Feynman integrals, toric geometry and mirror symmetry

Understand

This expository text is about using toric geometry and mirror symmetry for evaluating Feynman integrals.

• We show that the maximal cut of a Feynman integral is a GKZ hypergeometric series.
• We explain how this allows to determine the minimal differential operator acting on the Feynman integrals.
• We illustrate the method on sunset integrals in two dimensions at various loop orders.