Simon Kirwan Donaldson  

Born 
August 20, 1957 Cambridge, England 
Nationality  British 
Fields  Mathematics 
Institutions  Imperial College London Institute for Advanced Study University of Oxford 
Alma mater  University of Oxford University of Cambridge 
Doctoral advisor  Michael
Atiyah Nigel Hitchin 
Known for  Topology of smooth (differentiable) fourdimensional manifolds 
Notable awards  Junior Whitehead Prize (1985) Fields Medal (1986) Crafoord Prize (1994) King Faisal International Prize (2006) Nemmers Prize in Mathematics (2008)) Shaw Prize in Mathematics (2009) 
Simon Kirwan Donaldson (born August 20, 1957, in Cambridge, England), is an English mathematician famous for his work on the topology of smooth (differentiable) fourdimensional manifolds. He is now a Chair in Pure Mathematics and President of the Institute for Mathematical Science at Imperial College London where he holds a professorship.
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 graduate student, Donaldson soon proved in 1982 a result that would establish his fame. He published the result in a paper Selfdual connections and the topology of smooth 4manifolds which appeared in 1983. In the words of Atiyah, the paper "stunned the mathematical world".
Whereas Michael Freedman classified topological fourmanifolds, Donaldson's work focused on fourmanifolds admitting a differentiable structure, using instantons, a particular solution to the equations of YangMills 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 fourmanifold. As a consequence, a large class of the topological fourmanifolds 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 fourmanifold. They made it possible to deduce the existence of "exotic" smooth structures  certain topological fourmanifolds could carry an infinite family of different smooth structures.
After gaining his DPhil degree from Oxford University in 1983, Donaldson was appointed a Junior Research Fellow at All Souls College, Oxford, he spent the academic year 1983–84 at the Institute for Advanced Study in Princeton, and returned to Oxford as Wallis Professor of Mathematics in 1985. In 1999, he moved to Imperial College London.
Donaldson received the Junior Whitehead Prize from the London Mathematical Society in 1985 and in the following year he was elected a Fellow of the Royal Society and, also in 1986, he received a Fields Medal. He was, however, turned down for fellowship of the Institute of Mathematics and its Applications on the grounds that he applied too soon after his doctorate. He was awarded the 1994 Crafoord Prize.
In February 2006 Professor Donaldson was awarded the King Faisal International Prize for science for his work in pure mathematical theories linked to physics, which have helped in forming an understanding of the laws of matter at a subnuclear level.
In April 2008, he was awarded the Nemmers Prize in Mathematics, one of the most prestigious mathematics prize awarded by Northwestern University.
In 2009 he was awarded the Shaw Prize in Mathematics (jointly with Clifford Taubes) for their many brilliant contributions to geometry in 3 and 4 dimensions.
A thread running through Donaldson's work is the creative application of mathematical analysis (especially the analysis of elliptic partial differential equations) to problems in geometry. The problems mainly concern 4manifolds, complex differential geometry and symplectic geometry. The following theorems rank among his most striking achievements:
Donaldson's recent work centers on a difficult problem in complex differential geometry concerning a conjectural relationship between algebrogeometric "stability" conditions for smooth projective varieties and the existence of "optimal" Kähler metrics, typically those with constant scalar curvature. Definitive results have not yet been obtained, but substantial progress has been made (see for example Donaldson 2001).
See also Donaldson theory.


