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Articles by Luke Oeding

BibTeX  | Google Scholar  | AMS
On the (non-)vanishing of syzygies of Segre embeddings, (with Claudiu Raicu and Steven Sam)
A New Generation of Brain-Computer Interfaces Driven by Discovery of Latent EEG-fMRI Linkages using Tensor Decomposition, Gopikrishna Deshpande, D Rangaprakash, Luke Oeding, Andrzej Cichocki, Xiaoping Hu
Frontiers in Neuroscience, section Neural Technology 11:246.
Border Ranks of Monomials
(submitted 2016)
arXiv  |  code  |  slides
Are all Secant Varieties of Segre Products Arithmetically Cohen-Macaulay?
(submitted 2016).
arXiv  |  slides  |  EACA Extended Abstract, in EACA 2016 Proceedings
Homotopy techniques for tensor decomposition and perfect identifiability (with Jon Hauenstein and Giorgio Ottaviani and Andrew Sommese)
J. Reine Angew. Math. (Crelle's Journal), Published Online Dec 2016.
journal  |  arXiv  |  code  |  slides
Symmetrization of Principal Minors (with Huajun Huang)
Linear and Multilinear Algebra (2016), 26 pages.
journal  |  arXiv  |  slides
The Quadrifocal Variety
Linear Algebra and its Applications, Volume 512, 1 January 2017, Pages 306-330.
journal  |  arXiv  |  code  |  slides
Decomposing Tensors into Frames (with Elina Robeva and Bernd Sturmfels)
Advances in Applied Mathematics 73 (2016) 125-153.
journal  |  arXiv  |  review  |  slides
Equations for the fifth secant variety of Segre products of projective spaces (with Steven Sam)
Experimental Mathematics, Volume 25, Issue 1, 2016, pages 94-99.
journal |  arXiv  |  review  |  code  |  slides
Computations and Equations for Segre-Grassmann Hypersurfaces (with Noah Daleo and Jon Hauenstein)
Portugaliae Mathematica, Vol. 73, Fasc. 1, 2016, 71-90.
journal |  arXiv  |  review  |  slides  |  10080 monomials
The \(3 \times 3 \times 3\) hyperdeterminant as a polynomial in the fundamental invariants for \(SL_3(\mathbb{C}) \times SL_3(\mathbb{C}) \times SL_3(\mathbb{C})\) (with Murray Bremner and Jiaxiong Hu)
Mathematics in Computer Science (Special Issue on Computational Algebraic Geometry), June 2014, Volume 8, Issue 2, pp 147-156.
journal  |  arXiv  |  review  |  Maple Hilbert function for invariant rings of tensors
Secant cumulants and toric geometry (with Mateusz Michalek and Piotr Zwiernik)
International Mathematics Research Notices, (2015) 12: 4019-4063.
journal  |  arXiv  |  review  |  slides
Tangential varieties of Segre-Veronese varieties (with Claudiu Raicu)
Collectanea Mathematica, September 2014, Volume 65, Issue 3, pp 303-330.
journal  |  arXiv  |  review
The ideal of the trifocal variety (with Chris Aholt)
Mathematics of Computation, 83 (2014), 2553-2574.
journal |  arXiv  |  review  |  slides  |  computations
Eigenvectors of tensors and algorithms for Waring decomposition (with Giorgio Ottaviani)
Journal of Symbolic Computation, Volume 54, July 2013, Pages 9-35.
journal  |  arXiv  |  review  |  slides  |  computations  |  minor erratum |  Sylvester's cat comic
Hyperdeterminants of polynomials
Advances in Mathematics, Volume 231, Issues 3-4, October-November 2012, Pages 1308-1326.
journal  |  arXiv  |  review  |  slides  |  computations
Secant varieties of \(\mathbb{P}^2 \times \mathbb{P}^n\) embedded by \(\mathcal{O}(1, 2)\) (with Dustin Cartwright and Daniel Erman)
Journal of the London Mathematical Society (2012) 85 (1): 121-141.
journal  |  arXiv  |  review  |  slides
Toward a salmon conjecture (with Dan Bates)
Experimental Mathematics, Volume 20, Issue 3, 2011, pages 358-370.
journal  |  arXiv  |  review  |  slides  |  computations  |  minor erratum |  2008 lecture
Set-theoretic defining equations of the tangential variety of the Segre variety
Journal of Pure and Applied Algebra, Volume 215, Issue 6, June 2011, Pages 1516-1527.
journal  |  arXiv  |  review  |  slides
Set-theoretic defining equations of the variety of principal minors of symmetric matrices
Algebra and Number Theory, Vol. 5 (2011), No. 1, 75-109.
journal  |  arXiv  |  review  |  slides  |  computations  |  updated slides
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian (with Pedro Macias Marques)
Le Matematiche, Vol. LXIV (2009) - Fasc. II, pp. 155-176.
journal  |  arXiv  |  reveiw  |  slides  |  computations
Dissertation: G-Varieties and principal minors of symmetric matrices (director: JM Landsberg).
thesis |  review  |  slides
Book Chapters
Weyman's method for subspace varieties of skew-symmetric tensors (with Ada Boralevi)
in J.M. Landsberg, Tensors: Geometry and Applications, (p405-407), AMS GSM, vol. 128, (2012).
Landsberg's book
Expository Work
Tensor Decomposition and Algebraic Geometry
(Simons BootCamp Lectures 2014)
Video: Lecture I, Lecture II  |  notes
Four lectures on secant varieties (with Enrico Carlini and Nathan Grieve)
Workshop on Connections Between Algebra and Geometry, Summer 2012,
PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhauser (2014).
journal  |  arXiv  |  review
AIM Report on "Geometry and representation theory of tensors for computer science, statistics and other areas."
article  |  arXiv
Electric network synthesis (with Shaowei Lin and Bernd Sturmfels)
2011 notes
Algebraic and Geometric Aspects of Audio Signal Processing (with Rolf Bardeli)
Applications of Secant Varieties and their Equations (Cortona 2009)
Undergraduate Thesis: Phase space quantum mechanics (supervised by Calvin Stubbins)