13 problems

Assume that $X$ is rational, $D$ is a smooth anticanonical curve on $X$, and $P\in D(\beta)$, where $D(\beta)$ is the finite set of points associated with the class $\beta$. Let…

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 $\phi:Y\to B$ be an elliptic fibration and let $D\subset Y$ be a normal crossing divisor such that $\phi(D)$ is a divisor in $B$. Assume that the generic fiber of…

Let $E$ be a smooth cubic in the projective plane $\mathbb{P}^2$. Consider the counts of rational curves of varying degree in $\mathbb{P}^2\setminus E$, and a pencil of affine plan…

Let $d$ denote the degree data used for the two non-tame pairs $\operatorname{dP}_1(0,4)$ and $\mathbb{F}_0(0,4)$, and let $q=\exp(\mathrm{i}\hbar)$. The q-binomial identities. The…

Let $Y(D)$ and $Y'(D')$ be nef two-component log Calabi–Yau surfaces with maximal boundary, and suppose the local geometries $E_{Y(D)}$ and $E_{Y'(D')}$ are deformation equivalent.…

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 $X$ 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…

The log-local principle. After dividing the log invariants by

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…

Constancy conjecture. The log BPS number is constant as the point $P$ varies in $E(\beta)$.

Let $D\subset X$ be a normal crossing divisor with smooth nef components $D_1,\ldots,D_k$, and let $\beta$ be a curve class such that … for every $i$. Write … for the forgetful map…