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The Casa Matemática Oaxaca (CMO) will host the "Hamiltonian PDEs: KAM, Reducibility, Normal Forms and Applications" workshop in Oaxaca, from June 9, 2019 to June 14, 2019. Since its early discovery, KAM theory and more generally Hamiltonian perturbation theory has been applied to physical problems and actually one of the main purpose of V. Arnold himself was to use it for the study of the stability of the solar system. The last years have seen a remarkable advance in perturbation theory for Hamiltonian partial differential equations so that it has become a tool applicable to the study of several physical models and recent developments are very promising for the study of further problems. The aim of this workshop is to put toghether a strong group of pure mathematicians working on Hamiltonian PDEs with more applied mathematicians, in order to make the point on the state of the art in particular regarding the applications to concrete models. The main goal is double: on the one side to understand the relevance of the theory for the explanation of experimental behaviors; on the other side to bring out new problems and inputs in order to stimulate new directions of development of the theory. The main important applications on which the conference will focus are: dynamics of Bose Einstein condensates (state of matter in which quantum properties like superfluidity occur at macroscopical level), Water Wave problem (flow of an incompressible and irrotational fuid with a free surface), dynamical stability of suspended bridges (problem related to the famous Tacoma bridge collapse), stability of numerical algorithm (how to design good integration algorithm for PDEs).