Publications

  1. Singular fibres of very general Lagrangian fibrations, preprint arXiv:1905.03386.
  2. Lagrangian fibrations by Prym varieties, Matemática Contemporânea, to appear.
  3. Moduli spaces of sheaves on K3 surfaces, Journal of Geometry and Physics 109 (2016), 68-82.
  4. A bound on the second Betti number of hyperkähler manifolds of complex dimension six, preprint arXiv:1511.09105.
  5. Isotrivial elliptic K3 surfaces and Lagrangian fibrations, preprint arXiv:1406.1233.
  6. 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.
  7. with Rebecca Glover, Generalized twistor spaces for hyperkähler manifolds, Journal of the London Mathematical Society (2) 91 (2015), no. 2, 321-342.
  8. A finiteness theorem for Lagrangian fibrations, Journal of Algebraic Geometry 25 (2016), no. 3, 431-459.
  9. Fourier-Mukai transforms, mirror symmetry, and generalized K3 surfaces, preprint arXiv:1209.3202.
  10. On Lagrangian fibrations by Jacobians II, Communications in Contemporary Mathematics 17, 1450046 (2015).
  11. Fibrations on four-folds with trivial canonical bundles, Geometriae Dedicata 171 (2014), 93-117.
  12. On Lagrangian fibrations by Jacobians I, Journal für die reine und angewandte Mathematik 701 (2015), 127-151.
  13. Foliations on hypersurfaces in holomorphic symplectic manifolds, International Mathematics Research Notices (2009), no. 23, 4496-4545.
  14. Deformations of holomorphic Lagrangian fibrations, Proceedings of the AMS 137
    (2009), no. 1, 279-285.
  15. Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds, Advances in Mathematics 218 (2008), no. 3, 828-864.
  16. On the discriminant locus of a Lagrangian fibration, Mathematische Annalen 341 (2008), no. 1, 201-221.
  17. Lagrangian fibrations on Hilbert schemes of points on K3 surfaces, Journal of Algebraic Geometry 16 (2007), no. 3, 477-497.
  18. 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.
  19. 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.
  20. 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.)
  21. 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.
  22. 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.
  23. 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.)
  24. 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.
  25. with Nigel Hitchin, Curvature and characteristic numbers of hyperkähler manifolds, Duke Mathematical Journal 106 (2001), no. 3, 599-615.
  26. 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.
  27. 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.
  28. Homomorphisms of semiholonomic Verma modules: an exceptional case, Acta Mathematica Universitatis Comenianae 68 (1999), no. 2, 257-269.

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).