Mathematical Colloquium Rough analysis and renormalisation

Rough analysis is a field that started in the 90s with the introduction of rough path theory, a pathwise approach to stochastic differential equations. The field now represents a powerful tool in the study of physical systems that exhibit roughness and oscillations on multiple scales. In this talk, I will give an introduction to rough analysis, focusing on the theory of regularity structures, which is especially suitable for the study of stochastic partial differential equations and their renormalisation.