English
Extremal eigenvectors, the spectral action, and the zeta spectral triple
Multi angle
Auteurs : Connes, Alain (Auteur de la Conférence)
CIRM (Editeur )
11M06 - $ \zeta (s)$ and $L(s, \chi)$
11M55 - Relations with noncommutative geometry
11R37 - Class field theory
14A15 - Schemes
14F20 - Étale and other Grothendieck topologies and cohomologies
57K10 - Knot theory
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3196/Slides/4-Stephan.pdf
CIRM (Editeur )
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Résumé :
I will first explain the joint work with Walter van Suijlekom on a new result about th zeros of the Fourier transform of extremal eigenvectors for quadratic forms associated to distributions on a bounded interval and its relation with the spectral action. Then I will explain how these results allow to advance in the joint work which I am doing with Consani and Moscovici on the zeta spectral triple. Finally, if time permits, I will discuss several ideas in connection with physics and non-commutative geometry.
Keywords : extremal eigenvectors; the spectral action; the zeta spectral triple
Codes MSC : Keywords : extremal eigenvectors; the spectral action; the zeta spectral triple
11M06 - $ \zeta (s)$ and $L(s, \chi)$
11M55 - Relations with noncommutative geometry
11R37 - Class field theory
14A15 - Schemes
14F20 - Étale and other Grothendieck topologies and cohomologies
57K10 - Knot theory
Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/3196/Slides/4-Stephan.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 18/04/2025 Date de captation : 10/04/2025 Sous collection : Research talks arXiv category : Number Theory ; Quantum Algebra ; Operator Algebras Domaine : Analysis and its Applications ; Geometry ; Number Theory Format : MP4 (.mp4) - HD Durée : 00:56:53 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-04-10_Connes.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time / Applications de la Géométrie Non Commutative aux Théories de Jauge, à la Théorie des Champs et aux Espaces-Temps QuantiquesOrganisateurs de la rencontre : Iseppi, Roberta Anna ; Martinetti, Pierre ; Masson, Thierry ; Nieuviarts, Gaston ; Organisateurs, . ; Vitale, Patrizia Dates : 07/04/2025 - 11/04/2025 Année de la rencontre : 2025 URL Congrès : https://conferences.cirm-math.fr/3196.html
Données de citation
DOI : 10.24350/CIRM.V.20340803Citer cette vidéo: Connes, Alain (2025). Extremal eigenvectors, the spectral action, and the zeta spectral triple. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20340803 URI : http://dx.doi.org/10.24350/CIRM.V.20340803 |
Voir aussi
- [Multi angle] T-Minkowski noncommutative spacetimes / Auteur de la Conférence Mercati, Flavio.
- [Multi angle] The BV quantisation in NCG: the case of finite spectral triple / Auteur de la Conférence Iseppi, Roberta Anna.
- [Multi angle] Quantum Galilei group as quantum reference frame transformations / Auteur de la Conférence Gubitosi, Giulia.
- [Multi angle] Quantum gravity from non-commutative geometry / Auteur de la Conférence Barrett, John.
Bibliographie
- CONNES, A., CONSANI, C., Weil positivity and trace formula the archimedean place. Sel. Math. New Ser. 27, 77 (2021) - https://doi.org/10.1007/s00029-021-00689-4
- CONNES, A., CONSANI, C., Spectral triples and ζ-cycles. Enseign. Math. 69 (2023), no. 1/2, pp. 93–148 - https://doi.org/10.4171/lem/1049
- A. Connes, C. Consani, H. Moscovici, Zeta zeros and prolate wave operators, ArXiv
:2310.18423 - https://doi.org/10.48550/arXiv.2310.18423
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