Quantum modular forms

In his study of quantum invariants of hyperbolic manifolds, Zagier discovered a strange form of modularity he called quantum modularity. This behaves much like usual modular forms twisted by a cocycle with strong analyticity properties. This was all clarified in his recent work with Garoufalidis. I will show that for an infinite family of examples these cocycles are the Borel resummation of their asymptotics. This proves conjectures of Garoufalidis-Gu-Marino and is based on joint work with Veronica Fantini.