Classification of Teichmüller curves

teichmller曲线是曲线模空间中的代数曲线，这些曲线对于teichmller度量来说是完全测地的。对这些曲线的兴趣源于寻找具有最优动力学行为的台球桌。近年来，利用数论和等分布技术的输入，对teichmller曲线的有限性结果取得了很大进展。该项目的目标是将这些方法结合起来，并努力实现对teichm<e:1>曲线的完整分类。

Teichmüller curves are algebraic curves in the moduli space of curves that are totally geodesic for the Teichmüller metric. Interest in these curves stems from the search for billiard tables with optimal dynamical behavior. Recently, a lot of progress has been made towards finiteness results for Teichmüller curves, both using input from number theory and from equidistribution techniques. The goal of this project is to combine these approaches and to work towards a full classification of Teichmüller curves.