English

Langlands duality for skein modules of 3-manifolds

Quantum Algebra 2023-03-01 v1 Geometric Topology Number Theory Representation Theory

Abstract

I introduce new Langlands duality conjectures concerning skein modules of 3-manifolds, which we have made recently with David Ben-Zvi, Sam Gunningham, and Pavel Safronov. I recount some historical motivation and some recent special cases where the conjecture is confirmed. The proofs in these cases combine the representation theory of double affine Hecke algebras and a new 1-form symmetry structure on skein modules related to electric-magnetic duality. This note is an expansion of my talk given at String Math 2022 in Warsaw, and is submitted to the String Math 2022 Proceedings publication.

Keywords

Cite

@article{arxiv.2302.14734,
  title  = {Langlands duality for skein modules of 3-manifolds},
  author = {David Jordan},
  journal= {arXiv preprint arXiv:2302.14734},
  year   = {2023}
}

Comments

Comments welcome!