Quantum modular forms from mock Jacobi forms

Quantum modular forms, introduced by Zagier in 2010, are functions that exhibit almost modular behavior on a subset of a rational numbers. Since their introduction, a handful of examples of these new objects have been generated. In this talk, I will explain some of the motivating examples behind Zagier’s definition and present an infinite family of quantum modular forms of arbitrary positive half-integral weight. This infinite family arises in a systematic way and connects other modular-like objects that have been studied over the last 100 years.