Royal Society Research Professor, Department of Mathematics, Imperial College, Queen's Gate, London, UK.
His research interests lies in the area of mathematics bordering geometry, topology, and analysis and having substantial connections with mathematical physics. Much of his 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 his work in this direction has focused on the special class of symplectic manifolds. He has shown that certain classical techniques from complex algebraic geometry can be adapted to this setting and he is currently pursuing the implications of this for the classification of symplectic manifolds. Another theme running through his research is the study of certain partial differential equations arising in complex differential geometry. In the 1980s he worked on equations related to holomorphic vector bundles and has recently been studying the application of similar ideas to Kahler metrics.
1986 Fields Medal, International Congress of Mathematics
1992 Royal Medal of Royal Society
1994 Crafoord Prize of Swedish Academy of Science (with S.T. Yau)
Donaldson, S. K. Floer Homology Groups in Yang-Mills Theory. CUP Tracts in Mathematics. January 2002.
Donaldson, S. K. Polynomials, vanishing cycles and Floer homology. Mathematics: frontiers and perspectives, 55--64, Amer. Math. Soc., Providence, RI, 2000.
Donaldson, S. K. Lefschetz pencils on symplectic manifolds. J. Differential Geom. 53 (1999), no. 2, 205--236.
Donaldson, S. K. Symmetric spaces, Kähler geometry and Hamiltonian dynamics. Northern California Symplectic Geometry Seminar, 13--33, Amer. Math. Soc. Transl. Ser. 2, 196, Amer. Math. Soc., Providence, RI, 1999.
Donaldson, Simon Geometry in Oxford c. 1980--85. Sir Michael Atiyah: a great mathematician of the twentieth century. Asian J. Math. 3 (1999), no. 1, xliii--xlvii.
Donaldson, S. K. One hundred years of manifold topology. History of topology, 435--447, North-Holland, Amsterdam, 1999.