John Duncan, Emory University
Title: Optimal Mock Jacobi Forms
Abstract: Mock Jacobi forms were introduced by Dadholkar—Murthy—Zagier in order to count quantum degeneracies of single-centered black holes in string theory. They also appear naturally in umbral moonshine, where they encode dimensions of representations of certain finite groups. Call a mock Jacobi form optimal if its Fourier coefficients grow as slowly as possible. In this talk we review these notions, and present a classification, obtained in joint work with Miranda Cheng, of the optimal mock Jacobi forms of weight one that have integral Fourier coefficients. A positivity condition distinguishes the examples that are associated to Niemeier lattices by umbral moonshine.