From Dyson-Schwinger equations to the Riemann-Hilbert correspondence

In this paper, with the study of combinatorial Dyson–Schwinger equations at the level of the universal Hopf algebra of renormalization and with the extension of the universality of this specific Hopf algebra and also category of flat equisingular vector bundles to the level of these equations, we are going to consider the notion of a geometric description from nonperturbative theory