Gandalf (Pure Maths Student Seminar): Many Moonshines: Monstrous, Mathieu and M(Umbral)
9 December 2015 16:00 in CM221
Mathieu Moonshine concerns a surprising observation relating string theory to the representation theory of a particular sporadic group, Mathieu 24. This is reminiscent of Monstrous Moonshine in which it was discovered that the coefficients of the modular j-function are related to the representation theory of the Monster group. In this talk we will introduce a topological invariant of string theories compactified on K3 surfaces, called the elliptic genus of K3, and see how Mathieu 24 appears in this context. To this date, the role of the large discrete symmetry M24 in String Theory is not properly understood. We will then discuss Umbral moonshine, which comprises of 23 examples of moonshine in which the Niemeier lattices are used to connect certain mock modular forms to finite groups.
Gandalf is the pure maths student seminar. Gandalf stands for the Geometry AND ALgebra Forum. It is run by and for pure postgraduates, but welcomes anyone who is interested in coming along.
Content from previous talks is available at the gandalf seminar home page.