The algebraic properties of scalar Feynman Diagrams

I work on the algebraic properties of scalar Feynman Diagrams, treating the integrals that give rise to these objects as elements in a Hopf Algebra rather than working in any particular theory. I focus on how a mathematical operation called "the coaction" applies on the integrals and how to interpret the decomposition into sub-algebras as Feynman diagrams and cuts. Results from this type of work are more commonly published in [hep-th].