3 problems

Let $r\geq 2$, let $L$ be the Gelfand–Dikii operator, and let $\Phi(T_*,\lambda)$ solve … Write $\phi=\log\Phi=\sum_{g\in\mathbb Z}\lambda^{g-1}\phi_g$, and let…

Let $r\ge 2$, let $L$ be the specified solution of the $r$-th Gelfand--Dickey hierarchy, and let $\Phi$ solve … with $\Phi|_{T_{\ge 2}=0}=1$. Write…

Let $r\ge 2$. For $g\ge 1$, denote by $\langle\tau^{\alpha_1}_{d_1}\cdots\tau^{\alpha_l}_{d_l}\sigma^k\rangle^{\frac{1}{r},o}_g$ the proposed open $r$-spin intersection numbers, an…