Three perspectives on $M_{24}$ moonshine in weight 2

Abstract: In this talk, I will describe three ways of repackaging the mock modular forms of $M_{24}$ moonshine into forms of weight two. In the first case, I will describe quasimodular forms as trace functions whose integralities are seen to be equivalent to divisibility conditions on the number of $\mathbb{F}_p$ points on the Jacobians of modular curves. In the second case, for certain subgroups of $M_{24}$, I will describe vertex operator algebraic module constructions whose associated trace functions are meromorphic Jacobi forms, thus giving explicit realizations of the divisibility conditions. In the third case, I will describe an association of weakly holomorphic modular forms to elements of $M_{24}$ with connections to the Monster group.

other condensed matterstatistical mechanicsstrongly correlated electronsgeneral relativity and quantum cosmologyHEP - theorymathematical physicsalgebraic geometrydifferential geometrydynamical systemsgroup theorynumber theoryquantum algebrarepresentation theory

Audience: researchers in the discipline

Number theory, Arithmetic and Algebraic Geometry, and Physics

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