The Mixmaster conjecture

Let $n+1\leq 10$, and consider vacuum space-times. The conjecture concerns inextendible geodesics along which the curvature is unbounded and allows unspecified natural geometric variables to describe the dynamics. Mixmaster conjecture. There exist open sets of vacuum metrics for which some natural geometric variables undergo oscillations of increasing complexity along inextendible geodesics of unbounded curvature. This is a deliberately loose formulation of the proposed oscillatory behavior near spacelike local singularities. The source notes rigorous evidence from generic Gowdy metrics, while emphasizing that those singularities are not oscillatory, and discusses indications that oscillations may disappear in dimensions above ten.