3 problems

Let $\beta=\beta^1\beta^2$ be the braid and let $r_1$ and $w$ be as in the construction of the open subset $\mathcal{U}_{r_1,w}(\beta)\subseteq X(\beta)$. Assume that…

Let $\eta$ be a braid word and let $X(\eta)$ denote the corresponding braid variety. A cluster algebra structure conjecture asserts that the coordinate ring of any braid variety…

Let $C$ be an irreducible plane curve singularity, let $L$ be the corresponding algebraic knot, and let $\beta$ be the corresponding braid on $n$ strands. Let $X(\beta\Delta;w_0)$…