Research interest

Publications and preprints

My research profile on ArXiv, Google Scholar, MathSciNet, zbMATH.
  1. Twisted Hodge groups and deformation theory of Hilbert schemes of points on surfaces via Hodge modules,
    Preprint 2024, arXiv: 2412.09975
  2. Hochschild cohomology of Hilbert schemes of points on surfaces, (with P. Belmans, A. Krug)
    Preprint 2023, arXiv: 2309.06244
  3. A remark on the higher torsion invariants for flat vector bundles with finite holonomy, (with Y. Zhang)
    Preprint 2022, arXiv:2203.02353
  4. Maximal real varieties from moduli constructions,
    Moduli (2025), to appear, arXiv: 2303.03368
  5. Unpolarized Shafarevich conjectures for hyper-Kähler varieties, (with Z. Li, T. Takamatsu, and H. Zou)
    Algebraic Geometry (2025), to appear, arXiv:2203.10391
  6. The Tate Conjecture for even dimensional Gushel-Mukai varieties in characteristic p≥5, (with B. Moonen)
    Journal of Algebraic Geometry 34 (2025) 233–298. Journal.
    Here are the Magma files we used and some documentation.
  7. Algebraic cycles on Gushel–Mukai varieties, (with B. Moonen)
    Épijournal de Géométrie Algébrique, special volume in honor of Claire Voisin, Article No. 17 (2024) Open access
  8. Cubic fourfolds, Kuznetsov components and Chow motives, (with Ch. Vial)
    Documenta Mathematica, 28 (2023), 827–856. , Open access
  9. Motives of moduli spaces of bundles on curves via variation of stability and flips, (with V. Hoskins and S. Pepin Lehalleur)
    Journal of the London Mathematical Society, (2) 108:1–53 (2023) Open access
  10. Motivic integration and the birational invariance of BCOV invariants, (with Y. Zhang)
    Selecta Mathematica (N.S.), (2023) 29:25. Journal.
  11. Derived categories of flips and cubic hypersurfaces, (with P. Belmans and T. Raedschelders)
    Proceedings of the London Mathematical Society, (3) 125 (2022), no. 6, 1452–1482. Journal.
  12. Special cubic fourfolds, K3 surfaces and the Franchetta property (with R. Laterveer)
    International Mathematics Research Notices no. 11, 8769–8802,(2022). Open access
  13. Stability manifolds of varieties with finite Albanese morphisms, (with C. Li and X. Zhao)
    Transactions of the American Mathematical Society, 375 (2022), no. 8, 5669–5690. arXiv:2103.07728
  14. Motives of moduli spaces of rank 3 vector bundles and Higgs bundles on a curve, (with V. Hoskins and S. Pepin Lehalleur)
    Special issue "Birational geometry and moduli of projective varieties"
    Electronic Research Archive Volume 30, Issue 1: 66-89 (2022), Open access
  15. The generalized Franchetta conjecture for some hyper-Kähler varieties, II, (with R. Laterveer and Ch. Vial)
    Journal de l'École polytechnique -- Mathématiques, Tome 8 (2021), pp. 1065-1097. Open access
  16. Categorical polynomial entropy, (with Y.-W. Fan and G. Ouchi)
    Advances in Mathematics, Volume 383, No. 107655 (2021). Open access!
  17. Supersingular O'Grady varieties of dimension six, (with Z. Li and H. Zou)
    International Mathematical Research Notices, 11, (2022), 8769–8802, Link.
  18. Supersingular irreducible symplectic varieties, (with Z. Li)
    Rationality of Algebraic Varieties, 147-200 (2021).
    Progress in Mathematics, volume 342, Birkhäuser. Link
  19. A motivic global Torelli theorem for isogenous K3 surfaces, (with Ch. Vial)
    Advances in Mathematics, Volume 383, No. 107674 (2021). Open access Here is a longer version with an extra Section A.5
  20. On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four, (with G. Menet)
    Mathematische Zeitschrift, 299 (2021), 203–231. Open access!
  21. Multiplicative Chow-Künneth decompositions and varieties of cohomological K3 type, (with R. Laterveer and Ch. Vial)
    Annali di Matematica Pura ed Applicata, 200(5), 2085-2126 (2021). Open access
  22. On the motive of O'Grady's ten-dimensional hyper-Kähler varieties, (with S. Floccari and Z. Zhang) Erratum.
    Communications in Contemporary Mathematics, Vol. 23, No. 04, 2050034 (2021). Open access
  23. Distinguished cycles on varieties with motive of abelian type and the Section Property, (with Ch. Vial)
    Journal of Algebraic Geometry, 29 (2020), 53–107.
  24. Hilbert squares: derived categories and deformations, (with P. Belmans and T. Raedschelders)
    Selecta Mathematica (N.S.) 25, no. 3, Paper No. 37 (2019). Open access
  25. Orbifold products for higher K-theory and motivic cohomology, (with M. T. Nguyen)
    Documenta Mathematica 24, 1769-1810 (2019).
  26. Motivic hyper-Kähler resolution conjecture: I. Generlized Kummer varieties, (with Z. Tian and Ch. Vial)
    Geometry & Topology, 23-1 (2019), 427-492.
  27. Finiteness of Klein actions and real structures on compact hyper-Kähler manifolds, (with A. Cattaneo)
    Mathematische Annalen (2019), Volume 375, Issue 3–4, 1783–1822.
  28. 2-cycles sur les hypersurfaces cubiques de dimension 5, (with Z. Tian)
    Mathematische Zeitschrift (2019) Volume 293, Issue 1–2, 661–676.
  29. Motivic multiplicative McKay correspondence for surfaces, (with Z. Tian)
    Manuscripta Mathematica (2019), 158 (3), 295-316.
  30. The generalized Franchetta conjecture for some hyper-Kähler varieties, (with R. Laterveer, Ch. Vial and M. Shen)
    Journal de Mathématiques Pures et Appliquées 130 (2019) 1–35.
  31. Motivic hyper-Kähler resolution conjecture: II. Hilbert schemes of K3 surfaces. (with Z. Tian)
    Preprint.
  32. Beauville-Voisin conjecture for generalized Kummer varieties.
    International Mathematics Research Notices (2015), no. 12, 3878-3898.
  33. Classification of polarized symplectic automorphisms of Fano varieties of cubic fourfolds.
    Glasgow Mathematical Journal, Volume 58, Issue 01, (2016), 17-37.
  34. On the action of symplectic automorphisms on the CH_0-groups of some hyper-Kähler fourfolds.
    Mathematische Zeitschrift, 280 (2015), no. 1-2, 307-334.
  35. Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections.
    Advances in Mathematics (2013), pp. 894-924.
  36. On the coniveau of certain sub-Hodge structures.
    Mathematical Research Letters 19 (2012), No. 05, 1097-1116.

Others

  1. Around hyper-Kähler varieties: motives, supersingularity and automorphisms.
    Habilitation thesis.
  2. Sub-Hodge structures, Chow rings and action of certain automorphisms.
    Ph.D. thesis (advisor: Claire Voisin).
  3. Cohomological operations in Chow theory.
    Master thesis (advisor: Bruno Kahn).
  4. Classes de conjugaison tordues des groupes de lacets et G-fibrés sur courbes elliptiques.
    Memoir of first year (with Tristan Roussel, advisor: David Hernandez)