Abstract: In 2010, Zagier defined the notion of a ``quantum modular form," and offered several diverse examples, including
Kontsevich's `strange' function. Here, we construct infinite families of quantum modular forms, and prove one of Ramanujan's remaining
claims about mock theta functions in his last letter to Hardy as a special case of our work. We will show how quantum modular forms
underlie new relationships between combinatorial mock modular and modular forms due to Dyson and Andrews-Garvan.
This is joint work with Ken Ono (Emory U.) and Rob Rhoades (CCR-Princeton).