8 problems

Fix $r\geq 2$, let $\overline g$ denote the doubled genus, and suppose $b,m>0$. Let the superscript $r\mathrm{BY}$ denote the Bertola–Yang intersection numbers and $r\star$ the num…

Let $Z_{\rm KP}$ and $Z_{\rm ABT}$ denote the partition functions associated with the Kontsevich–Penner and Alexandrov–Buryak–Tessler constructions. KP–ABT equality conjecture. One…

Extended refined Kontsevich–Penner conjecture. For any $N$ we have

Let $\mathcal{M}_{(g,b),k,l}$ be the moduli space of Riemann surfaces with boundary of genus $g$, with $b$ boundary components, $k$ boundary marked points, and $l$ interior marked…

Q-graded correlator conjecture. These correlators are the $Q$-graded correlators for open intersection numbers. The proposed grading is intended to separate contributions by bounda…

Let $F^o(s,t_0,t_1,\ldots;u)$ be the open free energy, with double brackets denoting its derivatives with respect to the variables $t_i$ and $s$, and let $F^c$ denote the closed fre…

Pandharipande–Solomon–Tessler's open Virasoro constraint conjecture. The partition function satisfies

Open Virasoro conjecture. The operators $\mathcal{L}_n$ annihilate the full partition function: