学术报告

Singular Hermitian-Yang-Mills connections and reflexive sheaves

报告题目: Singular Hermitian-Yang-Mills connections and reflexive sheaves

报告人:孙崧 副教授(加州大学伯克利分校)

报告时间:2020年7月26号(周日)上午10:30-12:00

线上报告:Zoom,会议 ID:960 5745 2191

摘要: The Donaldson-Uhlenbeck-Yau theorem relates the existence of Hermitian-Yang-Mills connections over a compact Kahler manifold with algebraic stability of a holomorphic vector bundle. This has been extended by Bando-Siu in 1994 to a class of singular Hermitian-Yang-Mills connections on reflexive sheaves. We study tangent cones of these singular connections in the geometric analytic sense, and show that they can be characterized in terms of certain algebro-geometric invariants of reflexive sheaves. In a sense, this can be viewed as a “local” version of the Donaldson-Uhlenbeck-Yau correspondence. Based on joint work with Xuemiao Chen (University of Maryland).

报告人简介: 孙崧,加州大学伯克利分校副教授。2010年获威斯康星大学麦迪逊分校博士学位。2018年起在加州大学伯克利分校任教。主要研究方向:凯勒几何。2018年国际数学家45分钟报告人,Veblen几何奖获得者。已在JAMS、Annals、Acta等国际数学顶级期刊发表多篇论文。