Multivariate reconstruction techniques over finite fields for scattering amplitudes
Tiziano Peraro (University of Edinburgh, UK)

I will describe an algorithm for the reconstruction of rational functions from their numerical evaluation over finite-fields. I will then discuss its application to several techniques related to the calculation of multi-loop scattering amplitudes. The method has good efficiency and scales well with the number of variables and the complexity of the problem. My main focus will be multi-loop integrand reduction via generalized unitarity in QCD. I will illustrate how finite-field techniques can be used in order to build an integrand basis, generate loop integrands over unitarity cuts, and reconstruct the analytic expression of a complete integrand representation of an amplitude.