Line bundles on moduli spaces/stacks of G-bundles were studied intensively in 90’s by many mathematicians including Beauville, Laszlo, Sorger, Faltings, Kumar, Narasimhan, Teleman, etc. The main problems are the Verlinde formula for the dimension of global sections of these line bundles, and the determination of the Picard groups of the moduli spaces/stack of G-bundles.In this talk, I will dis...
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...