A work on Mirzakhani's earthquakes (2020)
"In the 1980s the idea of the earthquake map was introduced by Thurston while he studied low dimension topology. Several mathematicians continued Thurston's studies. In particular, Kerckhoff, who published some of Thurston's unpublished work. But the dynamic properties of the earthquake map were not described in detail. It was until 2008 when Mirzakhani proved the conjugacy between the earthquake flow and the unipotent flow. The latter one has been better studied, in particular, thanks to Ratner's work. The conjugacy is explained in this document, and it starts for interested new readers exposing the hyperbolic plane. In the latter chapters, the document explains with more detail the natural space of hyperbolic structures on a surface, which is the Teichmüller space. Measured foliations and the dynamics of the earthquake flow are discussed at the end of this work."--Tomado del Formato de Documento de Grado