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.