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Modern numerical methods for hyperbolic conservation laws rely on polynomials of high degree, mostly orthogonal polynomials, on triangular or quadrilateral meshes. Due to shocks stability is an issue and modern means of filtering like spectral viscosity is required. Additional TV-filters are needed in most cases as postprocessors and the choice of the solver for the differential equations to integrate in time is crucial. The workshop was organised to bring together researchers from different areas of mathematics in order to fuel the research on high-order efficient and robust numerical methods.