Abstract: I will give a basic introduction to automorphic forms on reductive groups and their Fourier coefficients with respect to different unipotent subgroups. I will review a series of papers joint with Dmitry Gourevitch, Axel Kleinschmidt, Daniel Persson and Siddhartha Sahi for how these Fourier coefficients can be computed by a reduction principle. In particular, we have shown that they simplify drastically for automorphic forms in small automorphic representations, and I will give a brief overview of applications of this work to scattering amplitudes in string theory.
