I will survey some results from the study of moduli spaces of higher dimensional varieties as well as the Hassett—Keel program for the moduli space of curves. I will then discuss applications of these techniques to the study of moduli spaces of K3 surfaces of low degree. Most of the original work presented in this talk will be based on joint work with Kristin DeVleming and Yuchen Liu.
org: Turchet Amos