English
Stable homology of braid groups with symplectic coefficients
Multi angle
Auteurs : Petersen, Dan (Auteur de la Conférence)
CIRM (Editeur )
14H10 - Families, moduli (algebraic)
20F36 - Braid groups; Artin groups
55P48 - Loop space machines, operads
18M70 - Algebraic operads, cooperads, and Koszul duality
CIRM (Editeur )
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Résumé :
There is a family of symplectic representations of the braid groups given by the "integral reduced Burau representation". I will explain a calculation of the stable homology of the braid groups with coefficients in this Burau representation, composed with any algebraic rational representation of the symplectic group. The answer has important consequences in analytic number theory. (Joint with Bergström-Diaconu-Westerland.)
Keywords : Scanning; homological stability; Burau representation; braid groups
Codes MSC : Keywords : Scanning; homological stability; Burau representation; braid groups
14H10 - Families, moduli (algebraic)
20F36 - Braid groups; Artin groups
55P48 - Loop space machines, operads
18M70 - Algebraic operads, cooperads, and Koszul duality
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 29/05/2024 Date de captation : 07/05/2024 Sous collection : Research talks arXiv category : Number Theory ; Algebraic Geometry ; Algebraic Topology ; Geometric Topology Domaine : Geometry ; Topology Format : MP4 (.mp4) - HD Durée : 01:04:31 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-05-07_Petersen.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Higher Algebra, Geometry, and Topology / Algèbre, Géométrie et Topologie SupérieuresOrganisateurs de la rencontre : Campos, Ricardo ; Cirici, Joana ; Dotsenko, Vladimir ; Vallette, Bruno Dates : 06/05/2024 - 10/05/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/2995.html
Données de citation
DOI : 10.24350/CIRM.V.20173703Citer cette vidéo: Petersen, Dan (2024). Stable homology of braid groups with symplectic coefficients. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20173703 URI : http://dx.doi.org/10.24350/CIRM.V.20173703 |
Voir aussi
- [Multi angle] Higher Lie theory in positive characteristic / Auteur de la Conférence Roca i Lucio, Victor.
- [Multi angle] Equivariant formality and reduction / Auteur de la Conférence Esposito, Chiara.
- [Multi angle] On analytic exponential functors on free groups / Auteur de la Conférence Vespa, Christine.
- [Multi angle] Poincaré duality fibrations and graph complexes / Auteur de la Conférence Berglund, Alexander.
Bibliographie
- BERGSTRÖM, Jonas, DIACONU, Adrian, PETERSEN, Dan, et al. Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions. arXiv preprint arXiv:2302.07664, 2023. - https://arxiv.org/abs/2302.07664
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