3 papers
math.SP2026
A counterexample to Fermi isospectral rigidity for two dimensional discrete periodic Schrödinger operators
Taylor Brysiewicz, Matthew Faust, Wencai Liu
Using numerical certification, we prove the existence of a nontrivial real-valued two dimensional periodic potential whose associated discrete Schrödinger operator is Fermi isospe…
math.SP2025
Rare Flat Bands for Periodic Graph Operators
Matthew Faust, Wencai Liu
As a corollary of our main results, we prove that for any connected -periodic graph, when edge weights and potentials are treated as variables, the corresponding peri…
math.SP2025
Extrema of spectral band functions of two dimensional discrete periodic Schrödinger operators
Matthew Faust, Wencai Liu, Ethan Luo
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 oper…