Rigidity of the spectral gap for non-negatively curved RCD spaces
First I will review results about the connection between spectral estimates and Ricci curvature for Riemannian manifolds and metric measure spaces. In particular for non-negatively curved spaces the spectral gap is $(\pi/diam)^2$. Moreover, an RCD(0,N) space has first Laplace eigenvalue equal to $(\pi/diam)^2$ if and only if it is a circle or an interval. This is joint work with Yu Kitabeppu and Sajjad Lakzian.