# Mathematics Institute News

## 13th August 2014: Martin Hairer wins a Fields Medal 2014

At the opening ceremony of the International Congress of Mathematicians 2014 on August 13, 2014 in Seoul, Korea, a Fields Medal was awarded to Professor Martin Hairer FRS for his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations. Martin has worked in Warwick since 2002, and in April 2014 was appointed to the Department's new Regius Professorship.

Short citation: A mathematical problem that is important throughout science is to understand the influence of noise on differential equations, and on the long time behavior of the solutions. This problem was solved for ordinary differential equations by Itô in the 1940s. For partial differential equations, a comprehensive theory has proved to be more elusive, and only particular cases (linear equations, tame nonlinearities, etc.) had been treated satisfactorily.

Hairer’s work addresses two central aspects of the theory. Together with Mattingly he employed the Malliavin calculus along with new methods to establish the ergodicity of the two-dimensional stochastic Navier–Stokes equation.

Building on the rough-path approach of Lyons for stochastic ordinary differential equations, Hairer then created an abstract theory of regularity structures for stochastic partial differential equations (SPDEs). This allows Taylor-like expansions around any point in space and time. The new theory allowed him to construct systematically solutions to singular non-linear SPDEs as fixed points of a renormalization procedure.Hairer was thus able to give, for the first time, a rigorous intrinsic meaning to many SPDEs arising in physics.

Press release (PDF)

List of 2014 prizewinners

Quanta magazine article

Video of Martin Hairer's work

Fields Medal Presentation

^{Photo Courtesy of Mark Pollicott}