The twisted Hodge numbers of the Quot schemes of zero dimensional quotients over curves

We study Quot schemes of rank 0 quotients on smooth projective curves. These Quot schemes exhibit a rich and highly structured geometry, with formal analogies to the Hilbert scheme of points on surfaces. In this talk, I will explain a formula for the twisted Hodge groups of the Quot scheme with values in tautological line bundles pulled back from the symmetric product.