Speaker: Prof. Xiaokui Yang (MCM)

Title: Positivity notions in complex differential and algebraic geometry

Time: 9:30, May 9, 2018

Place: N818

Abstract: In this presentation, we will describe the relationship between various positivity notions in complex differential geometry and complex algebraic geometry. We derive several new vanishing theorems for partially positive vector bundles. As applications, we characterize uniruled and rationally connected projective manifolds by using partially positive curvature tensors. In particular, we confirm a conjecture of Yau that a compact Kahler manifold with positive holomorphic sectional curvature is projective algebraic and rationally connected.