5 problems

Wilkinson–Austin's conjecture. For all frequencies $b1$,

Avila–Jitomirskaya's conjecture. If $1<|\lambda|<e^{2\beta(\alpha)}$, then $H_{\lambda,\alpha,\theta}$ has purely singular continuous spectrum; if $|\lambda|>e^{2\beta(\alpha)}$, t…

Let $\mathfrak{G}$ be the class of multi-frequency quasiperiodic Schrödinger operators whose spectrum is an interval, and let the potentials be real trigonometric polynomials with…

Type I genericity conjecture. Type I energies are open and dense in $\Sigma$ for generic analytic one-frequency Schrödinger operators, where generic means open and dense in the spa…

Spectral transition conjecture. For an $\alpha$-Diophantine, and hence almost every, phase $\theta$, $H_{\lambda,\alpha,\theta}$ satisfies Anderson localization—that is, it has onl…