## (pre)publications

- (With Andrei Neguț and Georg Oberdieck) Motivic decompositions for the Hilbert scheme of points of a K3 surface. arXiv:1912.09320.
- (With Andrew Harder, Zhiyuan Li, and Junliang Shen) P = W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds. arXiv:1908.07510.
- (With Junliang Shen, appendix by Claire Voisin) Topology of Lagrangian fibrations and Hodge theory of hyper-Kähler manifolds. arXiv:1812.10673.
- (With Georg Oberdieck and Junliang Shen) Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants. Adv. Math. 357 (2019), 106829, 28 pp.
- (With Junliang Shen) K3 categories, one-cycles on cubic fourfolds, and the Beauville-Voisin filtration. J. Inst. Math. Jussieu 19 (2020), no. 5, 1601-1627.
- (With Dan Petersen and Mehdi Tavakol) Tautological classes with twisted coefficients. Ann. Sci. Éc. Norm. Supér., to appear.
- (With Junliang Shen and Xiaolei Zhao) Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties. Compos. Math. 156 (2020), no. 1, 179-197.
- (With Rahul Pandharipande) Relations in the tautological ring of the moduli space of K3 surfaces. J. Eur. Math. Soc. (JEMS) 22 (2020), no. 1, 213-252.
- (With Nebojsa Pavic and Junliang Shen) On O'Grady's generalized Franchetta conjecture. Int. Math. Res. Not. IMRN (2017), no. 16, 4971-4983.
- (With Zhi Jiang) On the Chow ring of certain rational cohomology tori. C. R. Math. Acad. Sci. Paris 355 (2017), no. 5, 571-576.
- (With Yi Zhu) A
^{1}-equivalence of zero cycles on surfaces, II. Ann. K-Theory 3 (2018), no. 3, 379-393. - (With Jim Bryan, Georg Oberdieck, and Rahul Pandharipande) Curve counting on abelian surfaces and threefolds. Algebr. Geom. 5 (2018), no. 4, 398-463.
- Cycles on curves and Jacobians: a tale of two tautological rings. Algebr. Geom. 3 (2016), no. 2, 179-210.
- (With Ben Moonen) Some remarks on modified diagonals. Commun. Contemp. Math. 18 (2016), no. 1, 1550009, 16 pp.
- Finite-dimensionality and cycles on powers of K3 surfaces. Comment. Math. Helv. 90 (2015), no. 2, 503-511.
- Tautological cycles on curves and Jacobians. PhD thesis, Université Paris VI and Radboud Universiteit Nijmegen, 2013.
- The generic nontriviality of the Faber-Pandharipande cycle. Int. Math. Res. Not. IMRN (2015), no. 5, 1263-1277.

## fall 2020

This semester's Topics in Algebraic Geometry is a reading course on

Mark Andrea A. de Cataldo and Luca Migliorini, The Hodge theory of algebraic maps. Ann. Sci. École Norm. Sup. (4) 38 (2005), no. 5, 693-750.

The following surveys may be helpful:

- Mark Andrea A. de Cataldo and Luca Migliorini, The decomposition theorem, perverse sheaves and the topology of algebraic maps. Bull. Amer. Math. Soc. (N.S.) 46 (2009), no. 4, 535-633.
- Mark Andrea de Cataldo, Perverse sheaves and the topology of algebraic varieties. Geometry of moduli spaces and representation theory, 1-58, IAS/Park City Math. Ser., 24, Amer. Math. Soc., Providence, RI, 2017.
- Geordie Williamson, The Hodge theory of the decomposition theorem. Séminaire Bourbaki. Vol. 2015/2016. Exposés 1104-1119. Astérisque No. 390 (2017), Exp. No. 1115, 335-367.

Here is a full list of references.

## ag activities

Together with Baohua Fu, Lei Fu, Xiaotao Sun, and Zhiyu Tian, I organize the Beijing Algebraic Geometry Colloquium. I also keep a (far from complete) list of algebraic geometry activities in China.

## contact info

BICMR, Peking University

78306 Jingchunyuan Courtyard 78

5 Yiheyuan Road, Haidian District

Beijing 100871, China

+86 (10) 6274 4086