9 problems

Gopakumar–Vafa conjecture. The large $N$ limit of $SU(N)$ Chern–Simons gauge theory on $S^3$ is equivalent to the closed topological-string theory on the resolved conifold.

Ooguri–Vafa conjecture. There exists a corresponding Lagrangian submanifold $\mathcal{D}_{\mathcal{K}}$ such that

Let $T_{m,n}$ be a torus knot, and let $\bar{\operatorname{rCS}}_{\lambda}(T_{m,n};a,q,t)$ denote its stable large $N$ refined Chern–Simons invariant, where the color $\lambda$ is…

Large N duality conjecture. The two generating functionals $\mathcal{F}_{Y;cl}^{(0)}$ and $\mathcal{F}_{(Y,L);op}^{(0)}$ should be equal, subject to a suitable identification of pa…

Consider $SU(N)$ Chern–Simons gauge theory on $S^3$, and let $M_6=T^{\ast}S^3$ be the cotangent bundle of the three-sphere. Witten's large N duality. This theory is conjecturally e…

Let $K$ be a framed, oriented knot, let $W_R(K)$ denote its gauge-theory invariant in ChernSimons theory, and let … be the resolved conifold with Lagrangian boundary condition…

Large-$N$ duality conjecture. These theories are exactly equivalent in the large-$N$ limit. This conjecture is motivated by the equality of their vacuum partition functions and is…

Brini–Eynard–Mariño's conjecture. This curve should be the correct B-model topological string large-$N$ dual to the knot $K$.

Let $Y$ be the ambient geometric object and $C^\circ$ a curve, and let $Z^{\mathrm{mot}}(Y,C^\circ,T,u)$ and $Z^{\mathrm{mot}}_{C^\circ}(q,a)$ be the motivic generating functions a…