Jean-Pierre Demailly will talk on 17th November, at 1.45pm UK time, or 2.45pm Belgian time. Jean-Pierre’s title is “Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles”. The abstract is below.
Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles
Given a vector bundle of arbitrary rank with ample determinant line
bundle on a projective manifold, we propose a new elliptic system of differential equations of Hermitian-Yang-Mills type for the curvature tensor. The system is designed so that solutions provide Hermitian metrics with positive curvature in the sense of Griffiths – and even in the dual Nakano sense. As a consequence, if an existence result could be obtained for every ample vector bundle, the Griffiths conjecture on the equivalence between ampleness and positivity of vector bundles would be settled. Another outcome of the approach is a new concept of volume for vector bundles.