Spaces with Ricci Curvature Lower Bounds

Explore recent advancements in the geometry and topology of spaces with nonnegative Ricci curvature in this 36-minute lecture by Guofang Wei from UC Santa Barbara. Delve into joint work with J. Pan, focusing on the construction of Ricci limit spaces where the Hausdorff dimension of the singular set exceeds that of the regular set, addressing a question posed by Cheeger-Colding in 2000. Discover two surprising types of fractal-like Weyl's laws for compact Ricci limit spaces, developed in collaboration with X. Dai, S. Honda, and J. Pan. Examine examples of manifolds with nonnegative Ricci curvature but nonproper Busemann function, resolving an open problem from the 1970s. Gain insights into these dramatic new features of Ricci curvature lower bounds and their implications for mathematical research.