华罗庚青年数学论坛综合报告：Kähler-Einstein metrics and K-stability of Fano varieties

中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 庄梓铨 博士（MIT）

题  目：Kähler-Einstein metrics and K-stability of Fano varieties

时  间：2022.03.18（星期五），09:00-10:00

地  点：数学院南楼N204室  腾讯会议：670-845-532

摘  要：In this talk, I'll present some recent joint works with Hamid Abban, Yuchen Liu and Chenyang Xu on the K-stability of Fano varieties (algebraic varieties whose first Chern class is positive). I'll focus on two particular aspects: the solution ofthe Yau-Tian-Donaldson conjecture, which says that the existence of Kähler-Einstein metrics on Fano varieties is equivalent to an algebro-geometric stability condition called K-polystability, and the existence of Kähler-Einstein metrics on many explicit Fano varieties.