Abstract:In this talk I describe recent joint work with Kiem, Kirwan and Woolf in which we describe intersection pairings on the cohomology of the moduli space M(n,d) of holomorphic bundles of rank n and degree d when n and d are not coprime, so the space M(n,d) is in general singular. We treat the intersection cohomology of M(n,d) and the ordinary cohomology of a partial resolution of singularities {\widetilde M}(n,d). We pay particular attention to the case M(2,0). We remark that although intersection cohomology does not in general have a ring structure, it is equipped with a pairing between classes of complementary dimensions.