Effective equidistribution of large dimensional measures on the moduli  space of translation surfaces

A translation surface is a collection of polygons with edge 
identifications given by translations. In spite of the simplicity of the 
definition, the space of translation surfaces has connections to 
different areas of math such as the moduli space of Riemann surfaces and 
rational billiards in the plane.

In this talk we consider the unstable foliation, that locally is given 
by changing horizontal components of period coordinates, which plays an 
important role in study of translation surfaces, including their 
deformation theory and in the understanding of horocycle invariant 
measures. We show that measures of "large dimension" equidistribute and 
give an effective rate. An analogous result in the setting of 
homogeneous dynamics is crucially used in the recent effective 
equidistribution results of Lindenstrauss-Mohammadi and 
Lindenstrauss--Mohammadi--Wang.

No prior knowledge of the words in the title is assumed.