Algebra / Topology Seminar

Speaker: Philip Engel

Title: Triangulations of the sphere and K3 moduli

Abstract: The moduli spaces F_g of polarized K3 surfaces are non-compact quotients of a symmetric space by the action of an arithmetic group. I will discuss arithmetic compactifications of F_g which enjoy some of the same properties as the famous Deligne-Mumford compactification of the moduli space M_g of genus g curves. Stable graphs are the cartoon depictions of stable curves, which appear at the boundary of M_g. For stable K3 surfaces appearing at the boundary of F_g, the cartoons are polygonal tilings of the two-sphere.