Feynman integrals and motives
This article gives an overview of recent results on the relation between quantum 
field theory and motives, with an emphasis on two different approaches: a “bottom-up” 
approach based on the algebraic geometry of varieties associated to Feynman graphs, and 
a “top-down” approach based on the comparison of the properties of associated categorical 
structures. This survey is mostly based on joint work of the author with Paolo Aluffi, along 
the lines of the first approach, and on previous work of the author with Alain Connes on 
the second approach.