3 problems

Let $\delta>0$, and let $rhob_{\delta}$ and $Vb_{\delta}$ be the density and velocity profiles defined by the sharp stratification and shear-flow setup. Let $\mathcal C_{\delta}(k)$…

Consider an elliptic periodic operator and vary its parameters, for example its periodic potential. Generic gap-edge non-degeneracy conjecture. For almost all such parameters, the…

Let $-elta+V$ be a Schrödinger operator on $\mathbb{R}^n$ with periodic potential, and let $\lambda_j(k)$ denote its band functions, with $k$ the quasimomentum. Spectral edges are…