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math.AG2026
Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils
Matthew Faust
We study reducibility of the characteristic polynomials of a class of finite Jacobi pencils. We classify the diagonal equality patterns for which generic connected couplings yield…
math.SP2026
Generic Irreducibility of Bloch Varieties for Periodic Graph Operators
Matthew Faust, Wencai Liu
We give a complete characterization of generic irreducibility for dispersion polynomials and Bloch varieties of periodic graph operators. More precisely, we prove that for a generi…
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 isospec…