Stable homology of braid groups with symplectic coefficients

Appears in collection : Higher Algebra, Geometry, and Topology / Algèbre, Géométrie et Topologie Supérieures

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.)

Information about the video

Date of recording 07/05/2024
Date of publication 29/05/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20173703
Cite this video Petersen, Dan (07/05/2024). Stable homology of braid groups with symplectic coefficients. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20173703
URL https://dx.doi.org/10.24350/CIRM.V.20173703

Domain(s)

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