The formality conjecture for hyperkähler Fukaya algebras

Let $M=(M,g,I,J,K)$ be a hyperkähler manifold, and let $L_1,\dots,L_k$ be closed $I$-complex submanifolds that are Lagrangian with respect to

$$\omega_{\mathbb{C}}:=\omega_J+i\omega_K.$$

Formality conjecture. The Floer--Fukaya $A_\infty$ algebra

$$CF^*(\oplus_i L_i,\oplus_i L_i),$$

defined with respect to $\omega_J$ on the real symplectic manifold $(M,\omega_J)$, is formal in characteristic zero. This is motivated by the formality of the $A_\infty$ algebra of chains on a compact Kähler manifold and predicts formality for collections of holomorphic Lagrangians in the hyperkähler setting; its resolution is not supplied here.