Martin Hairer

Martin Hairer, 2014

Martin Hairer (born November 14, 1975 in Geneva ) is an Austrian mathematician and Fields Medalist (2014) who deals with stochastic partial differential equations (SPDE) with applications in statistical mechanics. He is Professor of Mathematics at Imperial College London .

life and work

Hairer went to school in Geneva. He is the son of the mathematician Ernst Hairer (professor in Geneva) and Evi Gröbner. He studied physics with mathematics as a minor (Diploma in Physics 1998, Systèmes Mécaniques couplés à des bains thermiques de températures différentes ) at the University of Geneva , where he received his doctorate in physics under Jean-Pierre Eckmann in 2001 ( Comportement Asymptotique d´Equations à Dérivées Partielles Stochastiques ). He then worked as an assistant at the Institute for Theoretical Physics in Geneva and from 2002 as a post-doctoral student at the University of Warwick , where he became a lecturer in 2004 , and associate professor in 2006, and in 2007Reader and in 2010 with a full professorship . Since 2013 he has been Regius Professor of Mathematics there . He has been a professor at Imperial College London since October 2017.

In 2009 he was Associate Professor at the Courant Institute of Mathematical Sciences of New York University . Among other things, he was visiting professor at the TU Berlin (2009), in Toulouse, Rennes, at the Imperial College and in China.

In 2008 he received the Whitehead Prize and the Leverhulme Prize. In 2009 he received the Wolfson Research Merit Award from the Royal Society . In 2006 he received a five-year EPSRC (Engineering and Physical Sciences Research Council) Advanced Research Fellowship. 2013 he received the Fermat Prize awarded for his contributions to the analysis of stochastic partial differential equations, especially for the well-posedness of problems, the regularity of solutions and convergence to equilibrium (eulogy). In particular, he created methods for the treatment of non-linear stochastic PDEs, for example the KPZ equation , which was introduced in 1986 by the namesake Mehran Kardar , Giorgio Parisi and Yi-Cheng Zhang and describes the randomly fluctuating interface between two media. It presented mathematicians with a problem because of their nonlinearity, which initially made the consideration of generalized solutions ( distributions ) impossible. Hairer developed (based on the Rough Path Method of Terry Lyons for ordinary stochastic differential equations ) for a theory of so-called. Regularitätsstrukturen (that is, he found a method that the noise separate from the dynamics and the system to regularize), first at the KPZ -Equation, later for many more nonlinear stochastic PDEs, also in higher dimensions (the KPZ equation describes the interface phenomenon as a one-dimensional curve). Nonlinear stochastic partial differential equations have many uses, for example in finance.

He also made significant advances with Jonathan Mattingly on the stochastic version of the Navier-Stokes equation , the fundamental equation of hydrodynamics. They were able to demonstrate the ergodicity in two dimensions.

He is co-editor of Probability Theory and Related Fields (from 2008), Nonlinear Differential Equations and Applications and the Annales Henri Poincaré (Ser.B) of the Institut Henri Poincaré (from 2011). In 2014 he was admitted to the Royal Society and received the Fröhlich Prize of the London Mathematical Society. In 2014 he received a Consolidator Grant from the European Research Council .

In 2014 he was invited speaker at the ICM in Seoul , where he received the Fields Medal for contributions to the theory of stochastic partial differential equations and in particular the development of a regularity structure for them. In 2015 Hairer was elected to the Academia Europaea and a member of the Leopoldina , in 2016 to the Berlin-Brandenburg Academy of Sciences , and in 2019 to the Academy of Sciences and Literature .

He is married to the mathematician Xue-Mei Li and also develops software for the Macintosh (audio processing, Amadeus at HairerSoft, from 1997). The early days of developing this software earned him the Swiss Youth Research Prize in 1995.

Fonts (selection)

with Jean-Pierre Eckmann : Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise. Comm. Math. Phys. 219 (2001), no. 3, 523-565.
with Jonathan Mattingly: Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing. Ann. of Math. (2) 164 (2006) no. 3, 993-1032.
Solving the KPZ equation. Ann. of Math. (2) 178 (2013), no. 2, 559-664.
A theory of regularity structures . Inv. Math. (2014) doi: 10.1007 / s00222-014-0505-4
with Peter Friz: A Course on Rough Paths: With an Introduction to Regularity Structures , Springer 2014