Speaker: Barak Weiss
(Tel-Aviv University):
Title:
Rel leaves of the Arnoux-Yoccoz surfaces

Abstract:
In a joint work with Hooper, we solved a geometrical problem regarding the existence of a dense leaf in a foliation of the moduli space of holomorphic one-forms called the "rel foliation". One of the inputs to the proof is an algebraic result of Bary-Soroker, Shusterman and Zannier about a certain sequence of number fields. The reduction to the algebraic question relies on the breakthroughs of Eskin and Mirzakhani, for which Mirzakhani was awarded a Fields medal in 2014.

I will give a quick introduction to the geometry and sketch some of the ideas of the proof, including a (not completely formal) statement of the Eskin-Mirzakhani theorem and related results of Mirzakhani and Wright.

The talk is intended for a wide audience.