37 problems

Simple Hurwitz numbers count branched coverings of the sphere with prescribed ramification over one branch point and simple ramification over the remaining branch points. The Chekh…

Let $q$-orbifold $r$-spin Hurwitz numbers be denoted by $h_{g,\mu_1,\dots,\mu_n}^{\circ,q,r}$. For each part, write its integral division by $qr$ as … Let…

Shadrin's ELSV-like formula conjecture. There should be an ELSV-like formula for one-part double Hurwitz numbers with completed cycles.

Let … where $i$ is an integer, and let $s$ be the unique formal power series in $x$ and $p$ satisfying … For the Hurwitz generating series $H_g(x,p)$, and for a partition $\theta$…

For $m\ge 1$, let $e_i$ denote the $i$-th elementary symmetric function in the variables used to define $f_m^{(1)}$. The closed formula conjecture for genus-one ramification polyno…

For $g=0$ and $m\ge 3$, or $g\ge 1$ and $m\ge 1$, let $f_m^{(g)}(\alpha_1,\ldots,\alpha_m)$ denote the rescaled ramification number associated with coverings of the sphere by a gen…

Let $m\ge 1$, let $\alpha=(\alpha_1,\ldots,\alpha_m)$ be a ramification type, and let $n=\alpha_1+\cdots+\alpha_m$. For $i=1,\ldots,m$, let $e_i$ be the $i$-th elementary symmetric…

Let the single Hurwitz generating series be formed from the single Hurwitz numbers, and perform the change of variables described in the source. A scaled coefficient is the coeffic…

Hurwitz-number congruence conjecture. If $d$ is not divisible by $4$, $6$, or $9$, then

Do–He–Robertson's coefficient-gap conjecture. The coefficients satisfy

Let $d\geq10$, and let $\nu$ be a partition of $d$ with $m_1(\nu)=1$ satisfying the exclusions stated in the conjecture. Let $z_\nu$ be the standard centralizer factor, and let…

Let $d\geq10$ and let $\nu$ be a partition of $d$ with $m_1(\nu)\geq2$. Let $z_\nu$ be the standard centralizer factor, and let $b^X_\nu(\mu^{(1)},\dots,\mu^{(s)},m)$ denote the co…

Let $d$ be the degree, let $\boldsymbol{\nu}$ be the ramification data, and let $\operatorname{logDR}_0(d,-\boldsymbol{\nu})$ denote the logarithmic double ramification cycle. Let…

Let $d$ be the degree, let $\boldsymbol{\nu}$ be the ramification data, and let $\operatorname{logDR}_0(d,-\boldsymbol{\nu})$ denote the logarithmic double ramification cycle. Let…

Let $d$ be the degree, let $\boldsymbol{\nu}$ be the ramification data, and let $\operatorname{logDR}_0(d,-\boldsymbol{\nu})$ denote the non-leaky logarithmic double ramification c…

Coulter–Do conjecture. There exists a collection of operators

Let $\boldsymbol{\text{?}}=(\boldsymbol{\text{?}})$ be a fixed ramification profile of size $d\boldsymbol{\text{?}}$, with $d\boldsymbol{\text{?}}$, and let…

Let $\boldsymbol{\text{?}}=(\boldsymbol{\text{?}})$ be a fixed ramification profile of size $d\boldsymbol{\text{?}}$, and let $C(\boldsymbol{\text{?}},m)$ be the coefficients in th…

Let $\boldsymbol{\text{?}}$ denote the monotone Hurwitz number with fixed ramification profile $\boldsymbol{\text{?}}$; for a partition…

Let $r>2$ and let $Q_1,\ldots,Q_r$ and $\Lambda$ be the parameters of the half Seiberg–Witten curve, with $B_{2g}$ denoting the Bernoulli number. Topological free-energy conjecture…

Fix positive integers $\mu_1,\ldots,\mu_n$ whose sum is $d$. Let the roots of the polynomial $\vec{H}^t_{g,n}(\mu_1,\ldots,\mu_n)$ be ordered from smallest to largest. Genus-asympt…

Let $g\geqslant 0$, $n\geqslant 1$, and let $\mu_1,\ldots,\mu_n\geqslant 1$. The deformed monotone Hurwitz number $\vec{H}^t_{g,n}(\mu_1,\ldots,\mu_n)$ is a polynomial in $t$. Two…

Goulden–Jackson–Vainshtein genus-one Hurwitz formula conjecture. The displayed formula holds for $b^1_{\boldsymbol{b1}}$.

Frobenius-manifold Lyashko–Looijenga degree conjecture. The degree of the map $LL(\mathcal{F}_g)$ equals

Quasi-Coxeter Lyashko–Looijenga degree conjecture. The number $F_W^{\mathrm{red}}(g)$ agrees with the degree of $LL_g$.