Classification of Teichmüller curves

Teichmüller 曲线的分类

• 批准号: 362419372
• 负责人: Professor Dr. Martin Möller
• 金额: --
• 依托单位: Schwerpunkt Algebra und Geometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/362419372?language=en
• 关键词: Classification; Teichm; ller; curves

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.

Teichmüller曲线是模空间中的代数曲线，这些曲线对于Teichmüller度量是全测地线的。对这些曲线的兴趣源于对具有最佳动力学行为的台球桌的搜索。最近，在利用数论和等分布技术的基础上，对Teichmüller曲线的有限性结果取得了很大的进展。该项目的目标是将这些方法联合收割机并致力于Teichmüller曲线的完整分类。