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<title>Cohomology in algebra, geometry, physics and statistics</title>
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Wednesday, 29 April 2026 - 13:30 to 14:30 <br />
Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1, ZOOM meeting
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Speaker: Roee Leder, Hebrew University of Jerusalem<br />
Title: Cohomology for linearized Ricci curvature
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Abstract <br />
<p>I will present full solvability and uniqueness conditions for the linearized Ricci curvature equations on compact Riemannian manifolds with boundary. These equations have long resisted analysis without restrictive curvature assumptions; the results I shall present are the first obtained without such restrictions in the interior. The approach 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 second cohomology vanishes if adapted to traceless-transverse (TT) tensors, and the boundary is round. I shall also discuss how this cohomological formulation captures the natural gauge group of geometric inverse problems and relates to the injectivity of the Lichnerowicz Laplacians on TT tensors.</p><p class="ql-align-justify">------------------------------------------------------------------------------------------------------------------------------------</p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">We shall open ZOOM meeting at 13.15 for virtual coffee and close ZOOM at 15.30</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Join Zoom Meeting</span></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><a href="https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(17, 85, 204);">https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09</a></p><p class="ql-align-justify"><br></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Meeting ID:99598413922</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">Passcode:Galois</span></p><p class="ql-align-justify"><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">-------------------------------------------------------------------------------------------------------------------</span></p><p><span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);">On Wednesday May 6, </span>Svatopluk Kryls shall give a lecture <span style="background-color: rgb(255, 255, 255); color: rgb(34, 34, 34);"> </span><a href="https://www.math.cas.cz/index.php/events/event/4134" rel="noopener noreferrer" target="_blank" style="background-color: rgb(255, 255, 255); color: rgb(0, 0, 0);"><strong>Cohomology of symplectic spinor twisted de Rham sequence and its subcomplexes</strong></a></p><p class="ql-align-justify"><br></p><p><br></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/16
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Cohomology in algebra, geometry, physics and statistics mailing list <br />
phk_seminar@math.cas.cz <br />
https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
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