Complex Geometry Seminar

时间: 周三15:20-16:55, 2019-9-11 ~ 12-4



Speaker: Yan Li (Peking University)

Title: Tian's $\alpha_{m,k}^{\hat K}$-invariants on group compactifications

Abstract: In this talk, we will first review Tian's $\alpha_{m,k}^{\hat K}$-invariant on a polarized manifold and a related conjecture. Then we give computation of $\alpha_{m,k}^{K\times K}$-invariants on $G$-group compactification, where $K$ denotes a connected maximal compact subgroup of $G$. Finally we prove that Tian's conjecture is true for $\alpha_{m,k}^{K\times K}$-invariant on such manifolds when $k=1$, but it fails in general by showing counter-examples when $k\geq2$.



Speaker: Laurant La Fuente-Gravy (University of Luxembourg)

Title: TBA

Abstract: TBA



Speaker: Yalong Shi (Nanjing University)

Title: TBA

Abstract: TBA



Speaker: Kewei Zhang (Peking University)

Title: TBA

Abstract: TBA



Speaker: Chuyu Zhou (Peking University)

Title: TBA

Abstract: TBA




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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