  We study intersections of complex Lagrangian in complex symplectic manifolds,
proving two main results.
  First, we construct global canonical perverse sheaves on complex Lagrangian
intersections in complex symplectic manifolds for any pair of {\it oriented}
Lagrangian submanifolds in the complex analytic topology. Our method uses
classical results in complex symplectic geometry and some results from
arXiv:1304.4508. The algebraic version of our result has already been obtained
by the author et al. in arXiv:1211.3259 using different methods, where we used,
in particular, the recent new theory of algebraic d-critical loci introduced by
Joyce in arXiv:1304.4508. This resolves a long-standing question in the
categorification of Lagrangian intersection numbers and it may have important
consequences in symplectic geometry and topological field theory.
  Our second main result proves that (oriented) complex Lagrangian
intersections in complex symplectic manifolds for any pair of Lagrangian
submanifolds in the complex analytic topology carry the structure of (oriented)
analytic d-critical loci in the sense of arXiv:1304.4508.
