I will present some recent works with Gunningham, Safronov, Vazirani, and Yang (in various combinations) and which compute GLN-, SLN– and PGLN-skein modules for the 3-torus T 3, and related work of Kinnear which generalizes this to mapping tori T 2 ×γ S1, for γ ∈ SL2(ℤ).
The proofs for GLN and SLN start with a description of the skein category of T 2 via the representation theory of double affine Hecke algebras, while for PGLN they rely on an instance of electric-magnetic duality.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop The Geometry of Double Affine Hecke Algebras and Coulomb Branches.
