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Stable homology of braid groups with symplectic coefficients

By Dan Petersen

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

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

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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