Resurgence, Quantum Modularity and Quantum Invariants in Three-Manifolds

Explore the intricate connections between resurgence, quantum modularity, and quantum invariants in this advanced mathematics lecture. Delve into the Witten-Reshetikhin-Turaev (WRT) quantum invariant of three-manifolds and its relation to the Chern-Simons partition function. Examine how resurgence techniques have led to significant discoveries in quantum Chern-Simons field theory, illuminating the interplay between compact and complexified gauge groups. Investigate the connection between the WRT quantum invariant and the BPS q-series invariant, including the radial limit conjecture and quantum modularity. Focus on the case of Seifert fibered homology spheres, exploring how the WRT quantum invariant determines complex Chern-Simons invariants through resurgence. Learn about recent proofs of the radial limit conjecture and quantum modularity based on resurgence formulas for the BPS q-series. Gain insights from William Mistegard's collaborative research with other mathematicians in this cutting-edge field of quantum topology and mathematical physics.