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): 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, Jan 2024, DOI: 10.48550/ARXIV.2401.09731 (Product of STODO; Accompanying code)
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 (Submitted): Irreducibility of the Dispersion Polynomial for Periodic Graphs by Matthew Faust, Jordy Lopez Garcia, Feb 2023, DOI: 10.48550/ARXIV.2302.11534
4. Preprint (Accepted): Critical points of discrete periodic operators by Matthew Faust, Frank Sottile, June 2022, DOI: 10.48550/ARXIV.2206.13649 (Accompanying materials)

Publications

1. 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
2. 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