In a recent study published in the journal “Inventiones Mathematicae”, researchers, led by Dr. Marcus Tempelmair from the Cluster of Advanced Experience “Mathematics” at the University of Munster, introduced a new method for solving a class of stochastic equations in partial derivatives. The work builds upon the groundbreaking theory developed by Fields medal laureate Professor Martin Hair in 2014.
The theory by Hair provided essential tools for solving singular stochastic equations in partial derivatives, but it was noted by Tempelmair that the theory was complex and challenging to apply in various situations. In their study, researchers explored alternative approaches to simplify and make the method more flexible for solving these equations.
Tempelmair, who worked on this research as a doctoral student under the guidance of Professor Felix Otto at the Max Planck Mathematics Institute, collaborated with several research groups to successfully apply this new method since its publication in 2021 as a preprint.
Stochastic equations in partial derivatives have a wide range of applications in simulating dynamic processes such as bacterial growth, liquid film evolution, and particle interactions in magnetism. Despite the challenges posed by stochastic elements, mathematicians focus on solving these equations using various techniques, including visual tree diagrams in Hair’s theory.
Researchers adopted an analytical approach in their study, which involved solving simple equations and combining their solutions to tackle complex equations. This strategy has proven effective and has been adopted by other research groups working on similar mathematical problems.