删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

Kewei Zhang:A pluripotential approach to the Kahler-Einstein problem (4)

本站小编 Free考研考试/2021-12-26



Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker: Kewei Zhang
Inviter:
Title:
A pluripotential approach to the Kahler-Einstein problem (4).
Time & Venue:
2021.09.07 14:00-15:00 S615
Abstract:
The Yau-Tian-Donaldson conjecture states that the existence of canonical metrics on polarized manifolds is equivalent to certain algebro-geometric stability condition. In the Fano case, this conjecture has been solved due to many authors' work, which involves many deep and insightful ideas. In this series of talks we will present a relatively more modern approach to this problem using mainly pluripotential theory. This approach has the merit that it requires very little prerequisite and can be generalized to the non-Fano setting, which gives rise to new criterions for the existence of twisted Kahler-Einstein metrics and constant scalar curvature Kahler metrics. The full details of the approach will be presented during this series of talks. We will first recall some classical puripotential theory and present BBEGZ's variational approach to solving complex Monge-Ampere equations on compact Kahler manifolds. Then we will collect some facts and recent progress in algebraic geometry on K-stability, with a emphasis on alpha and delta invariants. Finally using a classical quantization argument we show that these algebraic invariants can be used to detect the solvability ofcomplex Monge-Ampere equations, which in particular yields a somewhat more elementary proof of the uniform Yau-Tian-Donaldson conjecture for the existence of twisted Kahler-Einstein metrics on polarized Kahler manifolds.

相关话题/

  • 领限时大额优惠券,享本站正版考研考试资料!
    大额优惠券
    优惠券领取后72小时内有效,10万种最新考研考试考证类电子打印资料任你选。涵盖全国500余所院校考研专业课、200多种职业资格考试、1100多种经典教材,产品类型包含电子书、题库、全套资料以及视频,无论您是考研复习、考证刷题,还是考前冲刺等,不同类型的产品可满足您学习上的不同需求。 ...
    本站小编 Free壹佰分学习网 2022-09-19