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}
}
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