Some problems in quasiperiodic Schrödinger operators

In the 1980s, research on quasiperiodic operators developed rapidly, leading Barry Simon to coin the term “almost periodic flu” [B. Simon, Adv. Appl. Math. 3(4), 463–490 (2000)]. This interest has persisted over the following decades, resulting in many significant breakthroughs. Nevertheless, several classical problems remain unsolved, and new questions continue to emerge. This note presents a selection of open problems centered on analytic quasiperiodic Schrödinger operators in one dimension, reflecting the author’s research interests.