Publications

  1. with Xuqiang Qin, Birational geometry of Beauville-Mukai systems III: asymptotic behavior, preprint arXiv:2210.03095.
  2. with Xuqiang Qin, Birational geometry of Beauville-Mukai systems II: general theory in low ranks, to appear in Mathematical Research Letters (2023), 33 pages.
  3. with Xuqiang Qin, Birational geometry of Beauville-Mukai systems I: the rank three and genus two case, Mathematische Zeitschrift 305, 23 (2023), https://doi.org/10.1007/s00209-023-03353-z.
  4. Topological bounds on hyperkähler manifolds, Experimental Mathematics (2023), 17 pages, https://doi.org/10.1080/10586458.2023.2172630.
  5. with Chen Shen, Deformations of compact Prym fibrations to Hitchin systems, Bulletin of the London Mathematical Society 54 (2022), no. 5, 1568-1583, https://doi.org/10.1112/blms.12643.
  6. A bound on the second Betti number of hyperkähler manifolds of complex dimension six, European Journal of Mathematics 8 (2022), 1196-1212, https://doi.org/10.1007/s40879-021-00526-0.
  7. Singular fibres of very general Lagrangian fibrations, Communications in Contemporary Mathematics 24 (2021), no. 9, 19 pp., https://doi.org/10.1142/S021919972150070X.
  8. Lagrangian fibrations by Prym varieties, Matemática Contemporânea 47 (2020), 182-227, https://doi.org/10.21711/231766362020/rmc479.
  9. with Kelly McKinnie, Sho Tanimoto, and Anthony Várilly-Alvarado, Brauer groups on K3 surfaces and arithmetic applications, Brauer groups and obstruction problems, 177-218, Progress in Mathematics 320, Birkhäuser/Springer, Cham, 2017, https://doi.org/10.1007/978-3-319-46852-5_9.
  10. Moduli spaces of sheaves on K3 surfaces, Journal of Geometry and Physics 109 (2016), 68-82, https://doi.org/10.1016/j.geomphys.2016.02.017.
  11. A finiteness theorem for Lagrangian fibrations, Journal of Algebraic Geometry 25 (2016), no. 3, 431-459, https://doi.org/10.1090/jag/673.
  12. Isotrivial elliptic K3 surfaces and Lagrangian fibrations, preprint arXiv:1406.1233.
  13. On Lagrangian fibrations by Jacobians II, Communications in Contemporary Mathematics 17, no. 5 (2015), 1450046, 23 pp, https://doi.org/10.1142/S0219199714500461.
  14. with Rebecca Glover, Generalized twistor spaces for hyperkähler manifolds, Journal of the London Mathematical Society (2) 91 (2015), no. 2, 321-342, https://doi.org/10.1112/jlms/jdu074.
  15. Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfaces, preprint arXiv:1209.3202.
  16. On Lagrangian fibrations by Jacobians I, Journal für die reine und angewandte Mathematik 701 (2015), 127-151, https://doi.org/10.1515/crelle-2013-0023.
  17. Fibrations on four-folds with trivial canonical bundles, Geometriae Dedicata 171 (2014), 93-117, https://doi.org/10.1007/s10711-013-9890-x.
  18. Foliations on hypersurfaces in holomorphic symplectic manifolds, International Mathematics Research Notices (2009), no. 23, 4496-4545.
  19. Deformations of holomorphic Lagrangian fibrations, Proceedings of the AMS 137
    (2009), no. 1, 279-285.
  20. Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds, Advances in Mathematics 218 (2008), no. 3, 828-864.
  21. On the discriminant locus of a Lagrangian fibration, Mathematische Annalen 341 (2008), no. 1, 201-221.
  22. Lagrangian fibrations on Hilbert schemes of points on K3 surfaces, Journal of Algebraic Geometry 16 (2007), no. 3, 477-497.
  23. Perturbative expansion of Chern-Simons theory, Geometry and Topology Monographs, Vol. 8 (2006), The interaction of finite-type and Gromov-Witten invariants (Banff 2003), 145-166.
  24. Derived equivalence of holomorphic symplectic manifolds, in Algebraic Structures and Moduli Spaces: CRM Workshop, Montreal 14-20 July 2003, CRM Proceedings & Lecture Notes Series, Volume 38 (2004), 193-211.
  25. Abelian fibred holomorphic symplectic manifolds, Turkish Journal of Mathematics 27 (2003), No. 1, 197-230. (Proceedings of the Ninth Gokova Geometry-Topology Conference, Turkey, 27th to 31st May 2002.)
  26. with Justin Roberts, Generalizations of Rozansky-Witten invariants, Geometry and Topology Monographs, Vol. 4 (2002), Invariants of knots and 3-manifolds (Kyoto 2001), 263-279.
  27. with Michael Eastwood, The Borel-Weil theorem for complex projective space, in Invitations to Geometry and Topology, Oxford Graduate Texts in Mathematics, OUP (2002), 126-145.
  28. Topological quantum field theory and hyperkähler geometry, Turkish Journal of Mathematics 25 (2001), No. 1, 169-194. (Proceedings of the Seventh Gokova Geometry-Topology Conference, Turkey, 29th May to 3rd June 2000.)
  29. with Nigel Hitchin, Curvature and characteristic numbers of hyperkähler manifolds, Duke Mathematical Journal 106 (2001), no. 3, 599-615.
  30. A new weight system on chord diagrams via hyperkähler geometry, Proceedings of the Second Meeting on Quaternionic Structures in Mathematics and Physics, Rome 6-10 September 1999, World Scientific (2001), 349-363.
  31. When is a Lie algebra not a Lie algebra?, Proceedings of the IXth Oporto Meeting on Geometry, Topology and Physics, September 29th to October 2nd, 2000, 1-16.
  32. Homomorphisms of semiholonomic Verma modules: an exceptional case, Acta Mathematica Universitatis Comenianae 68 (1999), no. 2, 257-269.
  33. The Rozansky-Witten invariants of hyperkähler manifolds, Proceedings of the 7th International Conference on Differential Geometry and Applications, Satellite Conference of ICM in Berlin, Aug. 10-14, 1998, Brno, Czech Republic (1999), 429-436.

Dissertations:

  1. Rozansky-Witten invariants of hyperkähler manifolds, PhD thesis, University of Cambridge (1999).
  2. Homomorphisms of semiholonomic Verma modules: an exceptional case, MSc thesis, University of Adelaide (1996).

Unpublished:

  1. Rozansky-Witten invariants for non-compact manifolds, August 2001.
  2. Actions of the mapping class groups on hyperkähler cohomology, May 2001.

Other:

  1. notes of lectures by Nigel Hitchin, Riemann surfaces and integrable systems, in Integrable Systems: Twistors, Loop Groups, and Riemann Surfaces, Oxford Graduate Texts in Mathematics, Clarendon Press (1999), 11-52.