# Meromorphic Jacobi forms in representation theory and physics

Jacobi forms are of central interest in representation theory of affine Kac-Moody Lie superalgebras, vertex algebras, Moonshine, N=2 SCFT, etc. They famously appeared in the groundbreaking work of Kac and Peterson on characters of integrable highest weight modules. More recently, meromorphic Jacobi forms have been studied in various contexts in string theory (e.g. as counting function of the quarter-BPS states in N=4 string theory) and in N=2 SCFT in four dimensions (e.g. as refined Schur indices in Argyres-Douglas theories).

Their Fourier coefficients have been studied from several different perspective. For instance, it is known that in many cases ”canonical” Fourier coefficients can be completed to obtain (almost) harmonic Maass forms. In my talk we will discuss coefficients of certain meromorphic Jacobi forms coming from vertex algebra associated to representations of affine Lie algebras away from positive integral levels. Although these objects are poorly understood they are a rich source of interesting modular-type objects.