Quantum modular form and quantum invariants

Quantum invariants are invariants of knots and 3-manifolds which relate deeply to mathematical physics and representation theory.
In recent years, it has become increasingly clear that it is also deeply related to number theory, that is, quantum modularity for quantum invariants.
This topic is interesting from a topological viewpoint since this is a refinement of establishing asymptotic expansions of quantum invariants, which is an important problem in quantum topology,
and is interesting from a number-theores[tic viewpoint since this gives examples of quantum modular forms, which are mysterious objects in number theory.

I obtained two linked results on topology and number theory:
Establishing explicit asymptotic expansions of quantum invariants for negative definite plumbed 3-manifolds and establishing quantum modularity of false theta functions in full generality.

In this talk, I will outline previous progress on quantum modularity for quantum invariants and my results.