Complex Geometry Seminar

时间: 周四15:20-16:55,2019-3-11 ~ 6-20



Speaker: Satoshi Nakamura (Fukuoka University)

Title: Deformation for coupled K\”ahler Einstein metrics

Abstract: The notion of coupled K\"ahler-Einstein metrics was introduced recently by Hultgren-Nystr\"om. In this talk we discuss the deformation of coupled K\"ahler-Einstein metrics on Fano manifolds. In particular we obtain a necessary and sufficient condition for a coupled K\"ahler-Einstein metric to be deformed to a coupled K\"ahler-Einstein metric for another close decomposition for Fano manifolds admitting non-trivial holomorphic vector fields. This generalizes Hultgren-Nystr\”om's result.



Speaker: Laurent La Fuente-Gravy (University of Liege, Belgium)

Title: Deformation quantization of Kähler manifolds

Abstract: I will start by a brief introduction to deformation quantization. Then, following the work of Karabegov, I will show how star products with the separation of variable property on Kähler manifolds are parametrized by formal deformations of the Kähler form. After that, I will describe one (or two) geometric ways to obtain star products with the separation of variable property on Kähler manifolds. If time permits, I will explain the role of the scalar curvature of the Kähler manifold in the notion of trace for star products.

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