This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining that the first Symanzik polynomial is the determinant of the period matrix of the graph, and the second Symanzik polynomial is expressed in terms of world-line Green's functions. We then review the relation between Feynman graphs and variations of mixed Hodge

more »

... ructures. Finally, we provide an algorithm for generating the Picard-Fuchs equation satisfied by the all equal mass banana graphs in a two-dimensional space-time to all loop orders. 1991 Mathematics Subject Classification. Primary 54C40, 14E20; Secondary 46E25, 20C20.