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Approximately 30,000 accelerators are currently used to diagnose and treat cancer and other diseases, improve manufacturing processes, and study energy, environmental and security issues. The operation and future improvement of particle accelerators requires the solutions to challenging mathematical problems related to single particle nonlinear dynamics and collective phenomena in high intensity particle beams interacting with electromagnetic fields and plasmas. These challenges include the effects of linear and nonlinear resonances and KAM dynamics in particle accelerators, regular and chaotic effects in many body systems, collective effects, particle beam instabilities and Landau damping. The workshop is dedicated to better understand and extend the mathematical methods available to accelerator physicists to make progress in understanding and controlling the physics and technology of these systems.