Professor Dr Martin Hairer

Research Priorities: Differential equations, stochastic partial differential equations, theory of regularity structures, rough paths
Martin Hairer is an Austrian-British mathematician. His research focuses on probability, PDEs and dynamics, and in particular on stochastic partial differential equations. He developed the theory of regularity structures that allows to describe the solution of some of these equations that were previously mathematically meaningless.
Differential equations can be used to describe many natural and technical processes, for example the course of a planetary orbit. There are often no closed formulas for these processes and changes. Only local connections are known, such as between location and speed. Martin Hairer focuses on stochastic partial differential equations that contain more unknown and also random elements. They are particularly difficult to solve and play a major role in the financial sector for example.
Martin Hairer researches equations that describe how a one-dimensional border between two substances or two phases behaves (Kardar-Parisi-Zhang equations). A paper set on fire burns unevenly because it has a random pattern of areas that burn slower or faster. The progression of a burnt edge (one-dimensional border) can be modelled using stochastic partial differential equations. Such random processes can also be seen in flowing gases or liquids. However, due to their random nature, these equations cannot be generalised. The theory of regularity structures developed by Martin Hairer makes stochastic differential equations predictable for particular applications and gives them a solid mathematical foundation.
In other work Martin Hairer has been able to further explain the foundational equation of hydrodynamics (Navier-Stokes equation). At the start of his scientific career he worked on computer software and wrote an audio processing programme which is still a standard tool used today.