希格斯层上的厄米特-杨-米尔斯热流

摘要

Higgs sheaves were introduced by Hitchin at 1980's.They they have a rich structure and play a role in many different areas including gauge theory,K(a)hler and hyperk(a)hler geometry,group representations and nonabelian Hodge theory.Here the basic concept of Higgs sheaves were reviewed first,and then the classical results of the Hermitian-Yang-Mills flow were surveyed.Finally,an introduction was given to introduce our recent work on the limiting behavior of the Hermitian-Yang-Mills flow.%希格斯层最先由Hitchin于20世纪80年代引入,经过30余年的发展,取得了非常丰富的研究结果,并且与其他数学研究领域有着密切联系,如规范理论、群表示论、凯勒与超凯勒几何、非阿贝尔霍奇理论等.本文首先回顾希格斯层的相关基本概念,在此基础上介绍厄米特-杨-米尔斯热流的相关经典结果及其发展历程,然后也介绍我们最近得到的关于厄米特-杨-米尔斯热流的收敛性结果.