Abstract: 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.
Joint work in progress with Jon Chaika and Alex Eskin, based on a far-reaching extension of a celebrated result of Eskin and Mirzakhani. All relevant notions will be explained in the lecture and no prior familiarity with dynamics on spaces of one forms will be assumed.
Join Zoom Meeting
Meeting ID: 876 6172 9208
Tue, 19/01/2021 - 14:00 to 15:00