the holomorphically symplectic orbifolds, the integral cohomology of quotients, the moduli spaces of stable sheaves on a K3 surface, the Lagrangian fibrations and the mirror symmetry of the hyperkähler manifolds. I also worked on the construction of G_2 instantons via twisted connected sums.

1. Integral cohomology of quotients via toric geometry, Épijournal de Géométrie Algébriqu, Volume 6, Article Nr.3 (Version arXiv).

2. On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four, Mathematische Zeitschrift, 299 (2021), no.1-2, 203-231 (Version arXiv).                       In collaboration with Lie Fu.                        

3. Construction of G_2-instantons via twisted connected sums. Mathematical Research Letters, 28 (2021), no.2, 471-509 (Version arXiv).   In collaboration with Johannes Nordström and Henrique N. Sa Earp.

4. Global Torelli theorem for irreducible symplectic orbifolds.                                           Journal de Mathématiques pures et appliquées, 137 (2020), no.9, 213-237 (Version arXiv).

5. Brane involutions on irreducible holomorphic symplectic manifolds. 
Kyoto Journal of Mathematics, 59 (2019), no.1, 195-235 (Version arXiv).
In collaboration with Emilio Franco and Marcos Jardim.

6. Integral cohomology of the generalized Kummer fourfold.                                      Algebraic Geometry, 5 (2018), no.5, 523-567 (Version arXiv).                                                   In collaboration with Simon Kapfer.

7. On the integral cohomology of quotients of manifolds by cyclic groups.                       Journal de Mathémariques pures et appliquées, 119 (2018), no.9, 280-325  (Version arXiv).

8. Holomorphic bundles for higher dimensional gauge theory.                                        Bulletin of the London Mathematical Society, 49 (2017), no.1,117-132 (Version arXiv). In collaboration with Marcos Jardim, Daniela M. Prata and Henrique N. Sa Earp.

9. Beauville-Bogomolov lattice for a singular symplectic variety of dimension 4.
Journal of Pure and Applied Algebra, 219 (2015), no. 5, 1455-1495  (Version arXiv).

10. Duality for relative Prymians associated to K3 double covers of del Pezzo surface of degree 2. Mathematische Zeitschrift: Volume 277, Issue 3 (2014), Page 893-907 (Version arXiv).

1. Thirty-three deformation classes of compact hyperkähler orbifolds (Version arXiv).

2. Wall divisors on irreducible symplectic orbifolds of M'-type (bientôt sur arXiv, version préliminaire en pdf). In collaboration with Ulrike Riess.

3. On the Kähler cone of irreducible symplectic orbifolds (Version arXiv). In collaboration with Ulrike Riess.

 

I defended my PhD, under the supervision of Dimitri Markushevich, the July 9th 2014 at Lille 1 university. A pdf version of my thesis, entitled Integral cohomology and Lagrangian fibration of some singular irreducible symplectic varieties, can be found here.