11 problems

Let $X=\mathcal{O}_{\mathbb{P}^1}(-1)\oplus\mathcal{O}_{\mathbb{P}^1}(-1)$ be the resolved conifold equipped with the anti-diagonal $C^*$-action on the fibers, and let the generati…

Anti-diagonal equivariant GW correspondence. The identity

Let $Q=e^{2\pi i t}$, and define … Let $F_{\mathrm{GV}}(\lambda,t)$ and $F_{\mathrm{NS}}(g,t)$ denote the Gopakumar–Vafa and Nekrasov–Shatashvili free energies, respectively. Hatsu…

Let $F_{\rm coni}^{\rm resum}(\lambda,t)$ be the analytic function considered in the source, and let $F_{\mathbb R_{>0}}(\lambda,t)$ denote the Borel summation along the positive r…

Let $F_{\rm GV}(\lambda,t)$ be the Gopakumar–Vafa free energy of the resolved conifold, and let $F_{\rm np}(\lambda,t)$ be the non-perturbative completion defined by … Here…

Let $X=\operatorname{Tot}_{\mathbb P^1}(\mathcal O(-1)\oplus\mathcal O(-1)\oplus\mathcal O)$, and let $\mathcal Z_X(y,q,Q)=\sum_{n,d}P_{n,d[\mathbb P^1]}(\mathcal O,y)q^nQ^d$ be it…

Let $X$ be the resolved conifold, let $\beta\in H_2(X,\bZ)$ be an effective class, and let $n$ be an integer. Denote by $\Omega(\beta,n)$ the BPS invariant associated with the corr…

Let $X_1$ be the resolved conifold $\mathcal{O}_{\mathbb{P}^1}(-1)\oplus\mathcal{O}_{\mathbb{P}^1}(-1)$ equipped with the anti-diagonal action, and consider its equivariantly Calab…

Let $C_0$ denote the resolved-conifold mirror curve in zero framing, and let $C_a$ denote the mirror curve in framing $a$, with coordinates $(x,y)$. Aganagic–Klemm–Vafa's framing t…

Let $\Psi_{0,1}^{(a)}(t;x)$ be the open-string one-point function for the resolved conifold with an outer brane in framing $a$. Let the mirror curve be a plane curve … which determ…

Let $\Psi^{(a)}_{0,1}(t;x)$ be the resolved-conifold open-string one-point function, and set $Q=-e^{-t}$. Half-integrality conjecture. There are half-integers $e^{(a)}_{k,m}$ such…