Feynman graphs in perturbative quantum field theory

Abstract

In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own right -- allow to derive algorithms for the computation of these graphs. Topics covered are the relations of Feynman integrals to periods, shuffle algebras and multiple polylogarithms.

Comments: 24 pages, talk given at the conference "Asymptotics in Dynamics, Geometry and PDEs; Generalized Borel Summation", Pisa, October 2009