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Abstract: I will present formulas for the Euler characteristics of tautological bundles over punctual Quot schemes that parameterize zero-dimensional quotients of a vector bundle E over C (based on joint work with Prof. Dragos Oprea). The formulas suggest analogies between the Quot schemes of curves and the Hilbert scheme of points of surfaces. Our proofs rely on Atiyah-Bott localization, universality results (of Ellingsrud, Göttsche, and Lehn), and the combinatorics of Schur functions. For higher rank quotients, I will report a few formulas and vanishing results when the genus is zero.
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