Abstract:
I will give an introduction to the Monster simple group and the phenomenon known as Monstrous Moonshine. The talk will focus on the subtle role of the number 24. It was conjectured by Mason (unpublished, 2010) and proved by Johnson-Freyd (2018) that the puzzling phase factors of order 24 were governed by a cocycle in the cohomology of the Monster group. This means that in its natural habitat, the Monster appears in a form that is best understood as the isomorphism classes of objects of a categorical group, the refined Monster. Just like a group, a categorical group wants to be realised as the symmetries of an object, and upon closer inspection, all the ingredients in the construction of the Monster have a categorical refinement. These categorical aspects of the theory have traditionally been ignored, and there is hope that they might, after all, be the natural habitat of the Monster, i.e., that the refined Monster consists of the (refined) symmetries of an object that is easily constructed and very natural to study. I will underpin this speculation with some concrete constructions.