Ergodicity of rel foliations on the space of holomorphic one forms

Group Actions and Dynamics
Event time: 
Monday, March 1, 2021 - 10:15am
Barak Weiss
Speaker affiliation: 
Tel Aviv University
Event description: 
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 (with help from 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.