报告题目：关于六维球面上复结构的存在性的最新进展

主 讲 人：关 庄 丹

单 位：WilliamHill中文官方网站

时 间：3月25日16:30

地 点：英国威廉希尔公司一楼报告厅

摘 要：

This is a joint work with Professor Wang Zhonghua. There is a long standing question: Is there a complex structure on the six dimensional sphere? Someone call this problem a complex Poincare problem, while someone call it the Chern’s last Theorem. After Chern claimed a proof for the nonexistence before he passed away, Professor Etesi gave a positive proof. It was published in 2015. However, none knew his proof was correct or not. In fact, Professor Atiyah gave a negative proof in 2016, for which none knew it is correct or not. In 2020, I published a paper in Pacific Journal of Mathematics, implying that Etesi’s further claim was completely wrong. Recently, we gave a further and clearer proof that Etesi’s further claim was wrong and we found a critical gap in Etesi’s publishedproof. The gap is related to the gauge group. We further found a way to check the gap with the complex five hyperquadratic as the projective tangent bundle of the six sphere. It is still possible that we overcome the gap and found a concrete complex structure on the six sphere.

简 介：

关庄丹，美国加州大学荣退教授，现任WilliamHill中文官方网站教授。毕业于厦门大学，获中科院数学所硕士，美国加州大学Berkeley分校博士。曾任教于Princeton大学七年。曾在InventionesMathematicae，Journal ofAlgebra，TransactionsofAMS，Mathematical Research Letters等国际著名杂志发表多篇论文，包括关于紧致复四维超凯勒流形上Hodge钻石的有限分类等结果。