Geometry of Feynman Integrals


I will teach four lectures in the IMPRS Ringvorlesung at MPI MiS Leipzig. We will study 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 highlight geometric aspects and computational tools from nonlinear algebra. Along the way, we will encounter convex polytopes, critical points, very affine varieties and more.

Lectures happen from 10h30 - 12h00 in E2 10. Here is the schedule: 

  • May 11: Newton polytopes and convergence
  • May 28: Limits and critical points
  • June 1: Twisted (co)homology
  • June 8: Differential and difference operators

I will follow an overview article which I am currently writing with Saiei-Jaeyeong Matsubara-Heo and Sebastian Mizera. The latest version can be downloaded here: