12 problems

Let $\mathcal{C}_{k,m}$ be the orbifold obtained from $\mathbb{P}^1$ by replacing neighborhoods of $0$ and $\infty$ with the orbifold discs $D_1/\mathbb{Z}_k$ and…

Explicit invariant formula. The orbifold three-point invariant is

Let $X$ be a smooth projective variety, let $D=D_1+\cdots+D_n$ be an effective reduced normal crossing divisor with smooth, irreducible, nef components, and let $I_1,\ldots,I_m$ pa…

Large-root stabilization and polynomiality conjecture. Genus-zero orbifold Gromov–Witten invariants of $X_{D,\vec r}$, after multiplication by suitable powers of the $r_i$, stabili…

Let $h_8(q)$ and $h_9(q)$ denote the generating functions for the orbifold insertions described above, and let $F_{0,3}$ and $F_{1,3}$ be the corresponding decompositions by the no…

Genus-bound conjecture. The condition $g\leq 1$ should be only a technical restriction, whereas the condition $n\geq 2$ should be essential.

Let $k$ and $m$ be positive integers, let $M_{k,m}$ be the Frobenius manifold of degree-$(k,m)$ Laurent polynomials, and let $D^{M_{k,m}}$ be its Givental total descendent potentia…

Remodeling conjecture. The differentials $d_1\cdots d_nG^{(r,s)}_{g,n}[x_1,\ldots,x_n;f]$ are symmetric differential forms on $C_f$ and satisfy the Eynard–Orantin recursion for the…

Let $\mathbb{P}^1$ be an orbifold of ADE type, with orbifold-point multiplicities $p$, $q$, and $r$, and let $t_n$ denote the distinguished coordinate appearing in the genus-zero F…

Let $\mathcal{X}$ be a proper orbifold of dimension $n$, with inertia components $\mathcal{X}_i$, age $\operatorname{age}(\mathcal{X}_i)$, and double inertia orbifold…

Let $\mathcal{X}$ be an orbifold, and let $II\mathcal{X}$ be its double inertia orbifold, whose points are triples $(x,g,h)$ with $x\in\mathcal{X}$ and commuting elements…

Let $\mathcal{X}$ be a compact orbifold, let $\mathcal{D}_\mathcal{X}$ denote its total descendant Gromov–Witten potential, and let $\mathcal{L}_m$ be the Virasoro operators define…