Moonshine in Spacetime: Genus Zero, Algebras, and String Compactifications

New examples of moonshine — relationships between finite groups and special classes of (mock) modular forms— have been proliferating in recent years, starting with the discovery of a Mathieu group moonshine apparently connected to conformal field theory (CFT) on the K3 surface. While many aspects of these new moonshines remain mysterious, in this talk we will stress the power of spacetime string theory—as opposed to worldsheet string theory or CFT — to shine light on some of moonshine's outstanding mysteries.