A renormalization program for Dyson–Schwinger equations (part I)

This Minicourse is based on the speaker's monograph "a mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory" (arXiv:1811.05333).  In this talk I plan to review the fundamental structure of the Connes--Kreimer renormalization Hopf algebra of Feynman diagrams and combinatorial Dyson--Schwinger equations. Then I explain a recent application of infinite graph theory to Quantum Field Theory which leads to build a renormalization machinery for infinite formal expansions of Feynman diagrams.