Stochastic PDEs and renormalisation: START Prize for Máté Gerencsér

The Austrian Science Fund FWF is awarding this year's START Prizes - one of which goes to mathematician Máté Gerencser from TU Wien.

Foto Mate Gerencser

© Matthias Heisler

Mate Gerencser

Foto Mate Gerencser

The START Prize of the Austrian Science Fund FWF is considered the most important award for young scientists in Austria. It is endowed with up to 1.2 million euros and is intended to enable researchers at an early stage of their career to establish their own research group at an international top level.


How to describe the world

Differential equations are probably the most important mathematical tool for the natural sciences today. They are equations whose solution is not merely a number, but usually a function. "For example, the shape of a wave, a temperature curve that depends on place and time, the turbulences in air or water," Máté Gerencsér explains.

The laws of nature that we know today are described in the form of differential equations - this applies to Newton's laws of motion as well as to the equations of electrodynamics or the Schrödinger equation - a partial differential equation that describes the behaviour of quantum particles. These are deterministic equations: If we know the state of a physical system at a certain point in time, the state of the system at any later time is also determined.


Incorporating Máté into the equation

The equations Máté Gerencsér is working with, however, are somewhat more complicated: "In our research group, we work with stochastic differential equations - that is, differential equations that also have a certain amount of randomness built into them, such as a certain kind of noise," he explains.

For example, you can use ordinary differential equations to calculate how fast a hot rod cools down in a cool environment. But what if there is also a randomly fluctuating heat source that heats up the rod? The Schrödinger equation can be used to calculate the motion of an electron. But what if the electron is disturbed completely randomly by other particles in the process?

In order to be able to take such randomness into account in the world of differential equations, one has to develop completely new mathematical tools. For example, it can happen that certain terms of these differential equations become infinitely large - this is called a singularity. Conventional mathematical methods fail in this situation. However, there are so-called renormalisation methods with which one can still determine reliable results even in this case. "There have been some stunning breakthroughs in this field in recent years," says Máté Gerencsér. The goal of the START project is to further develop these ideas and answer important open questions.


Máté Gerencsér

Máté Gerencsér is from Hungary. He studied mathematics at Eötvös Loránd University in Budapest, and finished his doctorate at the University of Edinburgh in 2016. He then worked as a postdoc at the University of Warwick with Fields Medal winner Martin Hairer until 2016. After that, he moved to Austria - first he did research at IST Austria, and in 2020 he finally received a career position at TU Wien.


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