Matthew Faust

activity

20242026

collaborators

4 papers

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…

math.AG2024

Irreducibility of the Dispersion Polynomial for Periodic Graphs

Matthew Faust, Jordy Lopez Garcia

We use methods from algebra and discrete geometry to study the irreducibility of the dispersion polynomial of a discrete periodic operator associated to a periodic graph after chan…