Exact Results in Quantum Theory

According to the BKL conjecture, Einstein's equations exhibitremarkable simplifications in the limit towards a spacelike (cosmological)singularity. At the same time there emerges evidence for a huge `hiddensymmetry' of indefinite Kac-Moody type that is closely related to theduality symmetries that have appeared in supergravity and superstringtheories. This lecture will provide a survey of these results at anintroductory level.