The goal of this project is to reinforce an existing collaboration between three European research groups and two Third country groups in the field of structure preserving numerical methods andhighly oscillatory problems. The Third country partners are the La Trobe University, Melbourne Australia and Massey University, Palmerston North, New Zealand. The European beneficiaries are two Norwegian universities (NTNU, Trondheim and University of Bergen) and the University of Cambridge, UK.The main objective of our research is to develop numerical methods which exactly preserve some important geometric structure in the physical model under consideration. Typically this could mean the preservation of symplecticity in Hamiltonian systems, or the preservation of volume in divergence free systems.The research teams involved in this exchange programme have gained considerableexpertise in complementary subfields of geometric numerical integration in the last two decades, and in particular Lie group methods (UiB, Cambridge, NTNU), structure preserving splitting methods (Massey, LaTrobe) and methods for highly oscillatory problems (Cambridge).The exchange will enable a transfer of knowledge between the groups including training of early stage researchers. We believe this will ultimately leadto the solution of challenging theoretical and practical problems in the structure preserving numerical solution of dynamical systems. This goal can not be achieved without sharing our expertise, and will allow us to establish enduring collaborations.