We set our sights to knot homology for (m,n)-torus knots. It was conjectured to be a certain sum over Dyck paths by Oblomkov-Rasmussen-Shende, and proved by Mellit via a geometric "sweeping" process of toric braids. In this talk we will discuss toric braids, the sweeping process, and the recursion by which one arrives at Dyck paths. Speaker(s): Nir Gadish (UM)