Luke Oeding's Research

Tensor Decompositions with applications to LU and SLOCC equivalence of multipartite pure states
(with Ian Tan) submitted 2.19.2024
arXiv

ExteriorExtensions: a package for Macaulay2
submitted 12.19.2023
arXiv | code

Maximally entangled real states and SLOCC invariants: the 3-qutrit case (with Hamza Jaffali, and Frédéric Holweck‬)
Journal of Physics A: Mathematical and Theoretical, Volume 57 Number 14 (2024)
journal | arXiv

Four-view Geometry with Unknown Radial Distortion, Petr Hruby, Viktor Korotynskiy, Timothy Duff, Luke Oeding, Marc Pollefeys, Tomas Pajdla, and Viktor Larsson
Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023, pp. 8990-9000
CVPR 2023 Proceedings

A Hyperdeterminant on Fermionic Fock Space (with Frédéric Holweck‬)
Annales de l'Institut Henri Poincaré D: Combinatorics, Physics and their Interactions, (2024), published online first
journal | arXiv

Restricted Secant Varieties of Grassmannians (with Dalton Bidleman)
Collectanea Mathematica (published online Mar. 2023)
journal | arXiv | slides

Jordan Decompositions of Tensors (with Frédéric Holweck‬)
preprint
arXiv

A Translation of "Classification of four-vectors of an 8-dimensional space," by Antonyan, L. V. , with an appendix by the translator
volume 83(2022) "Trudy Moskovskogo matematicheskogo obshchestva"
(= Transactions of the Moscow mathematical society).
journal | arXiv

Towards Learning in Neuromorphic Circuits Based on Quantum Phase Slip Junctions, Michael C. Hamilton, Ran Cheng, Uday S Goteti, Harrison Walker, Keith M Krause, Luke Oeding
Frontiers in Neuroscience - Neural Technology: 15:765883. doi: 10.3389/fnins.2021.765883
journal

Analysis of the Stochastic Alternating Least Squares Method for the Decomposition of Random Tensors (with Yanzhao Cao, Somak Das, and Hans-Werner Van Wyk)
preprint
arXiv | slides

Learning Algebraic Models of Quantum Entanglement (with Hamza Jaffali)
Quantum Information Processing 19, 279 (2020).
review | arXiv | journal | slides

Hyperdeterminants from the \(E_8\) discriminant (with Frédéric Holweck‬)
Journal of Algebra (2022) https://doi.org/10.1016/j.jalgebra.2021.10.017
review | arXiv | anc files | slides | journal

On the (non-)vanishing of syzygies of Segre embeddings (with Claudiu Raicu and Steven Sam)
Algebraic Geometry 6 (5) (2019) 571--591
doi:10.14231/AG-2019-026
review | arXiv | journal

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.
journal | slides

Border Ranks of Monomials
preprint
arXiv | code | slides

Are all Secant Varieties of Segre Products Arithmetically Cohen-Macaulay?
preprint
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 | review | arXiv | code | slides

Symmetrization of Principal Minors and Cycle Sums (with Huajun Huang)
Linear and Multilinear Algebra (2016), 26 pages.
journal | review | arXiv | slides

The Quadrifocal Variety
Linear Algebra and its Applications, Volume 512, 1 January 2017, Pages 306-330.
journal | review | 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

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

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

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

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

Decisions are Happening Over Dinner
SIAM NEWS, AG23, Volume 56 | Number 08 | October 2023
article

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

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

Notes

Electric network synthesis (with Shaowei Lin and Bernd Sturmfels)
2011 notes

Algebraic and Geometric Aspects of Audio Signal Processing (with Rolf Bardeli)
slides

Applications of Secant Varieties and their Equations (Cortona 2009)
slides

Undergraduate Thesis: Phase space quantum mechanics (supervised by Calvin Stubbins)
thesis

Articles by Luke Oeding