Members’ Seminar

Quantum modular forms were defined in 2010 by Zagier; they are somewhat analogous to ordinary modular forms, but they are defined on the rational numbers Q as opposed to the upper half complex plane H, and they transform in Q under the action of the modular group, but only up to a suitably analytic error function. In 2016, Bringmann and the author defined the notion of a quantum Jacobi form, naturally marrying the concept of a quantum modular form with that of a Jacobi form (the latter being a two variable modular form on C x H, originally developed by Eichler and Zagier in the 1980s). In this talk we will give an accessible overview of these intertwined topics, emphasizing recent developments and applications in the subject of quantum Jacobi forms. In particular, we will discuss applications to mock modular forms, combinatorics, topology (torus knots), and representation theory (VOAs).