报告题目： Some progress in the loop group method
时 间：2023年11月27日（星期一）下午14：00—16：00
地 点：腾讯会议：574747015，密码：1127
主 办：数学与统计学院、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）、 福建师范大学数学研究中心
参加对象：相关专业师生
报告摘要：Abstract: When differential geometric objects (mostly under certain curvature conditions) come in families, their moving frames naturally sit in loop groups. The loop group method for integrable systems has succeeded in generalizing two most classic results in differential geometry: Backlund-Darboux transformations and Weierstrass representation. This talk will report some progress in them:
1. All rational dressings (including nilpotent ones) are generated by Terng-Uhlenbeck's generalized Backlund transformations via simple rational projective elements. This is a counter-intuitive theorem in all related areas. (Joint work with my PhD student Gang Wang in CAS-WIPM before and Oliver Goertsches, published in J. Inst. Math. Jussieu 21 (2022) 459-485.)
2. An elementary eigenvector method has been found to compute loop group decompostions for the celebrating DPW representation (Dorfmeister-Pedit-Wu's generalization of Weierstrass representation) in equivariant case, generalizing Burstall-Kilian's work. (Joint work with Josef Dorfmeister and Gang Wang, preprint.)
Both works had been motivated by studying affine spheres. In the end, some links to tiling problems (the speaker's another field of interest in recent years) and discretisations will be discussed.
报告人简介： 王二小（WANG Erxiao），浙江师范大学双龙特聘教授；本科毕业于南开大学数学试点班，博士毕业于美国东北大学；曾任MSRI 博士后，UT Austin 讲师，新加坡国立大学访问助理教授，中科院海外归国杰出青年、科研组长，德国慕尼黑工大访问教授，香港科技大学访问学者。长期探索微分几何和可积系统的交叉领域，在贝克隆-达布变换方向合作做出反常识突破，并拓展魏尔斯特拉斯表示的构造性算法。近几年合作建立一套理论方法解决球面密铺里的百年难题，在国际公认的数学顶尖期刊Adv. Math.上同时发表三篇长文系列研究这一问题。