DFG will support new Research Unit on "Rough Paths, Stochastic PDEs and Related Topics"
The Research Unit "Rough Paths, Stochastic Partial Differential Equations and Related Topics" intends to apply the mathematical theory of so-called "rough paths" to stochastic partial differential equations (SPDEs) and will focus on the investigation of regularity structures, which represent a multidimensional extension of rough path theory. The theory of rough paths allows the gap between conventional and stochastic differential equations to be bridged. Equations like this are needed in the modelling of time-dependent processes which are subject to random influences and in which special smoothness requirements no longer apply, not only in the natural sciences and engineering sciences, but also in economics and social sciences. The qualitative characteristics of SPDEs with rough noise, their dynamics and their numerics are still largely unknown. This opens up new questions, which the members of the Research Unit will address.
(Spokesperson: Professor Dr. Peter Karl Friz, Host University: Technical University of Berlin)