Abstract: 

Higgs bundle was introduced by Hitchin, it closely related to multiple fields such as non-abelian Hodge correspondence, algebraic geometry, K\"ahler geometry and group representations. In this talk, we introduce our recent work on the existence of canonical critical Hermitian structures on Higgs bundles. As its applications, we obtain a generalized Bogomolov type inequality on Higgs bundles and a Miyaoka-Yau inequality for minimal K\"ahler models. These works are joint with Chao Li, Chuanjing Zhang and Shiyu Zhang.

报告人简介：

张希，南京理工大学数学与统计学院教授，主要从事微分几何、几何分析、复几何等方面的研究。在典则度量存在性及相关非线性偏微分方程等方面取得多项研究成果：合作解决Hermitian-Yang-Mills流中的Bando-萧荫堂猜想、给出非凯勒情形数值平坦丛的微分几何刻画、得到带锥奇点凯勒-瑞奇流的收敛性结果，相关工作发表在Adv. Math., Crelle’s Journal, CMP, J.EMS, JFA, Math. Ann., TAMS等数学杂志上。