(Joint work with Michael Green and Pierre Vanhove)

String theory predicts low-energy correction terms to Einstein's 4-graviton scattering amplitude. In type II string theory these arise as special automorphic functions having interesting number theory properties. We identified the first two of these as certain Eisenstein series on exceptional groups. Studying their constant terms then gives information about which Feynman diagrams contribute to these interactions. These two terms are expected to have 1/2-BPS and 1/4-BPS properties, which demands that several of their non-constant Fourier coefficients vanish identically. We proved this statement by showing that these special Eisenstein series are automorphic representations having very low Gelfand-Kirillov dimension. Moreover, the intuition and computations involved in studying this string theory question can be used to construct several related unitary representations, in particular establishing the unitarity of a number of Arthur's unipotent representations (thus giving new information about the unitary dual of split exceptional groups).