Cohomology of non-reductive GIT quotients and hyperbolicity

The aim of this talk is to describe joint work with Gergely Berczi using a recent extension to non-reductive actions of geometric invariant theory, and its links with moment maps in symplectic geometry, to study hyperbolicity of generic hypersurfaces in a projective space. Using intersection theory for non-reductive GIT quotients applied to  compactifications of bundles of invariant jet differentials over complex manifolds leads to a proof of the Green-Griffiths-Lang conjecture for a generic projective hypersurface of dimension n whose degree is greater than n^6. A recent result of Riedl and Yang then implies the Kobayashi conjecture for generic hypersurfaces of degree greater than (2n-1)^6.