Some explicit K-moduli of Fano varieties

Fano varieties are projective algebraic varieties which are normal and have ample anticanonical bundle. Recently, using K-stability (which originates from Kähler-Einstein metrics in differential geometry), moduli spaces for klt K-polystable Fano varieties have been constructed; these moduli spaces are projective and are called "K-moduli". In this talk, after reviewing some basics of the theory of K-moduli of Fano varieties I will discuss certain explicit examples.