On the recent progress of the existence problem of a complex structure on the six sphere

：关庄丹
：2021-07-24 10:30
：海韵园实验楼106报告厅（线下）；腾讯会议APP ID:901 2531 9369（Pwd：202107）（线上）

报告人：关庄丹（河南大学）

时  间：7月24日上午10:30

地  点：海韵园实验楼106报告厅（线下）；腾讯会议APP ID:901 2531 9369（Pwd：202107）（线上）

内容摘要:

This is a join 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 published proof. 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. We then overcome the gap. So the question still remains.

个人简介：

关庄丹是美国加州大学荣退教授。 现任河南大学教授。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Inventiones Mathematicae, Journal of Algebra, Transactions of AMS, 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。

 

联系人：钟春平