Deformation quantization and perverse sheaves

Abstract

Given a holomorphic symplectic manifold and a pair of oriented holomorphic lagrangiansubmanifolds, the lagrangian intersection caries a canonical perverse sheaf known as the DTsheaf. On the other hand, the theory of deformation quantization provides another, seemingly quitedifferent, construction of a perverse sheaf. l will explain some recent results with Pavel Safronoy inwhich we identify these two constructions, shedding new light on Joyce's conjectural description ofthe holomorphic Fukaya category. Time permitting, l will outline a potential application of theseresults, in which we related the skein module of a 3-manifold to the sheaf-theoretic Floer homologyof Abouzaid and Manolescu.