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Monday, October 28, 2013

**Abstract:** Let $(M, \omega)$ be a symplectic manifold with nonempty boundary, $W$. The restriction of $\omega$ to $W$, $\omega_W$, has a one dimensional kernel which defines the characteristic foliation of $W$. If $W$ is a boundary of contact type then it admits a tubular neighborhood comprised of hypersurfaces whose characteristic foliations are all conjugate to those of $W$. Since these hypersurfaces lie in the interior one might guess (or hope) that the interior of $(M, \omega)$ determines $omega_W$ or at least some of its symplectic invariants. Several questions in this direction were raised by Eliashberg and Hofer in the early nineties. In this talk I will describe the resolution of some of these questions. I will prove that neither $\omega_W$ or its action spectrum is determined by the interior of $(M, \omega)$. This involves the construction of a new dynamical symplectic plug. The construction uses only soft techniques (Moser's method) and so should hopefully be accessible to all.