Scheme: Wolfson Research Merit Awards
Organisation: Imperial College London
Dates: Oct 2012-Jan 2014
Summary: This project summary is not available for publication.
Scheme: Royal Society Research Professorship
Dates: Oct 2001-Sep 2012
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.