Title: Coisotropic Branes in Symplectic Torus and 1-Shifted Symplectic Holomorphic Stack

Abstract: Kapustin-Orlov proposed that coisotropic branes exist as objects inside Fukaya categories besides Lagrangian branes. However, a satisfactory Floer theory involving coisotropic branes stands as a long time open problem. Making using the rich symmetries of symplectic torus, we can predict certain Floer homologies involving coisotropic branes. On the other hand, Gaiotto-Gukov-Witten proposed an approach to geometric quantization by studying the Hom complex between the canonical brane and Lagrangian branes in a holomorphic manifold. From the 1-shifted symplectic geometry perspective, coisotropic branes induces holomorphic 1-shifted Lagrangian branes, which in turn produces (weakly) holomorphic symplectic spaces through Lagrangian intersections . And this view point make a bridge between general coistropic branes intersection theory and geometric quantization.