Ergodicity of rel foliations on the space of holomorphic one forms

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.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

Series comments: On the week of the seminar, an announcement with the Zoom link is mailed to the seminar mailing list. To receive these e-mails, please sign up by writing to Lev Buhovsky (http://www.math.tau.ac.il/~levbuh/).