Cherednik algebras and Khovanov-Rozansky homology

I will describe a model for the HOMFLY homology of the $(m,n)$ torus knot using the finite-dimensional irreducible representation $L_m/n$ of the
rational Cherednik algebra with parameter $m/n$. The $m-n$ symmetry of this construction and connections to the $q,t-$ Catalan numbers of A. Garsia and M. Haiman will be also discussed. The talk is based on a joint work with
A.Oblomkov, J. Rasmussen and V. Shende.