Random Surfaces and Higher Algebra

Classical vector valued paths are widespread across pure and applied mathematics: from stochastic processes in probability to time series data in machine learning. Parallel transport (or path development) and path signatures provide an effective method to characterize such paths while preserving the concatenation structure of paths. In this talk, we extend this framework to build structure-preserving characterizations of random and possibly nonsmooth surfaces using surface holonomy. This is based on joint work with Harald Oberhauser.