BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ilaria Mondello (Paris-Est Créteil) DTSTART:20210330T124500Z DTEND:20210330T134500Z DTSTAMP:20260423T005716Z UID:BOWL/20 DESCRIPTION:Title: Li mits of manifolds with a Kato bound on the Ricci curvature\nby Ilaria Mondello (Paris-Est Créteil) as part of B.O.W.L Geometry Seminar\n\n\nAbs tract\nStarting from Gromov pre-compactness theorem\, a vast theory about the structure of limits of manifolds with a lower bound on the Ricci curva ture has been developed thanks to the work of J. Cheeger\, T.H. Colding\, M. Anderson\, G. Tian\, A. Naber\, W. Jiang. Nevertheless\, in some situat ions\, for instance in the study of geometric flows\, there is no lower bo und on the Ricci curvature. It is then important to understand what happen s when having a weaker condition. \n\nIn this talk\, we present new result s about limits of manifolds with a Kato bound on the negative part of the Ricci tensor. Such bound is weaker than the previous $L^p$ bounds consider ed in the literature (P. Petesern\, G. Wei\, G. Tian\, Z. Zhang\, C. Rose\ , L. Chen\, C. Ketterer…). In the non-collapsing case\, we recover part of the regularity theory that was known in the setting of Ricci lower boun ds: in particular\, we obtain that all tangent cones are metric cones\, a stratification result and volume convergence to the Hausdorff measure. Aft er presenting the setting and main theorem\, we will focus on proving that tangent cones are metric cones\, and in particular on the study of the ap propriate monotone quantities that leads to this result.\n LOCATION:https://researchseminars.org/talk/BOWL/20/ END:VEVENT END:VCALENDAR