Stratification of punctual Hilbert schemes on curves x^u y^v=0 via weak diagonal partitions yields explicit Poincaré polynomials for u=1,2 and v-2,v-1,v, plus a proof of the colored ORS conjecture for Hopf links at u=1.
Torus link homology
2 Pith papers cite this work. Polarity classification is still indexing.
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Defines HOMFLY polynomial of forest quivers recursively, equates it to plabic link HOMFLY, and gives closed form via independent sets.
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Hilbert scheme of points on non-reduced nodal curves
Stratification of punctual Hilbert schemes on curves x^u y^v=0 via weak diagonal partitions yields explicit Poincaré polynomials for u=1,2 and v-2,v-1,v, plus a proof of the colored ORS conjecture for Hopf links at u=1.
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The HOMFLY Polynomial of a Forest Quiver
Defines HOMFLY polynomial of forest quivers recursively, equates it to plabic link HOMFLY, and gives closed form via independent sets.