Curvature Positivity and $\bar\partial$ Equation with Optimal $L^2$ Estimate - ICBS 2024

Explore recent advancements in complex geometry and analysis through this 48-minute conference talk by Xiangyu Zhou at BIMSA. Delve into the latest findings on multiplier ideal sheaves, including the resolution of Demailly's strong openness conjecture. Examine new developments in multiplier submodule sheaves associated with singular hermitian metrics on holomorphic vector bundles. Investigate recent results on converse L^2 theory, encompassing converses of L^2 existence theorems and L^2 extensions. Learn about a newly established criterion for Nakano semipositivity of holomorphic vector bundles, based on solving the ∂̄ equation with optimal L^2 estimates. Discover how this criterion provides a solution to Lempert's problem on Nakano semipositivity, bridging complex geometry and functional analysis.