The Frobenius-manifold Lyashko–Looijenga degree conjecture

Let $W$ be an irreducible real reflection group, let $g$ be a quasi-Coxeter element in $W$, and assume that the Frobenius manifold $\mathcal{F}_g$ exists. Let $LL(\mathcal{F}_g)$ denote its Lyashko–Looijenga map, and let $F_W^{\mathrm{red}}(g)$ be the number of reduced reflection factorizations of $g$.

Frobenius-manifold Lyashko–Looijenga degree conjecture. The degree of the map $LL(\mathcal{F}_g)$ equals

$$F_W^{\mathrm{red}}(g).$$

For Coxeter elements, the analogous equality is known and relates reduced reflection factorizations to the degree of a weighted-homogeneous Lyashko–Looijenga map. The conjecture extends this relationship to quasi-Coxeter elements when the corresponding Frobenius manifold exists; the source gives no resolution status.