5 problems

Let $K$ be a knot, let $G=SU(N)$, and consider the totally symmetric representation. Write … and let $\alpha_{-k-1}(K;N,q)$ denote the coefficients appearing in the inverted Habiro…

Let $M$ be a knot complement, and let $\widehat{Z}(M)$ denote its homological block. Consider its positive or negative expansion, and let $\mathcal{P}_Q(\mathbf{x})$ denote a motiv…

The universal radial-limit conjecture. The invariant $N_\ell(M^3,\omega)$ is conjectured to satisfy

The modularity conjecture. For general lens spaces, the homological blocks are conjectured to satisfy

Let $Z_a$ denote the homological blocks associated with the three-manifold under consideration. Gukov–Pei–Putrov modular-transform conjecture. There is a modular transform of the h…