Infirri's formality conjecture for Hermitian Yang–Mills moduli spaces

Let $M^{\bullet,\bullet}=\bigwedge^{\bullet,\bullet}V^*\otimes\operatorname{End}(R)$, let $\alpha\in\mathcal{N}_0\cap\mu^{-1}(\zeta)$, and let $((M^{0,\bullet})^\Gamma,\overline{\partial}_\alpha)$ be the associated differential graded Lie algebra. Infirri's formality conjecture. For all such $\alpha$ and generic $\zeta$, the differential graded Lie algebra $((M^{0,\bullet})^\Gamma,\overline{\partial}_\alpha)$ is formal; consequently, $M_\zeta$ has, for these $\zeta$, at worst quadratic algebraic singularities. This predicts a particularly simple local deformation-theoretic structure for the moduli spaces; the source gives no resolution of the conjecture.