The moduli space M_{0,n} parametrizes all ways of labelling n distinct points on the Riemann sphere P^1, up to change of coordinates by Mobius transformations. 'Hurwitz correspondences' are a class of multivalued maps (similar to the 'square root' map on the set of complex numbers) from M_{0,n} to itself. They arise in topology and Teichmuller theory by works of Thurston and Koch. I will introduce both M_{0,n} and Hurwitz correspondences, and talk about the latter from the point of view of complex dynamics. Speaker(s): Rohini Ramadas (University of Michigan)