Umbral Moonshine

Umbral moonshine is a recently discovered association between distinguished mock modular forms and the Niemeier lattices. It is reminiscent of monstrous moonshine, but includes some new features, such as connections to the geometry of K3 surfaces. We will review the umbral moonshine conjectures, and describe some recent progress in understanding the umbral moonshine modules. These are the algebraic structures which should serve as the umbral analogues of the monstrous moonshine vertex operator algebra of Frenkel–Lepowsky–Meurman.