朱锦天，北京大学北京国际数学研究中心

In this talk, I'll make a discussion on recent progress in the research of scalar curvature. I'll review the backgrounds from Gauss-Bonnet formula to the aspherical conjecture, and then focus on the following Gauss-Bonnet inequality: if the universal covering of a closed manifold with nonnegative scalar curvature has “homological dimension two”, then either it is flat or its Gauss-Bonnet quantity is no greater than $8\pi$.