Growth of Fourier Coefficients of Families of Modular Functions
In mathematics there is a long history of studying the asymptotic growth of the Fourier coefficients of modular objects. Over the past few decades, physicists have also become very interested in this topic due to the rise of holography and the study of the entropy of black holes. Motivated by this, I will talk about the growth of Fourier coefficients of certain families of modular functions. A typical example of such families comes from the Borcherds lift of the j-invariant. I will talk about the connection of such lifts to vertex operators algebras, and the growth properties of the lifts of weak Jacobi forms.