\newcommand{\arxiv}[1]{\href{http://arxiv.org/abs/#1}{{\tt arXiv:#1}}}
@article{oeding2024LU,
  AUTHOR = {Oeding, Luke and Tan, Ian},
   TITLE = {{Tensor decompositions with applications to LU and SLOCC equivalence of multipartite pure states}},
    YEAR = {2024},
    NOTE = {\arxiv{2402.12542}},
}

@article{oeding2023exteriorextensions,
  AUTHOR = {Oeding, Luke},
   TITLE = {ExteriorExtensions: A package for Macaulay2},
    YEAR = {2023},
    NOTE = {\arxiv{2312.11368}},
}

@article{jaffali2023maximally,
  AUTHOR = {Hamza Jaffali and Frédéric Holweck and Luke Oeding},
   TITLE = {{Maximally entangled real states and SLOCC invariants: the 3-qutrit case}},
    YEAR = {2023},
JOURNAL = {Journal of Physics A: Mathematical and Theoretical},
VOLUME = { 57},
NUMBER = {14},
YEAR = {2024},
DOI = {https://iopscience.iop.org/article/10.1088/1751-8121/ad3193},
    NOTE = {\arxiv{2307.00970}},
}

@misc{holweck2023hyperdeterminant,
 AUTHOR = {Frédéric Holweck and Luke Oeding},
  TITLE = {{A hyperdeterminant on Fermionic Fock Space}},
   YEAR = {2024},
   NOTE = {\arxiv{2301.10660}}, 
JOURNAL = {Annales de l'Institut Henri Poincaré D: Combinatorics, Physics and their Interactions},
}

@InProceedings{Hruby_2023_CVPR,
   AUTHOR = {Hruby, Petr and Korotynskiy, Viktor and Duff, Timothy and Oeding, Luke and Pollefeys, Marc and Pajdla, Tomas and Larsson, Viktor},
    TITLE = {Four-View Geometry With Unknown Radial Distortion},
BOOKTITLE = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
    MONTH = {June},
     YEAR = {2023},
    PAGES = {8990-9000}
}

@ARTICLE{BidlemanOeding,
  AUTHOR = {Bidleman, Dalton and Oeding, Luke},
   TITLE = {Restricted Secant Varieties of Grassmannians},
 JOURNAL = {Collectanea Mathematica},
    NOTE = {\arxiv{2211.01469}},
     DOI = {10.1007/s13348-023-00399-4},
    YEAR = {2023}
}

@ARTICLE{HolweckOeding22,
  AUTHOR = {Holweck, Frederic and Oeding, Luke},
   TITLE = {Jordan Decompositions of Tensors},
    YEAR = {2022},
     DOI = {10.48550/ARXIV.2206.13662},
    NOTE = {\arxiv{2206.13662}}
}

@ARTICLE{Antonyan-translation,
  AUTHOR = {Oeding, Luke},
   TITLE = {A Translation of ``{Classification of four-vectors of an 8-dimensional space},'' by {A}ntonyan, {L}. {V}. , with an appendix by the translator},
    NOTE = {\arxiv{2205.09741}},
    YEAR = {2022},
  VOLUME = {83},
   ISSUE = {2},
   PAGES = {269--296},
FJOUNRAL = {``Trudy Moskovskogo matematicheskogo obshchestva'' (Transactions of the Moscow mathematical society)},
 JOURNAL = {Tr. Mosk. Mat. Obs.},
     URL = {\url{http://mi.mathnet.ru/mmo674}},
}

@ARTICLE{neuromorphic,
  AUTHOR = {Michael C. Hamilton, Ran Cheng, Uday S Goteti, Harrison Walker, Keith M Krause Luke Oeding},
   TITLE = {Towards Learning in Neuromorphic Circuits Based on Quantum Phase Slip Junctions},
 JOURNAL = {Frontiers in Neuroscience - Neural Technology},
  VOLUME = {15},
   PAGES = {1470},
    YEAR = {2021},
     URL = {https://www.frontiersin.org/article/10.3389/fnins.2021.765883},
     DOI = {10.3389/fnins.2021.765883},
    ISSN = {1662-453X}
}

@ARTICLE{CDOvW,
   AUTHOR = {{Cao}, Yanzhao and {Das}, Somak and {Oeding}, Luke and {van Wyk}, Hans-Werner},
    TITLE = "{Analysis of the Stochastic Alternating Least Squares Method for the Decomposition of Random Tensors}",
     YEAR = 2020,
     NOTE = {\arxiv{2004.12530}}
}

@ARTICLE{JaffaliOeding,
   AUTHOR = {{Jaffali}, H. and {Oeding}, L.},
    TITLE = "{Learning Algebraic Models of Entanglement}",
  JOURNAL = "{Quantum Information Processing}",
   NUMBER = {9},
    PAGES = {279},
   VOLUME = {19},
     NOTE = {\arxiv{1908.10247}},
     YEAR = {2020}
}

@ARTICLE{HolweckOeding,
   AUTHOR = {{Holweck}, F. and {Oeding}, L.},
    TITLE = "{Hyperdeterminants from the E8 Discriminant}",
  JOURNAL = {J. Algebra},
     NOTE = {\arxiv{1810.05857}},
      DOI = {https://doi.org/10.1016/j.jalgebra.2021.10.017},
     ISSN = {0021-8693},
     YEAR = {Accepted 10/2021},
      URL = {https://www.sciencedirect.com/science/article/pii/S0021869321004919},
}

@ARTICLE{OedingRaicuSam,
   AUTHOR = {{Oeding}, L. and {Raicu}, C. and {Sam}, S.~V},
    TITLE = "{On the (non-)vanishing of syzygies of Segre embeddings}",
  JOURNAL = {Algebraic Geometry},
   VOLUME = 6,
    ISSUE = 5,
    PAGES = {571-591},
      DOI = {10.14231/AG-2019-026},
     NOTE = {\arxiv{1708.03803}},
     YEAR = {2019}
}

@ARTICLE{brain,
  AUTHOR = {Deshpande, Gopikrishna and Rangaprakash, D and Oeding, Luke and Cichocki, Andrzej and Hu, Xiaoping},
   TITLE = {A New Generation of Brain-Computer Interfaces Driven by Discovery of Latent EEG-fMRI Linkages using Tensor Decomposition},
 JOURNAL = {Frontiers in Neuroscience},
  VOLUME = {11},
   PAGES = {246},
    YEAR = {2017},
     URL = {http://journal.frontiersin.org/article/10.3389/fnins.2017.00246},
     DOI = {10.3389/fnins.2017.00246},
    ISSN = {1662-453X}
}

@ARTICLE{monomials,
   AUTHOR = {{Oeding}, L.},
    TITLE = "{Border Ranks of Monomials}",
     NOTE = {\arxiv{1608.02530}},
     YEAR = {2016}
}

@ARTICLE{HuangOeding,
   AUTHOR = {{Huang}, H. and {Oeding}, L.},
    TITLE = "{Symmetrization of Principal Minors and Cycle-Sums}",
     NOTE = {\arxiv{1510.02515}},
journal = {Linear and Multilinear Algebra},
year = {2016},
doi = {10.1080/03081087.2016.1233932}
}

@ARTICLE{OedingRobevaSturmfels,
   AUTHOR = {{Oeding}, L. and {Robeva}, E. and {Sturmfels}, B.},
    TITLE = "{Decomposing Tensors into Frames}",
  JOURNAL = {Advances in Applied Mathematics},
   VOLUME = {73},
     NOTE = {\arxiv{1504.08049}},
     YEAR = {2016},
    PAGES = {125--156}
}

@ARTICLE{OedingSam,
   AUTHOR = {{Oeding}, L. and {Sam}, S.~V.},
    TITLE = "{Equations for the fifth secant variety of Segre products of projective spaces}",
  JOURNAL = {Experimental Mathematics},
     YEAR = 2016,
   VOLUME = 25,
    ISSUE = 1,
    PAGES = {94--99},
     NOTE = {\arxiv{1502.00203}}
}

@ARTICLE{Oeding_quadrifocal,
   AUTHOR = {{Oeding}, L.},
    TITLE = "{The Quadrifocal Variety}",
  JOURNAL = {Linear Algebra and its Applications},
   VOLUME = "512",
   NUMBER = "",
    PAGES = "306 - 330",
     YEAR = "2017",
     ISSN = "0024-3795",
      DOI = "http://dx.doi.org/10.1016/j.laa.2016.09.034",
      URL = "http://www.sciencedirect.com/science/article/pii/S0024379516304335",
     NOTE = {\arxiv{1501.01266}}
}

@article{HauensteinOedingOttavianiSommese,
   AUTHOR = {Jonathan D. Hauenstein and Luke Oeding and Giorgio Ottaviani and Andrew J. Sommese},
    TITLE = {Homotopy techniques for tensor decomposition and perfect identifiability},
    PAGES = {1--22},
   VOLUME = {2019},
   NUMBER = {753},
  JOURNAL = {Journal für die reine und angewandte Mathematik (Crelles Journal)},
      DOI = {doi:10.1515/crelle-2016-0067},
     YEAR = {2019},
     NOTE = {\arxiv{1501.00090}},
      URL = {https://doi.org/10.1515/crelle-2016-0067}
}

@ARTICLE{DaleoHauensteinOeding,
   AUTHOR = {{Daleo}, N.~S. and {Hauenstein}, J.~D. and {Oeding}, L.},
    TITLE = "{Computations and Equations for Segre-Grassmann hypersurfaces}",
  JOURNAL = {Portugaliae Mathematica},
     YEAR = {2016},
   Volume = {73},
    Issue = {Fasc. 1},
    Pages = {71--90},
     NOTE = {\arxiv{1408.2105}}
}

@incollection{CarliniGrieveOeding,
   AUTHOR = {{Carlini}, E. and {Grieve}, N. and {Oeding}, L.},
    TITLE = {Four Lectures on Secant Varieties},
BOOKTITLE = {Connections Between Algebra, Combinatorics, and Geometry},
   VOLUME = {76},
   SERIES = {Springer Proceedings in Mathematics & Statistics},
   EDITOR = {Cooper, Susan M. and Sather-Wagstaff, Sean},
      DOI = {10.1007/978-1-4939-0626-0_2},
     YEAR = {2014},
     ISBN = {978-1-4939-0625-3},
      URL = {http://dx.doi.org/10.1007/978-1-4939-0626-0_2},
PUBLISHER = {Springer New York},
    PAGES = {101--146},
     NOTE = {\arxiv{1309.4145}}
}

@article{BremnerHuOeding,
   AUTHOR = {Bremner, Murray and Hu, Jiaxiong and Oeding, Luke},
    TITLE = "{The $3 \times 3 \times 3$ Hyperdeterminant as a Polynomial in the Fundamental Invariants for $SL_3(\mathbb{C}) \times SL_3(\mathbb{C}) \times SL_3(\mathbb{C})$}",
  JOURNAL = {Mathematics in Computer Science},
     YEAR = {2014},
     ISSN = {1661-8270},
      DOI = {10.1007/s11786-014-0186-9},
      URL = {http://dx.doi.org/10.1007/s11786-014-0186-9},
PUBLISHER = {Springer Basel},
    PAGES = {1--10},
     NOTE = {\arxiv{1310.3257}}
}

@ARTICLE{MichalekOedingZwiernik,
   AUTHOR = {{Michalek}, M. and {Oeding}, L. and {Zwiernik}, P.},
    TITLE = {Secant cumulants and toric geometry},
  JOURNAL = {International Mathematics Research Notices},
   VOLUME = {2015},
   NUMBER = {12},
    PAGES = {4019--4063},
     YEAR = {2015},
      DOI = {10.1093/imrn/rnu056},
      URL = {http://imrn.oxfordjournals.org/content/2015/12/4019.abstract},
     NOTE = {\arxiv{1212.1515}}
}

@article{OedingRaicu,
   AUTHOR = {Oeding, Luke and Raicu, Claudiu},
    TITLE = {Tangential varieties of Segre-Veronese varieties},
  JOURNAL = {Collectanea Mathematica},
     YEAR = {2014},
     ISSN = {0010-0757},
    PAGES = {1--28},
PUBLISHER = {Springer Milan},
      DOI = {10.1007/s13348-014-0111-1},
      URL = {http://dx.doi.org/10.1007/s13348-014-0111-1}
}

@ARTICLE{AholtOeding,
  AUTHOR = {{Aholt}, C. and {Oeding}, L.},
   TITLE = "{The ideal of the trifocal variety}",
FJOURNAL = {Mathematics of Computation},
 JOURNAL = {Math. Comp.},
    NOTE = {\arxiv{1205.3776}},
    YEAR = 2014,
   MONTH = April,
     DOI = {10.1090/S0025-5718-2014-02842-1}
}

@article {OedingOttaviani,
  AUTHOR = {Oeding, Luke and Ottaviani, Giorgio},
   TITLE = {Eigenvectors of tensors and algorithms for {W}aring decomposition},
 JOURNAL = {J. Symbolic Comput.},
FJOURNAL = {Journal of Symbolic Computation},
  VOLUME = {54},
    YEAR = {2013},
   PAGES = {9--35},
    ISSN = {0747-7171},
 MRCLASS = {15A69},
MRNUMBER = {3032635},
     DOI = {10.1016/j.jsc.2012.11.005},
     URL = {http://dx.doi.org/10.1016/j.jsc.2012.11.005}
}

@article {Oeding_hyperdet,
    AUTHOR = {Oeding, Luke},
     TITLE = {Hyperdeterminants of polynomials},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {231},
      YEAR = {2012},
    NUMBER = {3-4},
     PAGES = {1308--1326},
      ISSN = {0001-8708},
     CODEN = {ADMTA4},
   MRCLASS = {14N05 (13A50 15A69 15A72 20G05)},
  MRNUMBER = {2964606},
MRREVIEWER = {Sylvain Petitjean},
       DOI = {10.1016/j.aim.2012.06.023},
       URL = {http://dx.doi.org/10.1016/j.aim.2012.06.023}
}

@article {CartwrightErmanOeding,
    AUTHOR = {Cartwright, D. and Erman, D. and Oeding, L.},
     TITLE = {Secant varieties of {$\Bbb P^2\times\Bbb P^n$} embedded by {$\scr O(1,2)$}},
   JOURNAL = {J. Lond. Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {85},
      YEAR = {2012},
    NUMBER = {1},
     PAGES = {121--141},
      ISSN = {0024-6107},
   MRCLASS = {14N05 (14M12)},
  MRNUMBER = {2876313},
       DOI = {10.1112/jlms/jdr038},
       URL = {http://dx.doi.org/10.1112/jlms/jdr038}
}

@article {BatesOeding,
    AUTHOR = {Bates, Daniel J. and Oeding, Luke},
     TITLE = {Toward a salmon conjecture},
   JOURNAL = {Exp. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {20},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {358--370},
      ISSN = {1058-6458},
   MRCLASS = {14M12 (14L30 14N05 20G05 68W30)},
  MRNUMBER = {2836258 (2012i:14056)},
MRREVIEWER = {Frank D. Grosshans},
       DOI = {10.1080/10586458.2011.576539},
       URL = {http://dx.doi.org/10.1080/10586458.2011.576539}
}

@article {Oeding_tangential,
    AUTHOR = {Oeding, Luke},
     TITLE = {Set-theoretic defining equations of the tangential variety of the {S}egre variety},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {215},
      YEAR = {2011},
    NUMBER = {6},
     PAGES = {1516--1527},
      ISSN = {0022-4049},
     CODEN = {JPAAA2},
   MRCLASS = {14N05 (14L30 14M12 15A69 15A72)},
  MRNUMBER = {2769247 (2012f:14106)},
MRREVIEWER = {Pietro De Poi},
       DOI = {10.1016/j.jpaa.2010.09.009},
       URL = {http://dx.doi.org/10.1016/j.jpaa.2010.09.009}
}

@article {Oeding_principal,
    AUTHOR = {Oeding, Luke},
     TITLE = {Set-theoretic defining equations of the variety of principal
              minors of symmetric matrices},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {5},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {75--109},
      ISSN = {1937-0652},
   MRCLASS = {14M12 (14L30 15A29 15A69 15A72)},
  MRNUMBER = {2833786 (2012j:14067)},
MRREVIEWER = {Pietro De Poi},
       DOI = {10.2140/ant.2011.5.75},
       URL = {http://dx.doi.org/10.2140/ant.2011.5.75}
}

@article {MaciasOeding,
    AUTHOR = {Macias Marques, Pedro and Oeding, Luke},
     TITLE = {Splitting criteria for vector bundles on the symplectic isotropic {G}rassmannian},
   JOURNAL = {Matematiche (Catania)},
  FJOURNAL = {Le Matematiche},
    VOLUME = {64},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {155--176},
      ISSN = {0373-3505},
     CODEN = {MTMTAA},
   MRCLASS = {14M15 (14J60)},
  MRNUMBER = {2800009 (2012d:14087)},
MRREVIEWER = {Francesco Malaspina}
}

@phdthesis{Oeding_thesis,
    AUTHOR = {{Oeding}, L.},
    SCHOOL = {Texas A\&M University},
     TITLE = {{G}-Varieties and the principal minors of symmetric matrices},
      YEAR = {2009}
}