Teaching:

Spring 2010:

MATH681 Introductory Topology

Publications (click on titles for abstracts and to download):

1. "Fibrations on four-folds with trivial canonical bundles", preprint arXiv:0904.0273.
2. "Foliations on hypersurfaces in holomorphic symplectic manifolds", preprint arXiv:0812.3939.
3. "A classification of Lagrangian fibrations by Jacobians", preprint arXiv:0803.1186.
4. "Deformations of holomorphic Lagrangian fibrations", Proceedings of the AMS 137 (2009), no. 1, 279-285.
5. "Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds", Advances in Mathematics 218 (2008), no. 3, 828-864.
6. "On the discriminant locus of a Lagrangian fibration", Mathematische Annalen 341 (2008), no. 1, 201-221.
7. "Lagrangian fibrations on Hilbert schemes of points on K3 surfaces", Journal of Algebraic Geometry 16 (2007), no. 3, 477-497.
8. "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.
9. "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.
10. "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.)
11. 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.
12. 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.
13. "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.)
14. "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.
15. with Nigel Hitchin, "Curvature and characteristic numbers of hyperkähler manifolds", Duke Mathematical Journal 106 (2001), no. 3, 599-615.
16. "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.
17. "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.
18. "Homomorphisms of semiholonomic Verma modules: an exceptional case", Acta Mathematica Universitatis Comenianae 68 (1999), no. 2, 257-269.

Dissertations:

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

Unpublished:

• "Rozansky-Witten invariants for non-compact manifolds", work in progress, August 2001.
• "Actions of the mapping class groups on hyperkähler cohomology", work in progress, May 2001.

Other:

• 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).

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