Abstract: Any complex algebraic plane curve singularity defines a link up to isotopy, via its intersection with a surrounding 3-sphere. The Oblomkov–Rasmussen–Shende conjecture describes the a, q, t-graded Khovanov–Rozansky homology of the link in terms of the punctual Hilbert schemes of the singularity. The t = –1 limit is a theorem of Maulik. However, no prior results managed to incorporate all three gradings, except in very simple examples. Oscar Kivinen and I introduce a different kind of Quot scheme, and prove that an analogue of the ORS conjecture for these Quot schemes does hold, with all three gradings, for many singularities of the form y^n = x^d. This motivates a further conjecture about how these new Quot schemes are related to the Hilbert schemes by a motivic substitution of variables. I have proven it for singularities y^3 = x^d with d coprime to 3. This, combined with the previous result, establishes the ORS conjecture for the same class of singularities. If time permits, I will mention how ORS relates to Gromov–Witten theory.