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Research Fellows Directory

Simon Donaldson

Professor Simon Donaldson FRS

Research Fellow

Organisation

Imperial College London

Research summary

My research area studies the interaction between algebraic geometry, shapes defined by polynomial equations, and partial differential equations. The equations in question can be seen as variants of Einstein's equation in General Relativity. The overall problem is to understand the algebraic conditions on the shape which allow a solution of the corresponding partial differential equation. This is a topic with a long history, going back to the 19th century in the case of "Riemann surfaces". More generally, great advances were made in the 1970's through the work of Yau, who showed the existence of solutions in many cases. The resulting "Calabi-Yau manifolds" have been very important in String theory, providing models for fundamental particle physics. However the general problem has been elusive, despite a great deal of work over the poast 30 years. This has been the main focus of my work since 2008 and in the past year my collaborators and I have found a complete solution to the problem.The solution has significance within the general mathematical areas of differential geometry, algebraic geometry and partial differential equations. It is quite possible that it could also interact with current developments in theoretical physics.

Grants awarded

Kähler-Einstein metrics and Gauge theory on manifolds of exceptional holonomy

Scheme: Wolfson Research Merit Awards

Dates: Oct 2012 - Jan 2014

Value: £75,000

Scheme: Royal Society Research Professorship

Dates: Oct 2001 - Sep 2012

Value: £1,378,808.42

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