Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry

CIRM, Luminy, Marseille

Date(s) : 15/01/2018 - 19/01/2018   iCal
0 h 00 min


« 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.

– Hugues Auvray (Univ. Paris-Sud)
– Hongnian Huang (Univ. New Mexico)
– Julien Keller (I2M, Marseille)
– Eveline Legendre (Univ. Paul Sabatier)
– Rosa Sena Dias (IST, Portugal)

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

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Autre lien : CIRM

CIRM, Luminy


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