  Topological defects attract much recent interest in high-energy and condensed
matter physics because they encode (non-invertible) symmetries and dualities.
We study codimension-1 topological defects from a hamiltonian point of view,
with the defect location playing the role of `time'. We show that the Weinstein
symplectic category governs topological defects and their fusion: each defect
is a lagrangian correspondence, and defect fusion is their geometric
composition. We illustrate the utility of these ideas by constructing S- and
T-duality defects in string theory, including a novel topology-changing
non-abelian T-duality defect.
