Gauge Theory and Complex Geometry

The interaction between gauge theory and complex geometry, which goes back to 1970s, has resulted in some of the most stunning achievements in both mathematics and in theoretical physics. These include twistor-theoretic construction of instantons on the 4-sphere, Donaldson's breakthrough results for algebraic surfaces, and the Hitchin-Kobayashi correspondence between stable holomorphic bundles and anti-self-dual connections. Both fields continue to influence each other and recent years have yielded a host of new developements and applications to new topics in both areas. Among these developements are applications of gauge-theoretic methods to non-Kaehlerian surfaces; gauge theory over complex manifolds with anti-holomorphic involution (so called orientifolds) leading to deep conjectures by C. Vafa and collaborators; the Donaldson-Thomas invariants, which allow application of gauge theoretic methods to higher-dimensional algebraic manifolds; and the geometry of the moduli spaces of Higgs bundles with their increasing relevance to the geometric Langlands programme.

The immediate impact of this research will be on other mathematicians. We anticipate a number of new collaborations to arise in the workshop and lead to new results, which will be of interest to pure mathematicians and mathematical physicists. In addition, our workshop will be attended by a number of graduate students, both EPSRC-supported and from overseas. The workshop will be a valuable training for these students and allow them to make contact with peers from other countries. Given the calibre of the speakers, the workshop will have a positive impact on the standing and international competetiveness of the UK mathematics.