Directions in Rough Analysis

Abstract

Rough path theory emerged in the 1990s and was developed in the 2000s as an improved approach to understanding the interaction of complex random systems. As a broader alternative to stochastic calculus, it simultaneously settled significant questions and substantially expanded the scope of classical methods in stochastic analysis. Subsequent related developments have had an impact at the highest level, Martin Hairer’s work on regularity structures being among the most prominent. In 2020, rough analysis gained its own AMS classification code, 60L, and this workshop focused on the currently most active areas of the subject among two central strands: (1) the mathematics of the signature transform, including its applications to data science and finance, and (2) rough path theory applied to novel areas in stochastic analysis, such as homogenization, SLE and rough PDEs.