English
Effective aspects of the geometry of tensors - Lecture 1
Multi angle
Auteurs : Ottaviani, Giorgio (Auteur de la conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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.
Mots-Clés : tensor rank; secant variety
Codes MSC : Mots-Clés : 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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 17/03/2022 Date de Captation : 28/02/2022 Sous Collection : Research School Catégorie arXiv : Algebraic Geometry Domaine(s) : Géométrie Complexe & géométrie Algébrique Format : MP4 (.mp4) - HD Durée : 01:35:48 Audience : Chercheurs ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2022-02-28_Ottaviani_Part1.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Francophone Computer Algebra Days / JNCF - Journées nationales de calcul formelOrganisateurs de la Rencontre : Boito, Paola ; Guerrini, Eleonora ; Koseleff, Pierre-Vincent ; Spaenlehauer, Pierre-Jean ; Vaccon, Tristan Dates : 28/02/2022 - 04/03/2022 Année de la rencontre : 2022 URL de la Rencontre : https://conferences.cirm-math.fr/2568.html
Données de citation
DOI : 10.24350/CIRM.V.19893503Citer cette vidéo: 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 |
Voir Aussi
- [Multi angle] About two geometric problems in computational structural biology - Lecture 1 / Auteur de la conférence Cazals, Frédéric.
- [Multi angle] Validated symbolic-numeric algorithms and practical applications in aerospace - Lecture 2 / Auteur de la conférence Joldes, Mioara.
- [Multi angle] Effective aspects of the geometry of tensors - Lecture 2 / Auteur de la conférence Ottaviani, Giorgio.
Bibliographie
- 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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