Rough Paths in geometric settings and their structure theory via a combinatorial approach

This seminar is given by Christian Litterer (University of York).

Abstract: We will give an overview of several different approaches to defining rough paths in geometric settings. Motivated by this problem we develop the basic structure theory for weakly geometric rough paths and their controlled paths using a direct, combinatorial approach that applies to paths of arbitrary roughness. The rough path lift of a controlled rough path is obtained as an explicit combinatorial object and allows us to derive fundamental identities that include the adjunction of pushforwards and pullbacks. Our approach differs from existing approaches as it does not rely on smooth approximations.