Mapping class group actions on the homology of configuration spaces of surfaces

Let S be a compact, connected, oriented surface of genus g with one boundary curve, and for n>=0 denote by F_n(S) and C_n(S), respectively, the ordered and the unordered configuration spaces of n distinct points in S. The mapping class group Mod(S) of isotopy classes of boundary-fixing homeomorphisms of S acts naturally on the homology of F_n(S) and C_n(S) with coefficients in any ring R. I will discuss what the kernel of this action is, emphasizing how the answer depends on n in the ordered case, but (almost) does not depend on n in the unordered case. This combines joint work with Jeremy Miller and Jennifer Wilson, and join work with Andreas Stavrou.