Classical general relativity close to a space-like singularity exhibits simplified dynamics as originally observed by Belinksi, Khalatnikov and Lifschitz in the 1970s. The modern reformulation of this behaviour is in terms of a (chaotic) dynamical system called a cosmological billiard that intriguingly exhibits arithmetic properties. I will review this phenomenon and show how upon quantisation automorphic forms appear and discuss consequences for the fate of the singularity. Time permitting I will also explore going beyond the billiard approximation and connections to Kac-Moody symmetric spaces and associated automorphic forms. This talk is based on work with Hermann Nicolai.
