Asymptotics and quantum modular forms (Campbell Wheeler-IHES Paris)

Zagier’s discovery of quantum modularity came from his numerical experiments with the Kashaev invariant of the figure eight knot. Since then, various authors showed that Zagier’s original cocycle can be lifted from a “better” function to an analytic function. I will discuss how this analytic cocycle can be obtained via resummation of the asymptotics of the Kashaev invariant. This I based on joint work with Veronica Fantini.