General arguments indicate that Feynman integrals can be thought as
period integrals. This talk aims to make this relation concrete on a certain class of quantum field theory amplitudes in a two-dimensional space-time. We will show, on some precise examples, how a Feynman integral is given by a period of a variation of a mixed Hodge structure.
We will discuss special cases which can be expressed in terms of elliptic multiple-polylogarithms.
This is based on the work [arXiv:1309.5865] done in collaboration with
Spencer Bloch, and in work in progress with Spencer Bloch and Matt Kerr.