Simon K. Donaldson
University of London
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Primary Section: 11, Mathematics Membership Type:
International Member
(elected 2000)
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Research Interests
My research interests lie in the area of mathematics bordering geometry, topology, and analysis and having substantial connections with mathematical physics. Much of my early work hinged on the application of the instanton solutions of the Yang-Mills equations--first introduced in particle physics--as tools to solve purely mathematical problems about the topology of four-dimensional manifolds. This has led to novel and wide-ranging results, not obtainable by other methods, that give a glimpse of the special nature of four-dimensional topology and geometry. More recently my work in this direction has focused on the special class of symplectic manifolds. I have shown that certain classical techniques from complex algebraic geometry can be adapted to this setting and am currently pursuing the implications of this for the classification of symplectic manifolds. Another theme running through my research is the study of certain partial differential equations arising in complex differential geometry. In the 1980s I worked on equations related to holomorphic vector bundles and have recently been studying the application of similar ideas to Kahler metrics.
