The first lecture will be quick background on the constant scalar curvature Kähler (cscK) problem [1-5] and the general setup on cscK cone metrics mainly from the paper . The second lecture will lead to the existence results for the cscK cone metrics, and more general, the singular cscK metrics . After all these preparation, the third lecture will present results on geometric applications, including links to log K stabilities and properties of the cscK cone path etc .
Basic knowledge of differential and Kähler geometry including Kähler metric, scalar curvature, cone singularities,...
 E. Calabi, Extremal Kähler metrics. Seminar on Differential Geometry, pp. 259–290, Ann. of Math. Stud., 102, Princeton Univ. Press, Princeton, N.J., 1982. MR0645743.
 E. Calabi, Extremal Kähler metrics. II. Differential geometry and complex analysis, 95–114, Springer, Berlin, 1985. MR0780039.
 X. Chen and J. Cheng, On the constant scalar curvature Kähler metrics I,II, J. Amer. Math. Soc. 34 (2021), no. 4, 909-1009.
 S. K. Donaldson, Scalar curvature and projective embeddings. I. (English summary) J. Differential Geom. 59 (2001), no. 3, 479–522. MR1916953
 S. K. Donaldson, Kähler metrics with cone singularities along a divisor, Essays in mathematics and its applications, Springer, Heidelberg, 2012, pp. 49-79. MR2975584.
 K. Zheng, Geodesics in the space of Kähler cone metrics II: Uniqueness of constant scalar curvature Kähler cone metrics, Comm. Pure Appl. Math. 72 (2019), no. 12, 2621-2701. MR4020314.
 K. Zheng, Existence of constant scalar curvature Kähler cone metrics, properness and geodesic stability, arXiv:1803.09506.
 T. Aoi, Y. Hashimoto, K. Zheng, On uniform log K-stability for constant scalar curvature Kähler cone metrics, arXiv:2110.02518.
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