Speaker: 李琼玲研究员，南开大学陈省身数学研究所

Title: The Non-Abelian Hodge Correspondence and Higher Teichmüller Theory

Language: Chinese

Time & Venue: 2026.10.14 15:30-17:00 南楼N204 Zoom Meeting ID：828 3060 3762 密码：123456

Abstract: Classical Teichmüller space connects the geometry of hyperbolic surfaces with discrete and faithful representations of surface groups into PSL(2,R). Higher Teichmüller theory extends this viewpoint to higher-rank Lie groups. The non-abelian Hodge correspondence provides a complex-geometric description of surface group representations in terms of Higgs bundles, with harmonic maps forming a bridge between the two sides. In this talk, I will introduce the main ideas of the correspondence and explain its role in higher Teichmüller theory, using Hitchin components as a guiding example. I will then discuss a natural but subtle question: how can we tell from a Higgs bundle whether the corresponding representation is discrete and faithful? This will illustrate both what the correspondence reveals and what remains difficult to see on the Higgs bundle side.