Avila's almost reducibility conjecture

A cocycle $(\alpha,A)$ consists of a frequency $\alpha$ and an analytic matrix-valued map $A$. It is subcritical when its Lyapunov exponent vanishes in a neighborhood of the relevant energy; it is almost reducible if the closure of its analytic conjugacies contains a constant. Avila's almost reducibility conjecture. Every subcritical cocycle is almost reducible. This conjecture is a central assertion in the study of analytic quasi-periodic cocycles and has important consequences for spectral theory, including the structure of the subcritical regime. The source states the conjecture but does not provide enough information here to determine its resolution.