# Modularity and Resurgence

# Modularity and Resurgence

The study of asymptotics as q approaches roots of unity is central to the theories of mock and quantum modular forms. In a collection of works, Gukov, Pei, Putrov, and Vafa proposed a candidate for a q-series invariant of closed 3-manifolds coming from physics. Many of these invariants are known to be mock and quantum modular forms, and this modularity has been integral to their study. Resurgent analysis is a natural tool to study this invariant from the perspective of physics, and is a theory centrally concerned with the relationship of functions to their asymptotic series. This has led to several questions on the interrelationship of resurgence and modularity. While this has been discussed across the subject, many questions remain. This talk will discuss ongoing work to make this connection explicit and natural from the perspective of number theory.