李彦霖:Differential geometry of singular submanifolds from singularity theory viewpoint

2019-06-20 来源:数学科学研究中心

活动地点:CMS 201

活动类型:学术报告

主讲人:李彦霖

活动时间:2019-06-20 14:00:00--2019-06-20 16:30:00

活动内容:


报告题目:Differential geometry of singular submanifolds from singularity theory viewpoint

报告人:李彦霖

时间:2019年6月20日(周四) 下午2:00

地点:数学中心201教室

摘要:Singular submanifold is a widespread research object, and is the breakthrough point of exploring new problems. Because of singularity, it’s difficult to study the properties of singular submanifolds. Singularity theory is one of the important mathematical tools to study singular submanifolds. In this presentation, I will talk about the differential geometry of singular submanifolds from singularity theory viewpoint. In the first part of the talk, I will introduce how to construct the moving frames of singular curves and singular surfaces by dimension promotion and study their singularity properties using singularity theory. Then, I will show how to combine singularity theory with clifford algebra to investigate singularity properties of dual spherical curves of ruled surfaces by the method of dimension reduction. At the same time, some singular submanifolds can be considered as envelopes of family of curves and surfaces, which makes it possible to study the singularity properties of singular submanifolds under the angle of envelope. Therefore, the envelope theory related with singular submanifolds will be discussed from Lagrangian and Legendrian singularity theory viewpoint.