This workshop aims to bring together researchers from number theory, automorphic representation theory, string theory and quantum field theory in order to explore connections between these topics that have recently come to light. The workshop will highlight connections that range from the study of scattering amplitudes, black hole physics and solvable lattice models to the understanding of Fourier coefficients and small representations of algebraic groups. The workshop is embedded in a longer programme at the INI centred around the same topics.