This years Shaw Prize in mathematics was awarded to Professor Nigel Hitchin, from the University of Oxford. This award was honoured to him due to “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.”
Hitchin’s innovative work has had a profound impact on a variety of areas in Mathematics, including algebraic geometry, differential geometry, complex analysis, topology, integrable systems, mathematical and theoretical physics.
One of his most notable achievements was deriving the self-duality equations, which are a “special class of solutions of the self-dual Yang-Mills equations“. He discovered that when described on a compact Riemann surface – a surface that can be covered by a finite collection of planes – a “surprisingly rich space of solutions” is produced.
A typical feature of Hitchin’s work is as follows: he proves that objects in theoretical physics define new concepts in algebraic or differential geometry, and then uses rigorous mathematics to produce powerful and elegant results.
Marta Mazzocco describes how
“… Hitchin defies the stereotype that mathematicians need to be in their early thirties to produce great results. When already in his sixties, Hitchin introduced the notion of co-Higgs bundle …“.
An apt winner of the Shaw Prize, I hope to hear of his work for many years to come.