Matilde Marcolli (Caltech) This talk is based on joint work with Paolo Aluffi. I will explain how the parametric form of Feynman integrals in perturbative quantum field theory gives rise to periods of algebraic variety, whose complexity depends on how complicated the cohomology of these varieties is from the point of view of Grothendieck's theory of motives. I will explain to what extent this can be controlled in terms of determinant hypersurfaces, whose motivic nature is well undertsood. I will also show how this circle of ideas leads to the construction of algebro-geometric Feynman rules with interesting properties.