7 problems

Let $(Y,D)$ be the rational elliptic surface mirror to $\mathbb{P}^2$. For each $r\in\mathbb{Z}_{>0}$ and each integer $c_1$ with $-r<c_1\leq 0$, let $h^{GW}_{r,c_1}(\tau)$ be the…

Let $(Y,D=D_1+\dots+D_l)$ be a log-smooth log Calabi–Yau pair of maximal boundary. For $\mathsf{m}=1,\dots,l+1$, let…

Let $S$ be the dual intersection complex of $D$, let $B$ be the cone over $S$, and let $B_0=B\setminus\{0\}$. The integer points $q\in B(\mathbb Z)$ index prime fundamental classes…

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

Let $X$ be a smooth projective variety and let $D=D_1+\cdots+D_n$ be an effective reduced normal crossing divisor whose components $D_i$ are smooth, irreducible, and nef. For a cur…

Toric transversality conjecture. In the definition of $N_{\beta}(q_1,\ldots,q_s)$, all curves in $\mathcal{M}^{\log}_{0,\Delta_{\mathbf q}}(\widetilde{Y}^{\dagger},\beta)$ satisfyi…

Weak Gromov–Witten Frobenius structure conjecture. There exists a product $*$ on $\operatorname{QH}_{\log}^0(Y,D)$ making it a commutative associative…