DAHAs and skein theory

We give a skein-theoretic realization of the ${\mathfrak{g}\mathfrak{l}}_n$ double affine Hecke algebra of Cherednik using braids and tangles in the punctured torus. We use this to provide evidence of a relationship we conjecture between the classical skein algebra of the punctured torus and the elliptic Hall algebra of Burban and Schiffmann.