BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Roee Leder (Hebrew University of Jerusalem) DTSTART:20260429T113000Z DTEND:20260429T123000Z DTSTAMP:20260502T072815Z UID:PHK-cohomology-seminar/157 DESCRIPTION:Title: Cohomology for linearized Ricci curvature\nby Roee Le der (Hebrew University of Jerusalem) as part of Prague-Hradec Kralove semi nar Cohomology in algebra\, geometry\, physics and statistics\n\nLecture h eld in ZOOM talk.\n\nAbstract\nI will present full solvability and uniquen ess conditions for the linearized Ricci curvature equations on compact Rie mannian manifolds with boundary. These equations have long resisted analys is without restrictive curvature assumptions\; the results I shall present are the first obtained without such restrictions in the interior. The app roach relies on a generalized Hodge theory\, based on microlocal methods\, to reduce the problem to the study of two newly identified cohomologies. By means of Bochner technique\, I also prove vanishing theorems for these cohomologies: notably\, by incorporating connections on Riemannian metrics \, the first cohomology vanishes if the boundary is convex\, and the secon d cohomology vanishes if adapted to traceless-transverse (TT) tensors\, an d the boundary is round. I shall also discuss how this cohomological formu lation captures the natural gauge group of geometric inverse problems and relates to the injectivity of the Lichnerowicz Laplacians on TT tensors.\n LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/157/ END:VEVENT END:VCALENDAR