Koszulity conjecture for cyclotomic quiver Schur algebras

Let $A^{\underline{\boldsymbol{\nu}}}$ be the cyclotomic quiver Schur algebra associated with the multicharge $\underline{\boldsymbol{\nu}}$. Koszulity conjecture. The cyclotomic quiver Schur algebra $A^{\underline{\boldsymbol{\nu}}}$ is Koszul. This conjecture predicts that the grading on these algebras has the homological regularity needed to relate their graded representation theory to canonical bases and graded decomposition numbers. The supplied context does not state whether the conjecture has been resolved.