讲座题目：L^2 estimates for \dbar equations and bundles with singular positive curvature
主讲人：周向宇 研究员
开始时间：2025-6-3 9:00
讲座地址：闵行校区数学楼102报告厅
主办单位：数学科学学院
报告人简介：
周向宇，中国科学院院士、中国科学院数学与系统科学研究院研究员，国际数学家大会报告人。主要研究领域为基础数学中的多复变和复几何，解决了在苏联《数学百科全书》被列为未解决问题的扩充未来光管猜想，该工作被写入史料性著作《二十世纪的数学大事》、《数学的发展：1950-2000》。曾获国家自然科学奖、陈省身数学奖等。
报告内容：
In this talk, we first recall some basic properties of multiplier ideal sheaves associated to pseudoeffective line bundles (or psh functions), e.g., a solution of Demailly's strong openness conjecture (Guan-Zhou), then present a characterization of Nakano positivity via solving \\dbar equations with L^2 estimates (Deng-Ning-Wang-Zhou), which is a converse proposition of Hörmander-Demailly's L^2 existence theorems. This gives a connection between differential geometry and differential equation via several complex variables. As an application of the characterization, we give an affirmative answer to Lempert's problem (Liu-Yang-Zhou), which asks whether the limit metric of an increasing sequence of hermitian metrics with Nakano semi positive curvature on holomorphic vector bundles is still Nakano semi-positive. As another application, one may define singular metric of positive curvature in the sense of Nakano on holomorphic vector bundles. Finally, we present recent results on the strong openness of the multiplier submodule sheaves (vector bundle version of multiplier ideal sheaves) by Liu-Xiao-Yang-Zhou and Le Poiter type isomorphism theorem between cohomology of the vector bundles twisted with the multiplier submodule sheaves and cohomology of the associated line bundles twisted with the multiplier ideal sheaves (Liu-Liu-Yang-Zhou).
