Stably complex homogeneous spaces

报告题目：Stably complex homogeneous spaces

报告时间：12月13日周五下午2: 30-3：30

报告地点：数学楼126

报告人：Andrei Moroianu（法国国家科学研究中心、巴黎-萨克雷大学）主任研究员/正教授

主持人：刘博

 报告人简介： Andrei Moroianu graduated at the Ecole Normale Supérieure in Paris in 1995 and got his PhD from the Ecole Polytechnique in 1996. He works for the CNRS since 1997, and his research topic is differential geometry. Since 2017 he is based at the Paris-Saclay University. He was awarded the Peccot Lecture at the Collège de France in 1998 and he held lectures at the Ecole Polytechnique from 2004 to 2016.

报告摘要： A real vector bundle over a smooth manifold is called complex if it is isomorphic to the underlying real bundle of a complex vector bundle (after "forgetting" the complex structure) and stably complex if it becomes complex after taking the direct sum with a trivial vector bundle. A smooth manifold M is called almost complex if its tangent bundle TM is complex, and stably complex if TM is stably complex. In this talk I will describe the  classification (joint with P. Gauduchon and U. Semmelmann) of stably complex compact homogeneous spaces with non-vanishing Euler characteristic. The key role in the proof is played by the Atyiah-Singer index theorem for twisted Dirac operators.