| Following the work of Broadhurst-Kreimer since the early 90s, it has been known that Feynman amplitudes in perturbative quantum field theory systematically evaulate to multiple zeta values for a large class of the corresponding Feynman graphs. The most recent attempt to understand this phenomena revolves around studying certain projective varieties naturally associated to those amplitudes. In particular, the work of Bloch-Esnault-Kreimer suggests the existence of motives
associated to those projective varieties for a certain class of Feynman graphs; this has led to an intriguing connection between arithmetic algebraic geometry and quantum field theory.
In this talk, I will provide an overview of these developments for non-experts. By the way of illustrating how algebraic geometry informs quantum field theory, I will also talk about a geometric interpretation of vertex and propagator corrections in scalar quantum field theory. The new results presented are joint work with Christoph Bergbauer. |