For an abelian category A with some finiteness properties, one can define an associative algebra, called the Hall algebra of A, which encodes the structure of extensions in A. If X is an elliptic curve over a finite field, Burban and Schiffmann gave an explicit description of the Hall algebra of the category Coh(X) of coherent sheaves on X. On the other hand, for any surface S, there is a topologically defined `skein algebra', which is spanned by links in S modulo the so-called HOMFLY skein relations. In this talk, we describe joint work with Morton, where we show that the Hall algebra of an elliptic curve and the HOMFLY skein algebra of the torus are isomorphic. This can be viewed as a manifestation of Mirror Symmetry for the torus. We also discuss some consequences for knot theory.