Group, Lie and Number Theory Seminar

For certain subgroups of $M_{24}$, I will describe vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms. These meromorphic Jacobi forms are canonically associated to the mock modular forms of Mathieu moonshine. The construction is related to the Conway moonshine module and employs a technique introduced by Anagiannis--Cheng--Harrison. This construction gives concrete vertex algebraic realizations of certain cuspidal Hecke eigenforms of weight two. In particular, the construction gives explicit realizations of trace functions whose integralities are equivalent to divisibility conditions on the number of $\mathbb{F}_p$ points on the Jacobians of modular curves. Speaker(s): Lea Beneish (Emory University)