10 problems

Let $G(t,-k)$ denote the generating function considered in the paper, with $t$ a formal variable and $k$ an integer. Generating-function conjecture. For every integer $k\geq 1$, ……

Let $(B,\vartheta)$ be a spin curve, let $g,d$ be integers, and let $k_1,\ldots,k_n$ satisfy … Write $\overline{c}_k=\sum_{\mu\ \textup{odd}}\kappa_{k,\mu}\cdot\mu$ for the spin co…

Let $g>0$ and let $\vec{\ell}\in\mathbb{Z}_{\geq0}^n$ satisfy $|\vec{\ell}|\leq g-1$, where $|\vec{\ell}|$ is the sum of the entries of $\vec{\ell}$. Let $D_{(\vec{\ell},i),2g+2}$…

Nonnegativity and log-concavity conjecture. The integers $c_{\vec{i},k}$ and $\widetilde{c}_{\vec{i},k}$ are nonnegative, and, for fixed $\vec{i}$, the sequences…

Let $\vec{i}$ be a tuple of nonnegative integers, with $|\vec{i}|$ denoting the sum of its entries. Let $D_{(\vec{i}),2g+2}$ and $d_{(\vec{i}),2g+2}$ denote the corresponding…

Let $g\geq 0$ and $n\geq 1$. For positive integers $\mu_1,\ldots,\mu_n$, let $h_{g;\mu}^{\circ,q,r}$ be the connected $q$-orbifold $r$-spin Hurwitz number, and define the formal sy…

Let $g\geq 0$, let $q,r\geq 1$, and let $\mu=(\mu_1,\ldots,\mu_n)$ be a partition with $n=\ell(\mu)$ and $|\mu|=\sum_{i=1}^n\mu_i$ divisible by $q$. Assume that…

Let $\overline{P}(\mathbf{x})$ be the moduli space appearing in the proposed ELSV formula for double Hurwitz numbers, and let $\Lambda_{2g}$ be its tautological Chow class of degre…

Let $\mathbf{x}=(x_1,\ldots,x_n)\in\mathbb Z^n$ satisfy $\sum_i x_i=0$, and let $H_g^r(\mathbf{x})$ be the double Hurwitz number, viewed piecewise polynomially on the chambers of t…

Let $g$ be fixed and let $\eta=(\eta_1,\ldots,\eta_n)$ be a ramification profile with $n=\ell(\eta)$. Set $r=2g-2+d+n$, where $d=\sum_i\eta_i$, and let $H_g(\eta)$ denote the corre…