Tropical sampling and its applications to Feynman integrals

by Michael Borinsky (ETH Zurich)

Tuesday 18 Oct 2022, 14:00 → Wednesday 14 Dec 2022, 13:00 Europe/Berlin

Tropical sampling is a mathematically streamlined version of the 
geometric sector decomposition approach to evaluate algebraic integrals 
numerically. If the structure of the Newton polytope of the integrand is 
precomputed or known from first principles, then tropical sampling 
offers the advantage of a significantly improved performance.  In the 
case of Euclidean Feynman integrals these polytopes are generalized 
permutahedra, a class of polytopes which is well-studied.  Employing 
this knowledge leads to a highly efficient and practical numerical 
Feynman integration algorithm which can compute scalar Euclidean Feynman 
integrals with arbitrary kinematics up to loop order ~20 on present-day 
hardware.