K-moduli of Fano varieties
Abstract: One main theme of the algebraic K-stability theory of Fano varieties is to use it to construct moduli spaces of Fano varieties. This has once been beyond algebraic geometers’ imagination, but K-stability is proven to give the right framework. By now except the properness, all other main ingredients have essentially been established, based on the recent development of our understanding of K-stability theory and other inputs. In this talk, we will give an outline of the construction, with the focus on the essential role that the new characterisation of K-stability plays, and its connection to minimal model program theory.