Structure preservation in numerical differential equations, known also as geometric numerical integration, has emerged in the last two decades as a central topic in numerical mathematics. Another, related area of an increasing importance is the computation of highly oscillatory problems. This symposium will focus on these two themes and their interaction, as well as on applications in astronomy, molecular dynamics, classical and quantum mechanics, electrical engineering, electromagnetism and acoustics. We intend to bring together brilliant scientists with overlapping interests in these vital areas of activity, encouraging new ideas and new interactions.