I will review how the Einstein equations in a near-singularity 'BKL' regime map onto hyperbolic billiard dynamics. Solutions to the Wheeler-DeWitt equation, i.e. the quantum wavefunctions of this system, are thus odd automorphic forms. I will explain how these quantum wavefunctions can be expressed as Green's functions for hopping dynamics on the Bruhat-Tits tree. This suggests a possible adelic dual description of spacetime singularities.
