A New Generation of Brain-Computer Interfaces Driven by Discovery of Latent EEG-fMRI Linkages using Tensor Decomposition,

Frontiers in Neuroscience, section Neural Technology**11**:246.

journal | slides

Frontiers in Neuroscience, section Neural Technology

journal | slides

Are all Secant Varieties of Segre Products Arithmetically Cohen-Macaulay?

(submitted 2016).

arXiv | slides | EACA Extended Abstract, in EACA 2016 Proceedings

(submitted 2016).

arXiv | slides | EACA Extended Abstract, in EACA 2016 Proceedings

Homotopy techniques for tensor decomposition and perfect identifiability
(with
and
and
)

J. Reine Angew. Math. (Crelle's Journal), Published Online Dec 2016.

journal | arXiv | code | slides

J. Reine Angew. Math. (Crelle's Journal), Published Online Dec 2016.

journal | arXiv | code | slides

Symmetrization of Principal Minors
(with
)

Linear and Multilinear Algebra (2016), 26 pages.

journal | arXiv | slides

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

Linear Algebra and its Applications, Volume 512, 1 January 2017, Pages 306-330.

journal | arXiv | code | slides

Decomposing Tensors into Frames
(with
and
)

Advances in Applied Mathematics**73** (2016) 125-153.

journal | arXiv | review | slides

Advances in Applied Mathematics

journal | arXiv | review | slides

Equations for the fifth secant variety of Segre products of projective spaces
(with
)

Experimental Mathematics, Volume 25, Issue 1, 2016, pages 94-99.

journal | arXiv | review | code | slides

Experimental Mathematics, Volume 25, Issue 1, 2016, pages 94-99.

journal | arXiv | review | code | slides

Computations and Equations for Segre-Grassmann Hypersurfaces
(with
and )

Portugaliae Mathematica, Vol. 73, Fasc. 1, 2016, 71-90.

journal | arXiv | review | slides | 10080 monomials

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 and )

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

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
and
)

International Mathematics Research Notices, (2015)**12**: 4019-4063.

journal | arXiv | review | slides

International Mathematics Research Notices, (2015)

journal | arXiv | review | slides

Tangential varieties of Segre-Veronese varieties
(with )

Collectanea Mathematica, September 2014, Volume 65, Issue 3, pp 303-330.

journal | arXiv | review

Collectanea Mathematica, September 2014, Volume 65, Issue 3, pp 303-330.

journal | arXiv | review

The ideal of the trifocal variety
(with )

Mathematics of Computation,**83** (2014), 2553-2574.

journal | arXiv | review | slides | computations

Mathematics of Computation,

journal | arXiv | review | slides | computations

Eigenvectors of tensors and algorithms for Waring decomposition
(with )

Journal of Symbolic Computation, Volume 54, July 2013, Pages 9-35.

journal | arXiv | review | slides | computations | minor erratum | Sylvester's cat comic

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

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 and
)

Journal of the London Mathematical Society (2012) 85 (1): 121-141.

journal | arXiv | review | slides

Journal of the London Mathematical Society (2012) 85 (1): 121-141.

journal | arXiv | review | slides

Toward a salmon conjecture
(with )

Experimental Mathematics, Volume 20, Issue 3, 2011, pages 358-370.

journal | arXiv | review | slides | computations | minor erratum | 2008 lecture

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

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

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 )

Le Matematiche, Vol. LXIV (2009) - Fasc. II, pp. 155-176.

journal | arXiv | reveiw | slides | computations

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:

thesis | review | slides

thesis | review | slides

Weyman's method for subspace varieties of skew-symmetric tensors
(with )

in J.M. Landsberg, Tensors: Geometry and Applications, (p405-407), AMS GSM, vol. 128, (2012).

Landsberg's book

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
Notes

(Simons BootCamp Lectures 2014)

Video: Lecture I, Lecture II | notes

Four lectures on secant varieties
(with
and )

Workshop on Connections Between Algebra and Geometry, Summer 2012,

PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhauser (2014).

journal | arXiv | review

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

article | arXiv