27 problems

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.

Let $A^*({\overline{\mathcal{M}}}_{0,2}({\mathbb P}^1,2))$ denote the Chow ring of the moduli space of stable maps, let $L_1$ and $L_2$ be the cotangent line bundles associated wit…

Let $X$ be any flag variety, and let $\mathcal M_{0,n}(X,\beta)$ be the open part of the moduli space of stable maps, parametrizing maps without boundary degenerations. Let the ind…

Let $G$ be a semisimple algebraic group, let $P$ be a parabolic subgroup, and let $X=G/P$ be a general flag variety. For nonnegative integers $n$ and curve class $\beta$, write…

Let $(X,D,f:X\to\mathbb{P})$ be a stable map, with $(X,D)$ semi-log-canonical, and fix suitable numerical invariants. Alexeev's proper moduli conjecture. Stable maps admit a proper…

Cohomology-ring presentation conjecture. The de Rham cohomology ring is

Let $X$ be a variety, let $V$ be a convex vector bundle on $X$, and let $Y\hookrightarrow X$ be the zero locus of a regular section of $V$. For $\beta\in H_2(X,\mathbb{Z})$ and…

Let $V$ be a Grassmannian variety. For each stable $V$-graph $\tau$, let $\overline{M}(V,\tau)$ be the corresponding stack of stable maps and let $[\overline{M}(V,\tau)]^0$ denote…

For integers $g\geq 1$, $n\geq 0$, and $d\geq 0$, let $\mathcal{M}_{g,n}(\mathbb{P}^r,d)$ denote the moduli stack of stable maps to projective $r$-space, and let its compactly supp…

Let ${\mathcal Y}$ be a projective smooth superscheme of dimension $r|s$, with bosonic reduction $Y$, and let $\beta_0\in A_1(Y)$. Let…

Let $X=G/P$ be a complex flag manifold. Let $w\in W^{\mathrm{comin}}$ and $u\in W$, let $e\in H_2(X,\mathbb Z)$ be effective, and let $M_{d(w,u)+e}(X_{w_0w},X^u)$ be the moduli spa…

Let $X=G/P$ be a complex flag manifold. Let $w\in W^{\mathrm{comin}}$ and $u\in W$, let $e\in H_2(X,\mathbb Z)$ be effective, and let $M_{d(w,u)+e}(X_{w_0w},X^u)$ be the moduli spa…

Let $X$ be a convex non-super scheme, and let $\beta\in H_2^+(X)$. Denote by $\overline{\mathcal{M}}_{0,k}(X,\beta)$ the moduli stack of super stable maps of genus zero with $k$ Ne…

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…

Let $a=(a_1,\ldots,a_n)$ be a vector of non-negative integers, and let $P_a(\alpha,t)$ be the power series defined by the double Hodge integrals in the paper. The notation $|a|$ de…

Let $\overline{\mathcal{M}}_n$ denote the moduli space considered in the paper, and let $\overline{\mathcal{M}}_{0,n+1}$ denote the corresponding genus-zero moduli space. Their Eul…

Let $r$ be a positive integer and $d$ a positive odd number. The classes $4c_1,c_24$ generate the polynomial ring describing the presentation, and let…

The Uniform Infinite Half-Planar Triangulation has an incipient infinite cluster whose boundary converges, after rescaling, to the infinite stable looptree…

Le Gall–Miermont self-avoiding faces conjecture. Faces in Le Gall and Miermont's $3/2$-stable maps should be self-avoiding.

Let $X$ be the homogeneous space under consideration, let $d\in\Pi_P$, and let $f_{P,d}\colon\mathbb{P}^1\hookrightarrow X$ be the diagonal curve morphism of degree $d$. Let…

Let $\pi_\Lambda:\mathcal{X}_\Lambda\to\mathcal{M}_\Lambda$ be the universal lattice-polarized K3 surface, let $L\in\Lambda$ be an admissible class, and let … be the evaluation map…

Let the space of analytic stable maps be equipped with its tropicalization map to the space of tropical stable maps. Continuity and polyhedrality conjecture. The tropicalization ma…

For a stable map $f:M\to N$, let $M(\underline{\eta})(f)$ be the closure of the locus of tuples of distinct points mapping to a common point, with the map-germ at each point having…

Le Gall–Miermont's supercritical gasket conjecture. If $h>h_c(N)$, the gasket of a large random decorated triangulation under $P_{g,h,N}$ converges, after suitable scaling, towards…

Let $G,d,m$ be as in the moduli problem, let $x$ be the marked point, and let $\overline{\mathcal M}^0_{G,1,d}(\mathbb{CP}^1)$ denote the relevant moduli space of stable maps. For…