Papers
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Dimer/ghor algebras:
• A generalization of cancellative dimer algebras to hyperbolic surfaces,
with Karin Baur, submitted, arxiv:2101.11512, 26 pp.
• The central nilradical of nonnoetherian dimer algebras,
submitted, arxiv:1902.11299, 27 pp.
• Dimer algebras, ghor algebras, and cyclic contractions,
Algebras and Representation Theory, online first, 2023, 41 pp. doi:10.1007/s10468-023-10224-y journal (open)/arxiv
• Examples of geodesic ghor algebras on hyperbolic surfaces,
with Karin Baur, AMS Contemporary Mathematics: Representations of Algebras, Geometry and Physics, 769, 2021.
doi:10.1090/conm/769/15414 journal/arxiv
• Noetherian criteria for dimer algebras,
Journal of Algebra, 585:294-315, 2021. doi:10.1016/j.jalgebra.2021.05.012 journal/arxiv
• On the central geometry of nonnoetherian dimer algebras,
Journal of Pure and Applied Algebra, 225(8), 2021. doi:10.1016/j.jpaa.2020.106590 journal/arxiv
• Cyclic contractions of dimer algebras always exist,
Algebras and Representation Theory, 22:1083-1100, 2019. doi:10.1007/s10468-018-9812-6 journal (open)/arxiv
• Nonnoetherian homotopy dimer algebras and noncommutative crepant resolutions,
Glasgow Mathematical Journal, 60(2):447-479, 2018. doi:10.1017/S0017089517000209 journal (open)/arxiv
• Morita equivalences and Azumaya loci from Higgsing dimer algebras,
Journal of Algebra, 453:429-455, 2016. doi:10.1016/j.jalgebra.2015.11.052 journal (open)/arxiv
• On the noncommutative geometry of square superpotential algebras,
Journal of Algebra, 371:207-249, 2012. doi:10.1016/j.jalgebra.2012.07.051​ journal (open)/arxiv
• Finitistic global dimensions of geodesic ghor algebras,
with Karin Baur, in preparation.
• Cancellativization of dimer models,
with A. Ishii and K. Ueda, arxiv:1301.5410, 16 pp.
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Nonnoetherian algebraic geometry:
• Nonnoetherian singularities and their noncommutative blowups,
Journal of Noncommutative Geometry, 17(2):469-498, 2023. doi:10.4171/JNCG/495 journal (open)/arxiv
• Nonnoetherian coordinate rings with unique maximal depictions,
Communications in Algebra, 46:2635-2647, 2018. doi:10.1080/00927872.2017.1392533 journal (open)/arxiv
• Nonnoetherian geometry,
Journal of Algebra and Its Applications, 15(09), 2016. doi:10.1142/S0219498816501760 journal (open)/arxiv
(Previously ranked #1 on the journals ‘Most Read’ list.)
• Nonnoetherian coordinate rings of intersecting one-dimensional points,
in preparation.
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Nonnoetherian (= quantum = 'internal') spacetime:
• Spacetime geometry of spin, polarization, and wavefunction collapse,
Journal of Geometry and Physics, 195, 2024. doi.10.1016/j.geomphys.2023.105026 journal (open)/OSF/arxiv
• A derivation of the standard model particles from internal spacetime,
International Journal of Geometric Methods in Modern Physics, 20(10), 2023. doi:10.1142/S0219887823501657 journal (open)/arxiv
• A combinatorial derivation of the standard model interactions from the Dirac Lagrangian,
International Journal of Geometric Methods in Modern Physics, 20(11), 2023. doi:10.1142/S0219887823501827 journal/arxiv
• The Bell states in noncommutative algebraic geometry,
International Journal of Quantum Information, 12(5), 2014. doi:10.1142/S0219749914500336 journal (open)/arxiv
(Previously ranked #2 on the journals ‘Most Read’ list.)
• On the spacetime geometry of quantum nonlocality,
revising, arxiv:1511.05205.
• An internal spacetime model of baryons and mesons,
in preparation.
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Thesis (partial):
• The geometry of noncommutative singularity resolutions,
arxiv:1102.5741, 42 pp.
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