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Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry

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 difficult (non linear 4-th order PDE, while the Einstein case turned out to be a Monge-Ampere
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

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