15 problems

Let $r$ be a positive integer, let $g$ and $n$ be nonnegative integers in the range where the moduli space $\ce\boverline{\mathcal M}_{g,n}$ and the Witten class are defined, and l…

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…

Let $r$ be a positive integer, and consider the moduli stack of smooth $r$-spin $1$-pointed curves of genus $1$. Jarvis–Picard finiteness conjecture. The Picard group of this modul…

A spin equation is associated with a quasi-homogeneous polynomial; in the simplest $A_{r-1}$ case it has the form … A marked point with trivial orbifold structure is called a Ramon…

Compact-type comparison conjecture. For all relevant $g$ and $n$,

Let $\overline{M}^{spin}_{0,k}(X,\beta)$ be the moduli stack of stable spin maps of genus zero with $k$ marked points and class $\beta$, and let $N_{(C,\phi)}$ be the SUSY normal b…

The moduli stack of stable spin curves is denoted by $\overline{M}^{spin}_{0,k}$, and for a stable spin curve $c\colon C\to B$ of genus zero with $k$ marked points and fixed tree t…

Let $g,n\geq 0$ and let $k$ be a positive odd integer. Let $\mu=(m_1,\ldots,m_n)\in\mathbb{Z}^n\setminus k\mathbb{Z}^n_{\geq 0}$ satisfy … with all entries of $\mu$ even. Let…

Let $k$ range over positive odd integers and let $\mu$ range over odd partitions. For a spin curve $(B,\vartheta)$, let $H_d^\bullet(B,\vartheta;\mu^1,\ldots,\mu^n)$ denote the dis…

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 $r\geq 2$ and let $\Theta^r$ be the negative $r$-spin Theta class, with descendant potential $Z^{\Theta^r}$. Let the $r$-BGW tau function denote the Brézin--Gross--Witten tau f…

Let $g,k,l$ be nonnegative integers, let $d_1,dots,d_l$ be nonnegative integers, and let $\overline{\mathcal{M}}_{2g,k,l,1}$ denote the moduli space of Riemann surfaces with bounda…

Let the $3$-spin relations be the tautological relations constructed from $3$-spin theory on the moduli space of curves. 3-spin generation conjecture. The $3$-spin relations genera…

Pixton's generalized vanishing conjecture. The same vanishing result as for ${\Omega_{g,A}}$ holds for ${\Omega_{g,A,k}}$, namely its codimension-$d$ part vanishes for all $d>g$. T…

Let $\bold{M}_g^{1/2}[\epsilon]$ denote the component of the moduli space of $2$-Spin Riemann surfaces with Arf invariant $\epsilon$, and let $\lambda$ and $\lambda^{1/2}$ be the c…