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.
朱小华，北京大学数学科学学院教授。2004年获得国家杰出青年自然科学基金。2005年获得 ICTP 意大利青年科学奖。2009年当选教育部长江学者特聘教授。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。