AbstractIn this talk, I will discuss a correspondence between the problem of finding a constant scalar curvature K\"ahler metric (cscK for short) on a polarized complex manifold and the CR-Yamabe problem on the associated circle bundle. I will then use a CR version of the Einstein-Hilbert functional to show K-semistability of polarised complex manifolds admitting cscK metrics. This is a joint w...
AbstractIn the preliminary part, we will go through the notion of irreducible holomorphic symplectic (IHS) manifolds, which is one of the high-dimensional generalizations of K3 surfaces. The action of holomorphic automorphisms on IHS manifolds is well-known, in terms of cohomology actions and characteristic currents (i.e., Green currents) that the automorphism induces. We will briefly go throug...
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