The intersection theory of the moduli space of bundles via spaces of morphisms

We will sketch a new approach to the problem of computing the intersection theory of the moduli space M of stable bundles on a Riemann surface. This proceeds by realizing intersections of natural classes on M as intersections on a different space, a Grothendieck Quot scheme compactifying holomorphic maps from the Riemann surface to a Grassmannian. This Quot scheme is endowed with a natural group action and a virtual fundamental class compatible with the action. Thus one can compute intersection numbers on it using the virtual localization formula of Graber and Pandharipande.