Johannes Schmitt (ETH – Zürich)

Inside the moduli space of smooth genus g curves with n markings, there are the loci of curves admitting a meromorphic k-differential with prescribed zeros and poles at the marked points. We explain a compactification of these loci proposed by Farkas-Pandharipande and describe its components and their dimensions. We present a conjectural relation between a weighted fundamental class of the compactification with a tautological cycle defined by Pixton. In recent joint work with David Holmes, we explain how the weights of the weighted fundamental class arise from intersection multiplicities inside a universal Jacobian.