Title: Moduli spaces of twisted k-differentials
Abstract: We present the definition of the moduli spaces of twisted k-differentials, which are closed substacks of \bar M_g,n constructed by Farkas and Pandharipande. On the open part M_g,n they are defined by the condition that a weighted sum of the marked points agrees, as a divisor class, with the k-th power of the canonical line bundle of the curve. We give an indication how to compute the dimension of their components and a conjectural expression of their (weighted) fundamental class in terms of a tautological cycle studied by Pixton.