学术报告

题      目： Isoparametric theoryand complex structures

报  告  人：彦文娇   教授  (邀请人：叶颀 )

                                    北京师范大学

时      间：4月27日  15：00-16：00

腾 讯 会 议 号：669-2471-6718

报告人简介:

       北京师范大学教授，博士生导师，主要研究方向为微分几何，特别是等参理论及其应用，至今已在《J.Diff.Geom.》，《Adv.Math.》等国际著名数学期刊上接受发表了多篇论文。代表性成果有完全解决了等参情形的丘成桐第一特征值猜想、给出陈省身猜想在任意维数的进展、给出IMJames 两个基本问题的进展等。2017年获得国家自然科学优秀青年基金。

摘      要：

      It is a longstanding problem that whether there exists a complex structureon the 6-dimensional sphere? Many famous mathematicians have made effortson this problem, such as Hopf, Wen-tsun Wu, Borel, Serre, Shiing-shen Chern,Atiyah, etc. Taking advantage of isoparametric theory, we construct almostcomplex and complex structures on certain isoparametric hypersurfaces inthe unit sphere. As a consequence, a complex structure on the product of6-dimensional sphere and a closed 8-dimensional manifold is constructedalthough we don't know the existence of any complex structure on the 6-di-mensional sphere. Besides, a complex structure on the product of l-dimen-sional， 2-dimensional ，and 3-dimensional spheres with vanishing firstChern class are also built. This talk is based on joint work with ProfessorZizhou Tang.