Tseng–You's root-stack Gromov–Witten determination conjecture

Work over $\mathbb{C}$. Let $X$ be a smooth proper Deligne–Mumford stack with projective coarse moduli space, let $D\subset X$ be an irreducible smooth divisor, and let $\mathcal{X}_r$ be the stack of $r$-th roots of $X$ along $D$, with inertia stacks $IX$ and $ID$. The natural restriction map is

$$H^*(IX)\to H^*(ID).$$

Root-stack Gromov–Witten determination conjecture. The Gromov–Witten theory of $\mathcal{X}_r$ is determined by the Gromov–Witten theory of $X$, $D$, and the restriction map $H^*(IX)\to H^*(ID)$.

This conjecture proposes a general determination of the Gromov–Witten theory of a root stack along a smooth divisor. The paper verifies it under an additional assumption, while the general case remains open.