Kac-Moody algebras and the structure of cosmological singularities: a new light on the Belinskii-Khalatnikov-Lifshitz analysis

The unexpected and fascinating emergence of hyperbolic Coxeter groups and Lorentzian Kac-Moody algebras in the investigation of gravitational theories in the vicinity of a cosmological singularity is briefly reviewed. Some open questions raised by this intriguing result, and some attempts to answer them, are outlined.