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
学术报告
报告人： 庄梓铨 博士（MIT）
题 目：Properness of the K-moduli space
时 间：2022.03.22（星期二），10:00-11:00
地 点：腾讯会议：146-907-827
摘 要：K-stability is an algebraic condition that characterizes the existence of Kähler-Einstein metrics on Fano varieties. Recently there has been a lot of work on the construction of the K-moduli space, i.e. a good moduli space parametrizing K-polystableFano varieties. Motivated by results in differential geometry, it is conjectured that this K-moduli space is proper and projective. In this talk, I'll discuss some recent progress in birational geometry that leads to a full solution of this conjecture. Basedon joint work with Yuchen Liu and Chenyang Xu.
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报告人： 庄梓铨 博士（MIT）
题 目：Compatible divisors and K-stability of explicit Fano varieties
时 间：2022.03.24（星期四），10:00-11:00
地 点：腾讯会议：270-272-828
摘 要：In this talk, I'll describe a birational geometric approach to proving K-stability of explicit Fano varieties. A key ingredient in this approach is the notion of compatible divisors. As applications, we will show that smooth Fano hypersurfacesof a given Fano index are K-stable (hence admit Kähler-Einstein metrics) as long as the dimensions become sufficiently big. Based on joint work with Hamid Abban.
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