Skein algebras and quantized Coulomb branches for surfaces of genus at most one

Let $S=S_{g,n}$ be a surface of genus $g\leq 1$ with $n>0$ boundary components, and let $(\widetilde{G},N)$ be the group and representation associated to a pants decomposition of $S$. Skein–Coulomb branch conjecture. If $g=0$, there is a $\mathbb{C}$-algebra isomorphism

$$\operatorname{Sk}_{A,\boldsymbol{\lambda}}(S)\cong K^{\widetilde{G}_{\mathcal{O}}\rtimes\mathbb{C}^*}(\mathcal{R}_{G,N}).$$

If $g=1$, there is a $\mathbb{Z}_2$-action on $\operatorname{Sk}_{A,\boldsymbol{\lambda}}(S)$ and a $\mathbb{C}$-algebra isomorphism

$$\operatorname{Sk}_{A,\boldsymbol{\lambda}}(S)^{\mathbb{Z}_2}\cong K^{\widetilde{G}_{\mathcal{O}}\rtimes\mathbb{C}^*}(\mathcal{R}_{G,N}).$$

This conjecture extends the stated isomorphisms for the four-holed sphere and one-holed torus to all surfaces with positive boundary and genus at most one, relating skein algebras to quantized Coulomb branches. The parser provides no evidence that the conjecture has been resolved.