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Transformation theorems for almost splitting maps and some applications
日期: 2024-01-08      信息来源:      点击数:

走向现代数学学术报告 - 黄显涛副教授(No. 683)

题目:Transformation theorems for almost splitting maps and some applications

报告人:黄显涛 副教授(中山大学)

时间:2024年1月12日 10:00

地点:东海岸校区-D324

摘要:The almost splitting map is a powerful tool in studying manifolds with Ricci curvature uniformly bounded from below and their Gromov-Hausdorff limits. In this talk, we will introduce a transformation theorem for almost splitting maps, generalizing the one obtained by Cheeger, Jiang and Naber, to possibly collapsed manifolds. We will also introduce some applications of this transformation theorem, one of which is a new smooth fibration theorem. More precisely, we introduce a notion, called the generalized Reifenberg condition, under which we prove a smooth fibration theorem for collapsed manifolds with Ricci curvature lower bound. This gives a unified proof of smooth fibration theorems in many previous works, including the classical ones by Fukaya and Yamaguchi respectively. Some other applications of the transformation theorem will be introduced in this talk. This talk is based on my joint work with Hongzhi Huang.

报告人简介:黄显涛,中山大学数学科学学院副教授。2014年博士于中山大学,博士毕业后在清华大学丘成桐数学中心做博士后,2016年8月迄今在中山大学工作。目前主要研究几 何分析中的几何流、正迷向曲率流形、具有Ricci曲率下界的度量测度空间等前沿课题。研究成果主要发表在《Crells Journal》、《Math. Ann.》等国际一流期刊。目前主持国家 自然科学基金面上项目。

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