Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	赵鹭天博士,University of Maryland
Inviter:
Title:	Nonabelian Hodge Correspondence for Parahoric Higgs bundles
Language:	Chinese
Time & Venue:	2023.05.19 09:00-10:00 腾讯会议：101-853-738 密码：0519
Abstract:	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.