On the Gauss-Bonnet-Chern formula on Poicare-Einstein manifolds

发布者:曹思圆发布时间:2025-05-15浏览次数:10

报告时间:5月16日周五下午14:30-15:30

报告地点:数学楼401报告厅

报告人: 袁伟

主持人:张德凯


报告人简介:袁伟,中山大学教授,2015年获得加州大学圣克鲁斯分校博士学位,主要研究方向为几何分析和广义相对论。曾赴法国巴黎第六大学/庞加莱研究所(IHP)、奥地利维也纳大学/薛定谔研究所(ESI)、韩国高等研究院(KIAS)等多地进行学术访问。相关研究成果发表Math Ann., Adv. Math., Trans. Amer. Math. Soc., Int. Math. Res. Not., Anal. PDE等期刊上。


报告摘要:Gauss-Bonnet-Chern formula is a remarkably fundamental result which builds a connection between differential geometry and topology. It has been successfully generated on Poicare-Einstein manifolds through renormalized curvature integral by Albin. With the aid of ambient space construction, we give a general formulism for renormalized curvature integral. In particular, we give a reformulation of Guass-Bonnet-Chern formula on Poicare-Einstein manifolds, which provides some interesting applications. This work is a joint work with Jeffrey S. Case, Ayush Khaitan, Yueh-Ju Lin and Aaron J. Tyrrell.