中国科学院数学与系统科学研究院

数学研究所

数学科学全国重点实验室

学术报告

拓扑讨论班

Speaker: 李一寒（南开大学）

Inviter:  王晋民

Language: Chinese

Title：Spectral Flow, Eta Invariant and Llarull's Rigidity Theorem in Odd Dimensions

Time&Venue：2025年11月13日（星期四）10:30 - 11:30 & 晨兴楼410

Abstract：In this talk, I will present the application eta invariant and spectral flow on the proof of the odd-dimensional part of Llarull’s Theorem and two of its extensions. Generally speaking, Atiyah-Singer index theory is one of the major tools in the study of Riemannian metrics of positive scalar curvature. In odd dimensions, the spectral flow of a family of twisted Dirac operators on a compact spin manifold can be used to provide a direct proof of Llarull’s rigidity theorem and the so called “spin-area convex extremality theorem”. Furthermore, combining with the deformed Dirac operator introduced by Bismut and Cheeger, this method can be used to prove noncompact extension of Llarull’s theorem, which provides a final answer to a question by Gromov. This talk is based on joint works with Guangxiang Su, Xiangsheng Wang and Weiping Zhang.