University of Oxford

The Geometry Group at Oxford University is world-renowned and includes leading scholars in various branches of geometry and several elite experts in moduli spaces. More generally, the Mathematics Department is among the several best in the world. Nigel Hitchin is the Savilian Professor of Mathematics and leads the Geometry Group at Oxford. He is the unparalleled expert on the moduli spaces of Higgs bundles over Riemann surfaces. He pioneered the study of these spaces in the late eighties and since then has made fundamental contributions to their study. They are related to a broad spectrum of geometric, analytic, and topological structures which he has implemented on these spaces with breathtaking elegance. The Hitchin system on these moduli spaces forms a cornerstone in his proof that the Hitchin connection in the geometric quantization of moduli spaces is projectively at an essential tool for the relation to the Reshetikhin-Turaev TQFT. His work on monopole moduli space in three dimensions joint with Sir Michael Atiyah and the instanton moduli spaces in four dimensions joint with Atiyah and Isadore Singer has been extremely influential and forms the very foundation for the study of these moduli spaces. In fact, extensions of this work were subsequently used by Hitchin's student, Fields Medalist Donaldson, to prove one of the biggest results in topology of the previous fty years. Hitchin has further contributed significantly to the development of Penrose twistor theory and linked it to the study of moduli spaces. It is only the limitation of space in this proposal that precludes us from further discussion of his many important contributions over the years. Going back to his graduate student days, QGM Center Leader Prof. Jørgen E. Andersen has had continuous inspired input from Hitchin, which has deeply affected his own research. Hitchin also spoke at the inaugural symposium for QGM. Hitchin has invented a new branch of mathematics call Generalized Complex Geometry which is of central interest currently in theoretical physics. It plays a role in the Geometric Langlands Program on the Higgs bundle moduli space in giving the correct mathematical formulation of a D-brane. Hitchin gave QGM Masterclass on this subject in 2011. This has been a marvelous linkage for QGM with the talent of the Geometry Group at Oxford through Hitchin's ongoing commitment to QGM, which we are certain will continue and in fact be extended with the addition of Professor Dominic Joyce, a world expert on special holonomy, derived geometry, Donaldson-Thomas theory and J-holomorphic curves and Dr. Alexander Ritter, an expert on symplectic geometry and Fukaya categories, to the Oxford QGM-group.

Oxford website
Oxford, Math Department