Date(s) - 15/01/2018 - 19/01/2018
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“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
Autre lien : CIRM