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Effective aspects of the geometry of tensors - Lecture 1
Multi angle
Authors : Ottaviani, Giorgio (Author of the conference)
CIRM (Publisher )
14Q20 - Effectivity
15A69 - Multilinear algebra, tensor products
15A72 - Vector and tensor algebra, theory of invariants, See Also { 13A50, 14D25}
14N07 - secant varieties, tensor rank, varieties of sums of powers
CIRM (Publisher )
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Abstract :
We introduce some effective computation of tensor rank and tensor decomposition through apolarity and nonabelian apolarity, with some examples described in detail. The first lecture regards the symmetric case, where symmetric tensors are identified with homogeneous polynomials. The second lecture regards the general case.
Keywords : tensor rank; secant variety
MSC Codes : Keywords : tensor rank; secant variety
14Q20 - Effectivity
15A69 - Multilinear algebra, tensor products
15A72 - Vector and tensor algebra, theory of invariants, See Also { 13A50, 14D25}
14N07 - secant varieties, tensor rank, varieties of sums of powers
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 17/03/2022 Conference Date : 28/02/2022 Subseries : Research School arXiv category : Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:35:48 Targeted Audience : Researchers ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-02-28_Ottaviani_Part1.mp4 
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Information on the Event
Event Title : Francophone Computer Algebra Days / JNCF - Journées nationales de calcul formelEvent Organizers : Boito, Paola ; Guerrini, Eleonora ; Koseleff, Pierre-Vincent ; Spaenlehauer, Pierre-Jean ; Vaccon, Tristan Dates : 28/02/2022 - 04/03/2022 Event Year : 2022 Event URL : https://conferences.cirm-math.fr/2568.html
Citation Data
DOI : 10.24350/CIRM.V.19893503Cite this video as: Ottaviani, Giorgio (2022). Effective aspects of the geometry of tensors - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19893503 URI : http://dx.doi.org/10.24350/CIRM.V.19893503 |
See Also
- [Multi angle] About two geometric problems in computational structural biology - Lecture 1 / Author of the conference Cazals, Frédéric.
- [Multi angle] Validated symbolic-numeric algorithms and practical applications in aerospace - Lecture 2 / Author of the conference Joldes, Mioara.
- [Multi angle] Effective aspects of the geometry of tensors - Lecture 2 / Author of the conference Ottaviani, Giorgio.
Bibliography
- J.M. Landsberg. Tensors: geometry and applications, volume 128 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2012. - https://bookstore.ams.org/gsm-128
- J.M. Landsberg, G. Ottaviani, Equations for secant varieties of Veronese and other varieties, Annali di Matematica Pura e Applicata, 192 (2013), 569-606 - http://dx.doi.org/10.1007/s10231-011-0238-6
- L. Oeding, G. Ottaviani, Eigenvectors of tensors and algorithms for Waring decomposition, Journal of Symbolic Computation, 54 (2013), 9–35 - https://doi.org/10.1016/j.jsc.2012.11.005
- J. Hauenstein, L. Oeding, G. Ottaviani, A. Sommese, Homotopy techniques for tensor decomposition and perfect identifiability, J. Reine Angew. Math. 753 (2019), 1-22 - https://doi.org/10.1515/crelle-2016-0067
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