My primary research studies the prime ideal structure of Noetherian rings. Other interests include invariants of orders that arise from an algebraic context and order theory more generally.
2023 A Structural Invariant On Certain Two-Dimensional Noetherian Partially Ordered Sets, Rocky Mountain Journal of Mathematics, Volume 53, No. 3, 711-724, DOI: 10.1216/rmj.2023.53.711
2022 (with S. Loepp) Gluing minimal prime ideals in local rings, Communications in Algebra, 51:1, 239-247,
2021 Enlarging localized polynomial rings while preserving their prime ideal structure, Journal of Algebra, Volume 575, Pages 14-30, https://doi.org/10.1016/j.jalgebra.2021.02.011.
2013 (with E. Burger, D. Clyde, G. Shin, and Z. Wang) Canonical Diophantine representations of natural numbers with respect to quadratic “bases.” J. Number Theory 133, no. 4, 1372-1388.
2012 (with E. Burger, D. Clyde, G. Shin, and Z. Wang) A generalization of a theorem of Lekkerkerker to Ostrowski’s decomposition of natural numbers. Acta Arith. 153 no. 3, 217-249.
[Referee report received; currently in revisions] (with S. Loepp) Every finite poset is isomorphic to a saturated subset of the spectrum of some Noetherian UFD. https://doi.org/10.48550/arXiv.2206.02867
[Manuscript in production] (with A. Lee) Rigid-flexible values for embeddings of ellipsoids into almost-square polydisks.
New and Emerging Projects
Degree functions on Noetherian orders.
Counting antichains in inductive sequences of finite partial orders.
On Two Dimensional Semi-Local Noetherian Spectra. https://doi.org/10.48550/arXiv.1801.02758
Current and Past Research Students