报告时间：11月24日下午3：00-4：30

报告形式：腾讯会议 902661589

Abstract: Spin structure and its higher analogies play important roles in index theory and mathematical physics. In particular, Witten genera for String manifolds have nice geometric implications. As a generalization of the work of Chen-Han-Zhang (2011), we introduce the general Stringc structures based on the algebraic topology of Spinc groups. It turns out that there are infinitely many distinct universal Stringc structures indexed by the infinite cyclic group. We then construct a family of the so-called generalized Witten genera for Spinc manifolds, the geometric implications of which can be exploited in the presence of Stringc structures. As in the un-twisted case studied by Witten, Liu, etc, in our context there are also integrality, modularity, and vanishing theorems for effective non-abelian group actions. We will give some applications of our vanishing theorem. This is a joint work with Haibao Duan and Fei Han.

个人简介：黄瑞芝于2017在新加坡国立大学获博士学位，2018-2020在中科院数学所做博士后，之后留所任助理研究员至今。其主要研究代数拓扑及其在流形拓扑、指标定理与数学物理中的应用。在拓扑领域，与合作者证明了同伦论的若干基本定理：如无穷Hopf空间的唯一分解定理、Moore空间的挠部分同伦群按指数增长等。在拓扑与几何的交叉领域，与合作者建立了复弦流形的代数拓扑、构造了广义Witten亏格并证明相应的消灭定理；证明了一组Witten-Freed-Hopkins关于三次型的奇异消解公式等。