Limits of manifolds: from Ricci to Kato

Thanks to the work of many mathematicians, we have now a good understanding of Gromov-Hausdorff limits of manifolds with a uniform bound on the Ricci curvature. However, this assumption may be too strong in some geometric situations. In this talk, I explain how in a joint work with G. Carron (Nantes) and D. Tewodrose (Bruxelles) we obtained regularity results for limit space with a much weaker curvature assumption.