Extrema of spectral band functions of two dimensional discrete periodic Schrödinger operators

We use Bézout’s theorem and Bernstein-Khovanskii-Kushnirenko theorem to analyze the level sets of the extrema of the spectral band functions of discrete periodic Schrödinger operators on ${\mathbb{Z}}^2$. These approaches improve upon previous results of Liu and Filonov-Kachkovskiy.