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H 1 $L^2$-cohomology and the theory of weights

Auteurs : Saper, Leslie (Auteur de la Conférence)
CIRM (Editeur )

Résumé : The intersection cohomology of a complex projective variety $X$ agrees with the usual cohomology if $X$ is smooth and satisfies Poincare duality even if $X$ is singular. It has been proven in various contexts (and conjectured in more) that the intersection cohomology may be represented by the $L^2$- cohomology of a Kähler metric defined on the smooth locus of $X$. The various proofs, though different, often depend on a notion of weight which manifests itself either through representation theory, Hodge theory, or metrical decay. In this talk we discuss the relations between these notions of weight and report on new work in this direction.

Codes MSC :
14F43 - Other algebro-geometric (co)homologies
55N33 - Intersection homology and cohomology

 Informations sur la Vidéo Langue : Anglais Date de publication : 01/07/16 Date de captation : 14/06/16 Collection : Research talks ; Algebraic and Complex Geometry ; Topology Format : MP4 Durée : 00:59:04 Domaine : Topology ; Algebraic & Complex Geometry Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2016-06-14_Saper.mp4 Informations sur la rencontre Nom de la rencontre : Analysis, geometry and topology of stratified spaces / Analyse, géométrie et topologie des espaces stratifiésOrganisateurs de la rencontre : Mazzeo, Rafe ; Leichtnam, Eric ; Piazza, PaoloDates : 13/06/16 - 17/06/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1422.htmlCitation Data DOI : 10.24350/CIRM.V.19000903 Cite this video as: Saper, Leslie (2016). $L^2$-cohomology and the theory of weights. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19000903 URI : http://dx.doi.org/10.24350/CIRM.V.19000903

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