Geometry of Feynman Integrals

In May-June 2023, I taught four lectures in the IMPRS Ringvorlesung at MPI MiS Leipzig. We studied a class of integrals which appears under different names in the literature: (generalized) Euler integrals, hypergeometric integrals, or Euler-Mellin integrals. These have gained recent interest because of their application in particle physics, where they appear as Feynman integrals. We highlighted geometric aspects and computational tools from nonlinear algebra. Along the way, we encountered convex polytopes, critical points, very affine varieties and more.

The lecture notes are published in this review article.