The Shaw Prize in Mathematical Sciences 2016 is awarded to Nigel J Hitchin,Savillian Professor of Geometry at the University of Oxford, UK, for his far-reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance.
Geometry has long been at the core of mathematics. It has close connections to other parts of mathematics such as representation theory, which is related to the study of symmetry, to differential equations, to number theory and more recently to theoretical high energy physics.
Hitchin is of one of the most influential geometers of our times. The impact of his work on geometry and on these allied subjects is deep and lasting. On numerous occasions, he has discovered elegant and natural facets of geometry that have proven to be of central importance. His ideas have stimulated work in areas far removed from the context in which they arose.
His work on Higgs bundles over Riemann surfaces provided algebraically integrable systems, called Hitchin fibrations, that are important examples of hyperkahler manifolds and have become fundamental objects in geometry. In addition, they have been an impetus to progress in the modern branch of representation theory called ‘geometric Langlands’, helping to guide the development of that subject. Hitchin fibrations are a foundational ingredient in Ngo’s recent Fields Medal winning work in the theory of automorphic forms and number theory. In a related work, Hitchin used this theory to construct projectively flat connections over the moduli spaces of Riemann surfaces, which had been predicted by Witten’s analysis of a 3-dimensional topological quantum field theory.
Hitchin’s work with Atiyah, Drinfeld and Manin on a description of the moduli space of instantons on four-space in terms of linear algebra, even now thirty years later, forms a basis for much work in both mathematics and theoretical physics. His formulation of the Kobayashi-Hitchin conjecture relating algebro-geometric stability and solutions to the instantons on complex algebraic surfaces has created a large new area of non-linear partial differential equations.
By exploring ignored corners of geometry, Hitchin has repeatedly uncovered jewels that have changed the course of developments in geometry and related areas and with it the way mathematicians think about these subjects.
Mathematical Sciences Selection Committee
The Shaw Prize
31 May 2016 Hong Kong