5 problems

Let $(X,E)$ be a smooth Looijenga pair with affine interior $U=X\setminus E$, let $u:\mathcal T\to X$ be the universal torsor, and set $G=\mathcal T|_U$. Let $V$ be the mirror to…

Let $(X,E)$ be a smooth Looijenga pair with affine interior $U=X\setminus E$, let $u:\mathcal T\to X$ be the universal torsor, and set $G=\mathcal T|_U$. Let $U^{\vee}$ and $V$ den…

Let $(X,D)$ be a nef Looijenga pair admitting a deformation to a pair $(X',D')$ with $X'$ toric, $D'_i$ prime toric divisors for $i<l$, and $D'_l$ nef. Let $(Y,L)$ be the correspon…

The higher genus log/open correspondence. One has

The genus zero log/local/open correspondence. The invariants satisfy