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Monday, February 8, 2016

**Abstract:** A Lagrangian (i.e. maximally isotropic) subspace of a symplectic space is called split if it has an isotropic complement. In finite dimensions, all Lagrangian subspaces are split, but there are more things to say when the symplectic space is infinite dimensional, e.g. a Hilbert or Frechet space, and depending whether the symplectic structure is weak or strong. In this talk we will discuss some aspects of the theory of split canonical relations, in particular, compositions and reductions, in the framework of Lagrangian field theories with boundary. We will prove that the evolution relations arising from certain topological theories are split.