8 problems

Let $g,m\geq 0$, $n\geq 1$, and let $\textbf{d}=(d_1,\ldots,d_n)\in(\Bbb Z_{\geq 0})^n$, with $|\textbf{d}|:=d_1+\cdots+d_n$. For a nondegenerate balanced genus-$g$ stable rooted t…

Oprea's conjecture. All tautological relations on $\overline{\mathcal{M}}_{0,n,\beta}(X)$ come from tautological relations on the moduli space of genus-zero curves.

Identification conjecture. For any such $g$, $n$, and $\overline{d}$,

Identification conjecture. For any such $g$, $n$, and $\overline{d}$,

Vanishing conjecture for $B^m_{g,\overline{d}}$. For any $m\ge 2$, $g\ge 0$, $n\ge 1$, and $\overline{d}$ such that $\sum d_i\ge 2g+m-1$, one has

Proportionality conjecture. For every such $n$, $t$, and $(a_1,\dots,a_n)$, one has

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…