Matthew Faust

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20242026

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math.SP2026

Algebraic Properties of the Ideal of Spectral Invariants for the Discrete Laplacian

Matthew Faust, Leo Friedman, Gavin O'Malley +2

Let $I^ = q_{1} Z \oplus q_{2} Z \oplus \dots \oplus q_{d} Z$ , with $q_{j} \in Z^{+}$ for each $j \in {1, \dots, d}$ , and denote by $I^$ the discrete Laplacian on…

math.SP2025

The Critical Point Degree of a Periodic Graph

Matthew Faust, Jonah Robinson, Frank Sottile

The critical point degree of a periodic graph operator is the number of critical points of its complex Bloch variety. Determining it is a step towards the spectral edges conjecture…

math.SP2025

The Spectral Edges Conjecture via Corners

Matthew Faust, Frank Sottile

The Spectral Edges Conjecture is a well-known and widely believed conjecture in the theory of discrete periodic operators. It states that the extrema of the dispersion relation are…