Simon Donaldson
| Simon Donaldson | |
|---|---|
 |
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| Born | Simon Kirwan Donaldson 20 August 1957 Cambridge, England |
| Nationality | British |
| Fields | Mathematics |
| Institutions |
Stony Brook University Imperial College London Institute for Advanced Study Stanford University All Souls College, Oxford |
| Alma mater |
Worcester College, Oxford Pembroke College, Cambridge |
| Thesis | The Yang-Mills Equations on Kähler Manifolds (1983) |
| Doctoral advisor |
Michael Atiyah Nigel Hitchin |
| Doctoral students |
Oscar Garcia-Prada Dominic Joyce Dieter Kotschick Graham Nelson Paul Seidel Vicente Muñoz Richard Thomas |
| Known for | Topology of smooth (differentiable) four-dimensional manifolds |
| Notable awards | Junior Whitehead Prize (1985) Fields Medal (1986) Royal Medal (1992) Crafoord Prize (1994) Pólya Prize (1999) King Faisal International Prize (2006) Nemmers Prize in Mathematics (2008) Shaw Prize in Mathematics (2009) Breakthrough Prize in Mathematics (2014) |
Sir Simon Kirwan Donaldson FRS (born 20 August 1957), is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds and Donaldson–Thomas theory. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University and a Professor in Pure Mathematics at Imperial College London.
Donaldson's father was an electrical engineer in the physiology department at the University of Cambridge, and his mother earned a science degree there. Donaldson gained a BA degree in mathematics from Pembroke College, Cambridge in 1979, and in 1980 began postgraduate work at Worcester College, Oxford, at first under Nigel Hitchin and later under Michael Atiyah's supervision. Still a postgraduate student, Donaldson proved in 1982 a result that would establish his fame. He published the result in a paper Self-dual connections and the topology of smooth 4-manifolds which appeared in 1983. In the words of Atiyah, the paper "stunned the mathematical world" (Atiyah 1986).
Whereas Michael Freedman classified topological four-manifolds, Donaldson's work focused on four-manifolds admitting a differentiable structure, using instantons, a particular solution to the equations of Yang–Mills gauge theory which has its origin in quantum field theory. One of Donaldson's first results gave severe restrictions on the intersection form of a smooth four-manifold. As a consequence, a large class of the topological four-manifolds do not admit any smooth structure at all. Donaldson also derived polynomial invariants from gauge theory. These were new topological invariants sensitive to the underlying smooth structure of the four-manifold. They made it possible to deduce the existence of "exotic" smooth structures—certain topological four-manifolds could carry an infinite family of different smooth structures.
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