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Topology of random real hypersurfaces

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  • Additional Information
    • Contributors:
      Algèbre, géométrie, logique (AGL); Institut Camille Jordan (ICJ); École Centrale de Lyon (ECL); Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS); European Project: 258204,EC:FP7:ERC,ERC-2010-StG_20091028,REALUMAN(2010)
    • Publication Information:
      HAL CCSD
    • Publication Date:
      2015
    • Collection:
      HAL Lyon 1 (University Claude Bernard Lyon 1)
    • Abstract:
      International audience ; 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 $\Sigma$.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/1409.5679; info:eu-repo/grantAgreement/EC/FP7/258204/EU/Real uniruled manifolds/REALUMAN; cel-01061947; https://cel.hal.science/cel-01061947; https://cel.hal.science/cel-01061947/document; https://cel.hal.science/cel-01061947/file/CIMPA.pdf; ARXIV: 1409.5679
    • Accession Number:
      10.15446/recolma.v49n1.54176
    • Online Access:
      https://doi.org/10.15446/recolma.v49n1.54176
      https://cel.hal.science/cel-01061947
      https://cel.hal.science/cel-01061947/document
      https://cel.hal.science/cel-01061947/file/CIMPA.pdf
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • Accession Number:
      edsbas.C481D89B