There is a universal combinatorial Hopf algebra structure hidden in the process of renormalization [ 1, 2, 3, 4, 5, 6]. The universality of this structure can be conveniently understood if one considers the UV singularities of Feynman graphs from the viewpoint of configuration spaces. Then, the combinatorial structure of renormalization can be summarized as follows. Each Feynman diagram has various sectors which suffer from shortdistance singularities. These sectors are stratified by rooted… CONTINUE READING