*The class on September 8 will be held in Room 505, Cosmology Hall, from 16:15 to 17:15.

1. Introduction & Purposes

There has been tremendous progress in understanding compactifications of moduli spaces of higher dimensional varieties (i.e. varieties of dimension at least two). The goal of these lectures is to discuss some of this progress, emphasizing recent wall-crossing results and its applications, with a focus on the setting of K-moduli of log Fano varieties.

2. Outline & Descriptions

We will begin by introducing and motivating the theory of compactifications of moduli spaces of higher dimensional varieties through examples. We will discuss wall-crossing phenomena: Hassett introduced alternate compactifications of the moduli space of stable pointed curves by attaching a weight vector to the marked points. He proved that there are natural “wall-crossing” morphisms on the level of moduli spaces as this weight vector varies. After reviewing this, we will discuss some generalizations of these wall-crossing results to the setting of higher dimensional moduli. We will focus on examples, and finish by discussing several applications of this theory, for example to understanding some explicit moduli problems.

3. Registration

https://forms.gle/qMeronZDWpBUT5SMA

**If you need to participate online, please contact Murphy Yu <murphyyu@ncts.tw>