讲座内容：

L2 theory is a core topic in several complex variables, primarily encompassing the L2 estimates for solutions of the dbar equation and the L2 estimates for the extension of holomorphic functions. This report introduces a converse of L2 theory that we have developed in recent years, mainly including the analytic characterization of the curvature positivity of holomorphic Hermitian vector bundles and the pseudoconvexity of domains. These results have been applied to study the curvature positivity of direct images of vector bundles and the properties of ample vector bundles, and have also been used to prove new results in convex analysis and give an affirmative solution to an open problem of Lempert.