New horizons in well-posedness of stochastic differential equations

This workshop aims at sharing and developing new methods in the study of stochastic (partial) differential equations (S(P)DEs). A surprising fact of S(P)DEs, and a relatively recent discovery, is that the presence of a random disturbance can restore and/or improve well-posedness even if the deterministic part of the equations fails to be regular or well-posed. This phenomenon of „regularization by noise“ has led to rapid and significant developments in the field and methods in the well-posedness theory show a strong link to other fields of mathematics, such as rough path theory and modern harmonic analysis. Thus it is necessary to, on the one hand, asses the field's current state-of-the-art in order to identify cornerstones of the existing analysis, and on the other hand, to discuss potential next steps to enable productive future endeavors. This workshop will address both sides by a mixture of formats: technique talks are given to educate the participants in existing methods, and forward-facing talks will give an outlook to possible future developments.