摘要：The famous Yau-Tian-Donaldson's conjecture asserts that the existence K/"ahler-Einstein metrics on Fano manifolds is equivalent to the K-stability. However, the K-stability is an infinite dimensional condition, which is related to study infinitely possible degenerations of the manifold. A natural question is how to verify the K-stability in finite steps. In this talk, we hope to give a picture for this question through a class of examples, such as toric Fano manifolds, $G$-manifolds in various views from differential geometry, algebraic geometry, and differential equation. Also I will give a general picture through Tian's CM-stability.

简介：朱小华，北京大学数学科学学院教授。2001年获得香港求是基金杰出青年奖。2004年获得国家杰出青年自然科学基金。2014年获得国家自然科学二等奖。2017年荣获第十六届陈省身数学奖。他的主要研究方向是微分几何，几何分析。已发表SCI数学论文40余篇。多篇发表在国际一流的数学杂志，如Acta Math., JAMS,  Duke J. Math, Amer. J. Math., Comm.Math. Helv., Advances in Math.，GAFA, Crelle, Tran. AMS 等。

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