Numerical methods for two-loop cosmological correlators and two-loop QCD amplitudes

An exciting precision physics program is ahead of us in cosmology and particle physics, as we anticipate detailed surveys of the Large Scale Structure and the precision measurements of the High Luminosity LHC. We believe that numerical methods can help us overcome challenges in obtaining theoretical predictions with analogous precision. I will describe the application of methods, rooted to an understanding of ultraviolet and infrared behaviour, to the two-loop dark matter power-spectrum, computed within the framework of the EFT of the Large Scale Structure. I will also describe the development of infrared subtraction methods, which also invoke simplifications due to gauge symmetry, for computing QCD amplitudes at two-loops. In particular, I will describe first results for multiple electroweak production at NNLO.