Abstract for the talk on 19.09.2023 (11:00 h)Geometry Seminar
Anthony Sanchez (University of California San Diego)
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.