  We establish an isomorphism between the Khovanov-Rozansky triply graded link
homology and the geometric triply graded homology due to the authors. Hence we
provide an interpretation of the Khovanov-Rozansky homology of the closure of a
braid $\beta$ as the space of derived sections of a $\mathbb{C}^*\times
\mathbb{C}^*$- equivariant sheaf $Tr(\beta)$ on the Hilbert scheme
$Hilb_n(\mathbb{C}^2)$, thus proving a version of Gorsky-Negut-Rasmussen
conjecture \cite{GorskyNegutRasmussen16}. As a consequence we prove that
Khovanov-Rozansky homology of knots satisfies the $q\to t/q$ symmetry
conjectured by Dunfield-Gukov-Rasmussen \cite{DunfieldGukovRasmussen06}. We
also apply our main result to compute the Khovanov-Rozansky homology of torus
links.
