华罗庚青年数学论坛综合报告：Nonabelian Hodge Correspondence for Parahoric Higgs bundles

中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 赵鹭天 博士（University of Maryland）

题  目：Nonabelian Hodge Correspondence for Parahoric Higgs bundles

时  间：2023.05.19（星期五），09:00-10:00

地  点：Zoom会议：874 7709 4257   密码：0519

摘  要：In this talk, I will explore the nonabelian Hodge correspondence for vector bundles over noncompact curves by focusing on parahoric Higgs bundles. To establish a comprehensive correspondence between Dolbeault and de Rham spaces for a general complex reductive group $G$, we introduce torsors associated with parahoric group schemes, following the Bruhat-Tits theory. By combining these findings with existing results on the Riemann-Hilbert correspondence for logarithmic parahoric connections, we successfully construct a full nonabelian Hodge correspondence from Higgs bundles to fundamental group representations over a noncompact curve. This research extends our understanding of the nonabelian Hodge correspondence beyond the $\text{GL}_n(\mathbb{C})$ case, providing valuable insights into the intricate relationships between parahoric Higgs bundles and nonabelian Hodge theory.