Resumen de Metal-insulator transition for the almost Mathieu operator

Svetlanaya Jitomirskaya

• We prove that for Diophantine ù and almost every è, the almost Mathieu operator, (Hù,ë,è )(n) = (n+1)+ (n.1)+ë cos 2ð(ùn+è) (n), exhibits localization for ë > 2 and purely absolutely continuous spectrum for ë < 2. This completes the proof of (a correct version of) the Aubry-Andr/e conjecture.