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Topology of random real hypersurfaces

Jean-Yves Welschinger 1 
1 AGL - Algèbre, géométrie, logique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : These are notes of the mini-course I gave during the CIMPA summer school at Villa de Leyva, Colombia, in July $2014$. The subject was my joint work with Damien Gayet on the topology of random real hypersurfaces, restricting myself to the case of projective spaces and focusing on our lower estimates. Namely, we estimate from (above and) below the mathematical expectation of all Betti numbers of degree $d$ random real projective hypersurfaces. For any closed connected hypersurface $\Sigma$ of $\R^n$, we actually estimate from below the mathematical expectation of the number of connected components of these degree $d$ random real projective hypersurfaces which are diffeomorphic to $\Sigma$.
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Submitted on : Monday, September 8, 2014 - 6:21:49 PM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM
Long-term archiving on: : Tuesday, December 9, 2014 - 12:41:34 PM



Jean-Yves Welschinger. Topology of random real hypersurfaces. Doctoral. Topology of random real hypersurfaces, Villa de Leyva, Colombia. 2014, 18 p. ⟨cel-01061947⟩



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