Dg categories of canonical Lagrangian D-branes, their quantizations, and virtual de Rham categories on holomorphic symplectic manifolds are formal when localized at countable collections of clean-intersecting compact Kähler Lagrangians, with Kaledin classes as obstructions to formality.
Formality conjecture
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Differential graded categories in holomorphic symplectic geometry
Dg categories of canonical Lagrangian D-branes, their quantizations, and virtual de Rham categories on holomorphic symplectic manifolds are formal when localized at countable collections of clean-intersecting compact Kähler Lagrangians, with Kaledin classes as obstructions to formality.