Speaker
Description
Quantum modularity is a fascinating phenomenon connecting mathematical physics, topology, and number theory.
Among its most important expected examples are quantum invariants of knots and 3-manifolds. These invariants originate from Chern–Simons theory, a 3-dimensional topological quantum field theory. A fundamental problem in Chern–Simons theory is to understand their asymptotic behavior in the large-level limit. Quantum modularity provides a number-theoretic structure related to such asymptotic phenomena.
In this talk, I will establish asymptotic expansions of the Witten–Reshetikhin–Turaev invariants for a broad class of non-hyperbolic 3-manifolds. A key step is to derive explicit quantum modular transformation formulas for general false theta functions, in analogy with the classical modular transformation of theta functions. I will explain how these number-theoretic structures lead to the asymptotic behavior of quantum invariants.
This talk is based on arXiv:2508.21710.