Time: 15:10-16:10, Thursday, July 10 2025
Venue: E10-212, Yungu Campus
Speaker: Prof. Xianzhe Dai, University of California, Santa Barbara
Title: Singular metrics of nonnegative scalar curvature and RCD
Abstract: The positive mass theorem of Schoen-Yau and Witten is one of the landmark results and it is closely related to the existence of positive scalar curvature metrics. Various motivations lead to consideration of singular metrics. I will first review these and recall some earlier work on on positive mass theorem and Geroch type theorem for singular metrics, including our work with Yukai Sun and Changliang Wang for isolated conical singularity. Then I will discuss our very recent work on singular metrics with nonnegative scalar curvature with small singularity, in particular confirming Schoen's conjecture for isolated singularity on spaces which are connected sums with the torus. Crucial to our approach is the novel connection with RCD spaces, singular spaces having some weak Ricci curvature bound. This part of the work is joint with Changliang Wang, Lihe Wang, and Guofang Wei.
