Simon Kirwan Donaldson ( born August 20, 1957 in Cambridge ) is an English mathematician who is best known for his work on the topology of four-dimensional manifolds.
Donaldson studied mathematics at Cambridge University, where in 1979 he received his BA obtained. He continued his studies at Nigel Hitchin and Michael Atiyah at the University of Oxford. While still a student he published in 1982 a work Self- dual connections and the topology of smooth 4- manifolds (Bulletin of the American Mathematical Society, 1983), which established his reputation. After Michael Freedman smooth ( ie continuous) had manifolds of dimension 4 classified topologically and at the same time proved the Poincare conjecture for this dimension, Donaldson examined differentiable structures on these manifolds by means of non - Abelian gauge theories (Yang -Mills theories, according to non-linear partial differential equations) and special, distinguished by topological invariants solutions of these theories, the instantons. He could necessary conditions for the cut shape ( intersection form) derived on such manifolds, which limited the possible differentiable structures strong.
He also found - in gauge theories - new polynomial invariants to characterize these differentiable structures and could thus show that there is in contrast to all other dimensions for " exotic" differentiable structures, ie 4 -manifolds, although topologically equivalent ( " homeomorphic " ) are the four -dimensional Euclidean space, but not in terms of differentiable structures (not " diffeomorphic ").
After his dissertation in 1983 in Oxford Donaldson was a Fellow of All Souls College, and went in 1983/84 to the Institute for Advanced Study at Princeton. In 1985 he received the Wallis Professorship of Mathematics at the University of Oxford. In 1999 he moved to Imperial College London.
In the 1990s he worked on, among others, with the application of Floer homology and symplectic topology and geometry.
His doctoral include Dominic Joyce, Paul Seidel and Dieter Kotschick.
In 1986 he was elected to the Royal Society and was awarded the Fields Medal in the ICM 1986 ( Lecture: Geometry of four - manifolds ). The Royal Medal of the Royal Society awarded him in 1992. In 1994 he was awarded the Crafoord Prize. In 2008 he was awarded the Nemmers Prize for mathematics. In 2009 he was awarded the Shaw Prize for Mathematics in collaboration with Clifford Taubes. In 1992 he gave a plenary lecture at the first European Congress of Mathematicians in Paris ( Gauge theory and four manifold topology ). In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Lefschetz fibrations in symplectic geometry ) and also in 1983 in Warsaw ( Gauge theory and topology ). In 2012 he was in the New Year Honours knighted ( Knight Bachelor kt. ) Beaten. He is a Fellow of the American Mathematical Society.
- An application of gauge theory to four- dimensional topology. , Journal of Differential Geometry Vol 18, 1983, pp. 279-315.
- Self- dual connections and the topology of smooth 4- manifolds, Bulletin of the American Mathematical Society Vol 8, 1983, p.81 -83.
- With Peter Kronheimer: The geometry of four - manifolds. Oxford Mathematical Monographs, New York, 1990, Oxford University Press, ISBN 0-19-853553-8.
- Remarks on gauge theory, complex geometry and 4 -manifold topology, in Atiyah, Iagolnitzer: Fields medalist lectures, World Scientific 1997
- Floer homology in Yang-Mills theory, Cambridge Tracts in 2002
- 100 years of manifold topology. In: Ioan James (Editor ) History of topology, North Holland 1999