Ergodicity of rel foliations on the space of holomorphic one forms

The rel foliation is a foliation of the moduli space of abelian differentials obtained by “moving the zeroes of the one form while keeping all absolute periods fixed”. It has been studied in complex analysis and dynamics under different names (isoperiodic foliation, Schiffer variation, kernel foliation). Until recent years the question of its ergodicity was wide open. Recently partial results were obtained by Calsamiglia-Deroin-Francaviglia and by Hamenstadt. In our work we completely resolve the ergodicity question.