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 AndrewsGarvan.
This is joint work with Ken Ono (Emory U.) and Rob Rhoades (CCRPrinceton).
