I'll explain joint work with D. Ben-Zvi and A. Brochier. We construct a partially defined 4D "Quantum Geometric Langlands" TFT from the quantum group U_q(g) associated to a reductive group G, and develop completely explicit computations of the QGL theory of arbitrary surfaces, using factorization homology of Francis. For once-punctured tori we recover algebras of quantum differential operators on G. For closed tori and G=GL_N, we expect to recover the double affine Hecke algebra associated to G.
The QGL theory of 3-manifolds yields knot invariants valued in modules for the DAHA, and hence is closely related to several recently conjectured knot invariants of Cherednik, Gukov, Oblomkov-Rasmussen-Shende, and Berest-Samuelson.