Regularisation techniques for (1,1) currents and applications to Kähler geometry

Jean-Pierre Demailly (Grenoble)

We will explain a new technique for proving regularity results for solutions of homogeneous Monge-Ampère equations, through an application of a smoothing procedure relying on the Legendre-Kiselman transform. Applications cover the regularity of geodesics in the space of Kähler metrics, the regularity of certain "supercanonical" metrics as well as partial results towards a conjecture on holomorphic Morse inequalities and asymptotic cohomology functions.