Topological Stability and Lower Ricci Curvature Bounds

 We investigate the topological stability of sequences of spaces with a uniform lower bound on Ricci curvature
and noncollapsed volume, converging in the Gromov-Hausdorff topology. This problem is both natural and fundamental
in many applications, particularly in light of Gromov's compactness theorem.
In this talk, we will review classical results and key examples before presenting recent progress, including novel
stability results in low dimensions, obtained in collaboration with Pigati and Semola.