New Directions in Rough Path Theory

Abstract

Rough path theory emerged as novel approach for dealing with interactions in complex random systems. It settled significant questions and provided an effective deterministic alternative to Itô calculus, itself a major contribution to 20th century mathematics. Its impact has grown substantially in recent years: most prominently, rough paths ideas are at the core of Martin Hairer’s Fields Medal-winning work on regularity structures, but there are also original and successful applications in other areas. The workshop focused on three areas that have been strongly influenced by the core ideas in rough path theory and which have witnessed considerable activity over the past few years: applications to data science, algebraic aspects and connections with stochastic analysis.