RUC几何分析研讨班第1期

报告题目：Non-Abelian Hodge correspondence

报告人：张希 教授（中国科学技术大学）

报告时间：2020年9月10日  周四 14:00-15:00

报告地点：（腾讯会议ID：475 3073 5615）

摘要：The non-abelian Hodge correspondence was established by Corlette-Donaldson-Hitchin-Simpson, it states that, on a compact K\"ahler manifold $(X, \omega )$, there is a one-to-one correspondence between the moduli space of semisimple flat complex vector bundles and the moduli space of poly-stable Higgs bundles with vanishing Chern numbers. In this talk, we extend this correspondence to the projectively flat bundles case and some non-K\"ahler case. The key to obtain the extended non-abelian Hodge correspondence lies in our recent works on semi-stable Higgs bundle and the existence of harmonic metric on semisimple projectively flat bundle. These works are joint with Jiayu Li, Yanci Nie, Changpeng Pan and Chuanjing Zhang.