Explore a compelling conference talk that delves into the relationship between Bakry-Émery curvature-dimension condition for weighted Riemannian manifolds and the Kato condition on Ricci curvature for Riemannian manifolds. Discover how the speaker and his collaborators, Gilles Carron and Ilaria Mondello, utilize a suitable time change to establish this connection. Learn about the improvements made to previous results on the structure of Kato limit spaces, which are Gromov-Hausdorff limits of Riemannian manifolds satisfying a uniform Kato condition on Ricci curvature. Gain insights into advanced concepts in differential geometry and geometric analysis during this 37-minute presentation, which was part of the Workshop on "Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension" held at the Erwin Schrödinger International Institute for Mathematics and Physics.