Theory Seminar

Functional interpolation techniques and their application to integration-by-parts reductions

by Jonas Klappert (RWTH Aachen University)

313 (Main)




Functional interpolation techniques over fields, also known as black-box interpolation problems, are actively studied in Computer Science for more than a half century. Despite their probabilistic nature, they offer a competitive alternative to purely algebraic approaches, especially when applied over finite fields. Using the latter, one can achieve fast and memory friendly implementations since a number swell of intermediate expressions can be avoided. Recently, these techniques have been applied to achieve remarkable results in the context of higher-order corrections to scattering amplitudes. In this talk, I review functional interpolation techniques and their implementation into the FireFly library. I show benchmarks for the interpolation of sparse and dense rational functions and focus specifically on features helpful in the context of integration-by-parts reductions with the program Kira.