4 problems

Let $\alpha$ be irrational and let $v\in C^\omega(\mathbb{T},\mathbb{R})$. Write $\Sigma_{v,\alpha}$ for the spectrum and $N_{v,\alpha}$ for the integrated density of states. An en…

Let $p$ and $q$ be coprime integers with $q$ odd, and let $\Sigma_{p/q}$ denote the periodic almost Mathieu spectrum. Let $C=0.915\ldots$ be Catalan's constant. Thouless-type spect…

Spectral transition conjecture. For $\lambda\in\mathcal{R}_1\cap\mathcal{R}_s$, the operator $H^{\mathrm{EHM}}_{\lambda,\alpha,\theta}$ has purely singular continuous spectrum if

Critical energy conjecture.