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H 1 The essential skeletons of pairs and the geometric P=W conjecture

Auteurs : Mauri, Mirko (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The geometric P=W conjecture is a conjectural description of the asymptotic behavior of a celebrated correspondence in non-abelian Hodge theory. In particular, it is expected that the dual boundary complex of the compactification of character varieties is a sphere. In a joint work with Enrica Mazzon and Matthew Stevenson, we manage to compute the first non-trivial examples of dual complexes in the compact case. This requires to develop a new theory of essential skeletons over a trivially-valued field. As a byproduct, inspired by these constructions, we show that certain character varieties appear in degenerations of compact hyper-Kähler manifolds. In this talk we will explain how these new non-archimedean techniques can shed new light into classical algebraic geometry problems.

    Keywords : Kontsevich-Soibelman skeleton, skeleton of pairs, geometric P=W conjecture, Berkovich geometry

    Codes MSC :
    14G22 - Rigid analytic geometry

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 17/12/2019
      Date de captation : 25/11/2019
      Collection : Research talks
      Format : MP4
      Durée : 00:55:12
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-11-25_Mauri.mp4

    Informations sur la rencontre

    Nom de la rencontre : Algebraic Geometry and Complex Geometry / Géométrie algébrique et géométrie complexe
    Organisateurs de la rencontre : Benoist, Olivier ; Floris, Enrica
    Dates : 25/11/2019 - 29/11/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2074.html

    Citation Data

    DOI : 10.24350/CIRM.V.19581303
    Cite this video as: Mauri, Mirko (2019). The essential skeletons of pairs and the geometric P=W conjecture. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19581303
    URI : http://dx.doi.org/10.24350/CIRM.V.19581303


    Voir aussi

    Bibliographie

    1. MAURI, Mirko, MAZZON, Enrica, et STEVENSON, Matthew. Essential skeletons of pairs and the geometric P= W conjecture. arXiv preprint arXiv:1810.11837, 2018. - https://arxiv.org/abs/1810.11837

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