Abstract: 
\hat{Z} is a 3d TQFT whose existence was predicted by S. Gukov, D. Pei, P. Putrov, and C. Vafa in 2017 using 3d/3d correspondence. To each 3-manifold equipped with a spin^c structure, \hat{Z} is supposed to assign a q-series with integer coefficients that is categorifiable and provides an analytic continuation of Witten-Reshetikhin-Turaev invariants. In 2019, S. Gukov and C. Manolescu initiated a program to mathematically construct \hat{Z} via Dehn surgery, and as part of that they conjectured that the Melvin-Morton-Rozansky expansion of the colored Jones polynomials can be re-summed into a two-variable series F_K(x,q). In this talk, I will explain how to prove their conjecture for a big class of links by “inverting” the R-matrix state sum.
 
 
virtual (zoom): Virtual: http://berkeley.zoom.us/j/93328405860?pwd=Um1GbHBCSUJMdUlWWnd0ZVMxQmwwdz09