Noncommutative Branched Rough Paths

Noncommutative stochastic processes and S(P)DEs driven by them naturally arise in the context of stochastic quantisation and the large N limits of random matrices.As a model for the full theory of Noncommutative Regularity Structures, we will present an introduction to Noncommutative Branched Rough Paths. This will cover how the algebra of iterated integrals must be adapted, the noncommutative Chen identity, noncommutative controlled rough paths, and a solution theory for suitably smooth nonlinearities.