10 problems

The $r$-spin theory is a cohomological field theory whose correlators are intersection numbers on the moduli space of $r$-spin curves. Its big phase space potential function is def…

Let $r$ be the parameter of the generalized Kontsevich model and let $\epsilon$ be a deformation parameter. Consider the deformed potential … After shifting the variables, Alexandr…

Let $r$ be the spin parameter, let $g\geq 2$, let $F_g^{x^r,o}$ denote the open $r$-spin potential, and let $\phi_g$ denote the corresponding closed $r$-spin potential. The notatio…

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…

Fix $r\geq 2$, and let $\langle\cdots\rangle^{r\mathrm{spin}}_{g,n;b,m}$ denote geometric open $r$-spin intersection numbers, while $\langle\cdots\rangle^{r\star}_{g,n;b,m}$ are th…

Fix $r\geq 2$. Let $\overline g=2g+b-1$, and denote by…

Consider the deformed generalized Kontsevich matrix model (GKM) with potential given by equation, and allow a shift of its variables. Deformed GKM conjecture. The shifted deformed…

Closed extended r-spin potential conjecture. For any $g\geq 0$,

Geometric construction conjecture. For these data, there is a geometric construction of correlators

The r-spin Witten conjecture. The function $\exp(F^{\frac{1}{r},c})$ becomes, after a certain rescaling of the variables $t^\alpha_d$, a tau-function of the $r$-th Gelfand–Dickey h…