## Research interest

- motives and algebraic cycles
- derived categories
- Calabi-Yau varieties
- holomorphic symplectic (a.k.a. hyper-Kähler) varieties
- moduli spaces of sheaves
- Hodge theory
- orbifold cohomology
- Fano varieties

## Publications and preprints

My research profile on ArXiv, Google Scholar, MathSciNet, zbMATH.- Hochschild cohomology of Hilbert schemes of points on surfaces, (with P. Belmans, A. Krug)

Preprint 2023, arXiv: 2309.06244 - Maximal real varieties from moduli constructions,

Preprint 2023, arXiv: 2303.03368 - Unpolarized Shafarevich conjectures for hyper-Kähler varieties, (with Z. Li, T. Takamatsu, and H. Zou)

Preprint 2022, arXiv:2203.10391 - A remark on the higher torsion invariants for flat vector bundles with finite holonomy, (with Y. Zhang)

Preprint 2022, arXiv:2203.02353 - The Tate Conjecture for even dimensional Gushel-Mukai varieties in characteristic p≥5, (with B. Moonen)

**Journal of Algebraic Geometry**(2024), to appear. arXiv: 2207.01122. Here are the Magma files we used and some documentation. - 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 - Cubic fourfolds, Kuznetsov components and Chow motives, (with Ch. Vial)

**Documenta Mathematica**, 28 (2023), 827–856. , Open access - 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 - Motivic integration and the birational invariance of BCOV invariants, (with Y. Zhang)

**Selecta Mathematica (N.S.)**, (2023) 29:25. Journal. - 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. - Special cubic fourfolds, K3 surfaces and the Franchetta property (with R. Laterveer)

**International Mathematics Research Notices**no. 11, 8769–8802,(2022). Open access - 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 - 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 - 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 - Categorical polynomial entropy, (with Y.-W. Fan and G. Ouchi)

**Advances in Mathematics**, Volume 383, No. 107655 (2021). Open access!

- Supersingular O'Grady varieties of dimension six, (with Z. Li and H. Zou)

**International Mathematical Research Notices**, 11, (2022), 8769–8802, Link. - Supersingular irreducible symplectic varieties, (with Z. Li)

Rationality of Algebraic Varieties, 147-200 (2021).

**Progress in Mathematics, volume 342, Birkhäuser.**Link - 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 - On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four, (with G. Menet)

**Mathematische Zeitschrift**, 299 (2021), 203–231. Open access! - 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 - 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 - Distinguished cycles on varieties with motive of abelian type and the Section Property, (with Ch. Vial)

**Journal of Algebraic Geometry**, 29 (2020), 53–107. - 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 - Orbifold products for higher K-theory and motivic cohomology, (with M. T. Nguyen)
**Documenta Mathematica**24, 1769-1810 (2019). - Motivic hyper-Kähler resolution conjecture: I. Generlized Kummer varieties, (with Z. Tian and Ch. Vial)

**Geometry & Topology**, 23-1 (2019), 427-492. - 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. - 2-cycles sur les hypersurfaces cubiques de dimension 5, (with Z. Tian)
**Mathematische Zeitschrift**(2019) Volume 293, Issue 1–2, 661–676. - Motivic multiplicative McKay correspondence for surfaces, (with Z. Tian)
**Manuscripta Mathematica**(2019), 158 (3), 295-316. - 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.

- Motivic hyper-Kähler resolution conjecture: II. Hilbert schemes of K3 surfaces. (with Z. Tian)

Preprint. - Beauville-Voisin conjecture for generalized Kummer varieties.

**International Mathematics Research Notices**(2015), no. 12, 3878-3898. - Classification of polarized symplectic automorphisms of Fano varieties of cubic fourfolds.

**Glasgow Mathematical Journal**, Volume 58, Issue 01, (2016), 17-37. - 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. - Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections.

**Advances in Mathematics**(2013), pp. 894-924. - On the coniveau of certain sub-Hodge structures.

**Mathematical Research Letters**19 (2012), No. 05, 1097-1116.

## Others

- Around hyper-Kähler varieties: motives, supersingularity and automorphisms.

Habilitation thesis. - Sub-Hodge structures, Chow rings and action of certain automorphisms.

Ph.D. thesis (advisor: Claire Voisin). - Cohomological operations in Chow theory.

Master thesis (advisor: Bruno Kahn). - Classes de conjugaison tordues des groupes de lacets et G-fibrés sur courbes elliptiques.

Memoir of first year (with Tristan Roussel, advisor: David Hernandez)