[PHK_seminar] [Cohomology]Wednesday 29 Apr, Roee Leder]

[Petr Somberg]

 This is just the reminder of our seminar!

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     Cohomology in algebra, geometry, physics and statistics




         Wednesday, 29 April 2026 - 13:30 to 14:30

         Place: Institute of Mathematics of ASCR, Žitná 25, Praha 1,  
ZOOM meeting




         Speaker: Roee Leder, Hebrew University of Jerusalem

         Title: Cohomology for linearized Ricci curvature



         Abstract


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.
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We shall open  ZOOM meeting at 13.15 for  virtual coffee and close ZOOM at
15.30


Join Zoom Meeting


https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09


Meeting ID:99598413922
Passcode:Galois
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On Wednesday  May 6,  Svatopluk Kryls shall  give  a lecture   Cohomology
of symplectic spinor twisted de Rham sequence and its subcomplexes










          For more information see the seminar web page at

          https://www.math.cas.cz/index.php/events/seminar/16




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