Research

Interests:

I am mainly interested in the application of algebraic and discrete geometry to spectral theory. My research focuses on applying algebraic geometry to study the spectrum of discrete periodic operators. I am also interested in algebraic statistics and applied (combinatorial) algebraic geometry in general.

Products:

Preprints

1. Preprint (Submitted): LikelihoodGeometry: Macaulay2 Package by David Barnhill, John Cobb, Matthew Faust, Nov 2024, DOI: 10.48550/ARXIV.2411.11165
2. Preprint (Submitted): Likelihood Correspondence of Statistical Models by David Barnhill, John Cobb, Matthew Faust, Dec 2023, DOI: 10.48550/ARXIV.2312.08501 (Accompanying code)
3. Preprint (Accepted): Irreducibility of the Dispersion Polynomial for Periodic Graphs by Matthew Faust, Jordy Lopez Garcia, Feb 2023, DOI: 10.48550/ARXIV.2302.11534

Publications

1. Floquet Isospectrality of the Zero Potential for Discrete Periodic Schrödinger Operators by Matthew Faust, Wencai Liu, Rodrigo Matos, Jenna Plute, Jonah Robinson, Yichen Tao, Ethan Tran, Cindy Zhuang, Journal of Mathematical Physics, (2024), DOI: 10.1063/5.0201744 (Product of STODO; Accompanying code)
2. Critical points of discrete periodic operators by Matthew Faust, Frank Sottile, Journal of Spectral Theory, (2024), DOI: 10.4171/JST/503 (Accompanying materials)
3. Surprising Accuracy of Benford's Law in Mathematics by Zhaodong Cai, Matthew Faust, A.J. Hildebrand, Junxian Li, Yuan Zhang, The American Mathematical Monthly, (2020), DOI: 10.1080/00029890.2020.1690387
4. Leading Digits of Mersenne Numbers by Zhaodong Cai, Matthew Faust, A.J. Hildebrand, Junxian Li, Yuan Zhang, Experimental Mathematics, (2019), DOI: 10.1080/10586458.2018.1551162