Ciocan-Fontanine–Kim higher-genus quasimap wall-crossing conjecture

Let $Z$ be a complete intersection in projective space, and fix $g,n\geq 0$. For each effective degree $\beta$, let $q^\beta$ be the corresponding Novikov monomial, let $\overline{\mathcal{M}}^{\epsilon}_{g,n}(Z,\beta)$ and $\overline{\mathcal{M}}^{\infty}_{g,n}(Z,\beta)$ denote the moduli spaces of $\epsilon$-stable and $\infty$-stable quasimaps, respectively, and let $\mu^{\epsilon}_{\beta}(z)$ be the relevant coefficients of the $I$-function of $Z$. For a tuple $\vec{\beta}=(\beta_1,\ldots,\beta_k)$, let $b_{\vec{\beta}}$ convert the additional marked points to basepoints, and let $c$ be the contraction morphism from $\infty$-stable to $\epsilon$-stable quasimaps. Ciocan-Fontanine–Kim's higher-genus wall-crossing conjecture. One has

$$\sum_{\beta}q^\beta[\overline{\mathcal{M}}^{\epsilon}_{g,n}(Z,\beta)]^{\mathrm{vir}}= \sum_{\beta_0,\beta_1,\ldots,\beta_k}\frac{q^{\beta_0}}{k!}(b_{\vec{\beta}})_*c_*\left(\prod_{i=1}^kq^{\beta_i}\operatorname{ev}_{n+i}^*(\mu^{\epsilon}_{\beta_i}(-\psi_{n+i}))\cap[\overline{\mathcal{M}}^{\infty}_{g,n+k}(Z,\beta_0)]^{\mathrm{vir}}\right).$$

More generally, if $Z=W\mathbin{/\!/_{\theta}}G$ for a complex affine variety $W$ and a reductive algebraic group $G$, there should be an explicit formula, depending only on coefficients of the $I$-function of $Z$, relating the virtual fundamental cycles of the moduli spaces of $\epsilon$-stable and $\infty$-stable quasimaps to $Z$. This is a proposed higher-genus extension of genus-zero quasimap wall-crossing; the displayed formula is presented as a conjecture, while the paper's abstract states that it proves the formula for complete intersections in projective space. The broader GIT-quotient formulation remains conjectural in the supplied text.