### Martin Hairer

Martin Hairer, * 14 November 1975 in Geneva, Switzerland

Fields-Medal (2014) “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 Hairer was born in Geneva. He is the son of Ernst Hairer, who is a professor of mathematics and a world expert in the numerics of ordinary differential equations. Martin Hairer grew up mainly in Geneva. Even as a schoolboy he developed a computer interface for building electronic circuits and a software for sound editing (which he still keeps updated). He studied mathematics and physics at the University of Geneva, where he took his Ph.D. at the Département de Physique Théorique with a thesis on the solution of certain stochastic partial differential equations (SPDEs) in 2001.

Afterwards he worked for a short time as an assistant at the University of Geneva before coming as a post doc to the University of Warwick in 2002, where he became lecturer in 2004, Associate Professor in 2006, Reader in 2007 and Full Professor in 2010. Since 2014 he is a Regius professor of mathematics on a chair created by the British Queen.

Hairer is one of the most innovative and creative researchers of SPDEs worldwide – and he is one of the most productive: he has already published more than 70 papers and he has received many awards for this work, for example the Whitehead-Prize of the London Mathematical Society (2008) and the Fermat Prize (2013). Martin Hairer is also a Fellow of the Royal Society since 2014.

Hairer studies the theory of stochastic partial and ordinary differential equations. Such equations are classic in physics, for instance for the description of fluids and streams. Differential equations provide information about the development of systems in space and time; stochastic differential equations are in addition also controlled by random forces.

The influence of randomness on differential equations has been in the focus of research for a long time. For ordinary differential equations there is a powerful theory available, developed by Kiyoshi Itô and Wolfgang Döblin in the 1940s. But many processes in the physical world can only be described by a more complex class of differential equations, the partial differential equations – for instance the mixing of stirred milk and coffee.

In a series of works, Hairer and Mattingly developed a theory of ergodicity for stochastic partial differential equations which allowed to establish minimal conditions for the ergodicity of the 2D stochastic Navier-Stokes equations. Hairer has also developed a new solution theory for a class of stochastic equations of Burgers type arising in the theory of paths sampling, as well as for the Kardar-Parisi-Zhang (KPZ) equation, a nonlinear stochastic partial differential equation which is important in physics due to its universal character. Recently, Hairer developed a general “theory of regularity structures” which provides a systematic way of solution theories for a large class of stochastic partial differential equations for which even the mathematical meaning of the equation was previously unclear.