Institut de Mathématiques de Marseille, UMR 7373




Rechercher


Accueil >

17 janvier 2018: 1 événement

Manifestation scientifique

  • Manifestations scientifiques (colloques, écoles,...)

    Du 15 au 19 janvier - COLLOQUE

    Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry

    Résumé : COLLOQUE,
    "Métriques à courbure scalaire constante en géométrie Kählérienne et Sasakienne"
    -
    The Yau-Tian-Donaldson conjecture restricted to a particular case has been proved in 2012 : the existence of Kahler-Einstein/Sasaki-Einstein metrics has been related to K-polystability after a breakthrough of X.X Chen, S.K. Donaldson and S. Sun.
    Originally the Y-T-D conjecture was sketched by the Fields medallist S-T. Yau, and refined later by G. Tian and the Fields medallist S.K. Donaldson.
    Complex geometers are turning now to the general version of the Y-T-D correspondence about existence of constant scalar curvature (csc) Kahler/Sasaki metrics (that do not belong to the anti-canonical class). This generalization is far from being a trivial question since the csc equation is much more di-fficult (non linear 4-th order PDE, while the Einstein case turned out to be a Monge-Amp-ere
    equation of 2-nd order). Many questions arise, and without being exhaustive we shall quote some of them now :
    - how to define the right notion of algebraic stability to obtain the correspondence ? how to check the stability in practice ?
    - what about the degenerations of metrics in relation with algebraic deformations ?
    - what about moduli space of metrics with special curvature properties (compactifications, topological invariants,...) ;
    - what is happening in the case of toric geometry ? Can we find explicit ansatz ?
    - study of the Calabi flow from the point of view of geometric analysis ;
    - classification in low dimension ;
    - study of the Kähler cone in the perspective of cscK metrics ;
    - relationship with mathematical physics etc.
    ​Young researchers and members of underrepresented groups will be financially helped as much as possible.
    -
    Organization :
    - Hugues Auvray (Univ. Paris-Sud)
    - Hongnian Huang (Univ. New Mexico)
    - Julien Keller (I2M, Marseille)
    - Eveline Legendre (Univ. Paul Sabatier)
    - Rosa Sena Dias (IST, Portugal)
    -
    Partenaires :
    - Agence Nationale de la Recherche (ANR)
    - Fédération CARMIN
    - Centre International de Rencontres Mathématiques (CIRM)
    - Centre National de la Recherche Scientifique (CNRS)
    - Institut de Mathématiques de Marseille (I2M)
    - Institut de Mathématiques de Toulouse (IMT)
    - LabEx Archimède
    - National Science Foundation (NSF)
    - Université Paris-Sud
    -

    Site web du colloque
    JPEG - 16.3 ko

    Autre lien : CIRM

    Lieu : CIRM - 163 avenue de Luminy
    Case 916
    13288 Marseille - Cedex 9
    France

    Exporter cet événement
    Document(s) associé(s) :

    En savoir plus : Manifestations scientifiques (colloques, écoles,...)