3 problems

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 releva…

Let $H_0$ be the Hamiltonian whose potential on the sites $n$ is the quasi-periodic function $v(n)=U\cos(2\pi\omega n)$, where $-2<U<2$ and $\omega$ is irrational. Assume that the…

Simon's conjecture. For all $d,v\in\mathbb{N}$ and all $\theta\in\mathbb{T}^{\nu}$, $\sigma_{sing}(H_{\alpha,\theta})$ is constant in $\theta$.