Two theorems of Odaka

I gave this talk on the 6th of February of 2025 for the study group on K-stability organised by Marc Truter.

The goal of the study group was to understand the basics of K-stability following these notes written by Harold Blum. In this talk, I explained two important theorems that Yuji Odaka proved. The first one solves the problem of which Calabi-Yau and canonically polarised varieties are K-stable. The second one shows that K-semistability imposes conditions on the possible singularities of a variety. These are the notes I wrote: