1. (With Andrei Neguț and Georg Oberdieck) Motivic decompositions for the Hilbert scheme of points of a K3 surface. arXiv:1912.09320.
  2. (With Andrew Harder, Zhiyuan Li, and Junliang Shen) P = W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds. arXiv:1908.07510.
  3. (With Junliang Shen, appendix by Claire Voisin) Topology of Lagrangian fibrations and Hodge theory of hyper-Kähler manifolds. arXiv:1812.10673.
  4. (With Georg Oberdieck and Junliang Shen) Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants. Adv. Math. 357 (2019), 106829, 28 pp.
  5. (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.
  6. (With Dan Petersen and Mehdi Tavakol) Tautological classes with twisted coefficients. Ann. Sci. Éc. Norm. Supér., to appear.
  7. (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.
  8. (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.
  9. (With Nebojsa Pavic and Junliang Shen) On O'Grady's generalized Franchetta conjecture. Int. Math. Res. Not. IMRN (2017), no. 16, 4971-4983.
  10. (With Zhi Jiang) On the Chow ring of certain rational cohomology tori. C. R. Math. Acad. Sci. Paris 355 (2017), no. 5, 571-576.
  11. (With Yi Zhu) A1-equivalence of zero cycles on surfaces, II. Ann. K-Theory 3 (2018), no. 3, 379-393.
  12. (With Jim Bryan, Georg Oberdieck, and Rahul Pandharipande) Curve counting on abelian surfaces and threefolds. Algebr. Geom. 5 (2018), no. 4, 398-463.
  13. Cycles on curves and Jacobians: a tale of two tautological rings. Algebr. Geom. 3 (2016), no. 2, 179-210.
  14. (With Ben Moonen) Some remarks on modified diagonals. Commun. Contemp. Math. 18 (2016), no. 1, 1550009, 16 pp.
  15. Finite-dimensionality and cycles on powers of K3 surfaces. Comment. Math. Helv. 90 (2015), no. 2, 503-511.
  16. Tautological cycles on curves and Jacobians. PhD thesis, Université Paris VI and Radboud Universiteit Nijmegen, 2013.
  17. 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:

  1. 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.
  2. 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.
  3. 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.

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