Fukaya categories of complex-symplectic manifolds and perverse sheaves

Certain exact complex-symplectic manifolds, such as hypertoric varieties and Nakajima quiver varieties, play a prominent role in parts of geometric representation theory.  I will talk about the wrapped Fukaya category of these manifolds. In particular, I will explain that the Fukaya category admits a t-structure whose heart contains closed exact holomorphic Lagrangians. The Floer homology of two such Lagrangians can be computed by a perverse sheaf. Joint work with Christopher Kuo, David Nadler and Vivek Shende.