On the probabilistic proof of the Atiyah-Singer index theorem of Dirac operator
Prof. Xiangdong Li
2023-10-24 15:30-17:00
MCM110&Online
Speaker: Prof. Xiangdong Li (AMSS, CAS)Time: 15:30-17:00 October 24, 2023 (Tuesday)
Place: MCM110 & Zoom (Zoom ID: 3329836068 Password: mcm1234)
Title: On the probabilistic proof of the Atiyah-Singer index theorem of Dirac operator
Abstract: In this talk, inspired by the works of M. Atiyah, J.-M. Bismut et al, I will first give a probabilistic representation formula of the index of the Dirac operator，then I will present a probabilistic proof of the Atiyah-Singer index formula for the Dirac operator on a spin manifold. Finally, I will discuss the construction of the Dirac operator on the loop space over a Riemannian manifold, a long standing open problem in the constructive quantum field theory, as pointed out by E. Witten.
