Title: K stability and birational geometry of moduli spaces of quartic K3 surfaces
Abstract: I will discuss various compactifications of moduli spaces of quartic K3 surfaces, coming from geometric invariant theory (GIT), Hodge theory, and K-stability. We will see that K-stability provides a natural interpolation between various other compactifications via wall crossings in K-moduli and prove conjectures of Laza and O'Grady along with new results. This is joint work with Kenneth Ascher and Yuchen Liu.