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Stable homology of braid groups with symplectic coefficients
Multi angle
Authors : Petersen, Dan (Author of the conference)
CIRM (Publisher )
14H10 - Families, moduli (algebraic)
20F36 - Braid groups; Artin groups
55P48 - Loop space machines, operads
18M70 - Algebraic operads, cooperads, and Koszul duality
CIRM (Publisher )
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Abstract :
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
MSC Codes : 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/05/2024 Conference Date : 07/05/2024 Subseries : Research talks arXiv category : Number Theory ; Algebraic Geometry ; Algebraic Topology ; Geometric Topology Mathematical Area(s) : Geometry ; Topology Format : MP4 (.mp4) - HD Video Time : 01:04:31 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-05-07_Petersen.mp4 
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Information on the Event
Event Title : Higher Algebra, Geometry, and Topology / Algèbre, Géométrie et Topologie SupérieuresEvent Organizers : Campos, Ricardo ; Cirici, Joana ; Dotsenko, Vladimir ; Vallette, Bruno Dates : 06/05/2024 - 10/05/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/2995.html
Citation Data
DOI : 10.24350/CIRM.V.20173703Cite this video as: 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 |
See Also
- [Multi angle] Higher Lie theory in positive characteristic / Author of the conference Roca i Lucio, Victor.
- [Multi angle] Equivariant formality and reduction / Author of the conference Esposito, Chiara.
- [Multi angle] On analytic exponential functors on free groups / Author of the conference Vespa, Christine.
- [Multi angle] Poincaré duality fibrations and graph complexes / Author of the conference Berglund, Alexander.
Bibliography
- 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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