Zak Dyrefelt (Toulouse) will give the geometry seminar on 4th October. His title is *“K-stability of constant scalar curvature Kähler manifolds”*. The talk will take place at 11am in the Salle de Profs, on the 9th floor of building NO. His abstract follows.

In this talk we introduce a variational/pluripotential approach to the study of K-stability of Kähler manifolds with transcendental cohomology class, thus extending a classical picture for polarised manifolds. Our approach is based on establishing a formula for the asymptotic slope of the K-energy along certain geodesic rays, from which we deduce that cscK manifolds are K-semistable. Combined with a recent properness result of R. Berman, T. Darvas and C. Lu we further deduce uniform K-stability of cscK manifolds, whenever the automorphism group is discrete.