Feynman Graph Theory

Feynman graphs (or diagrams) and their associated Feynman Integrals are the building blocks of perturbative Quantum Field Theory, and thus serve as a basis for Standard model theory predictions for experiments such as the LHC. The higher the precision required the more complicated the integrals become. But their mathematical properties are also interesting in their own right. I will discuss the Hopf algebras of Feynman graphs, which underly renormalisation of UV and certain IR divergences, as well as certain asymptotic expansions. I will conclude with some applications in collider physics and condensed matter physics.