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This, the 20th in a series of Workshops in Alpbach, will feature minicourses given by world class researchers and invited talks by younger researchers, covering topics in various areas of number theory, including but not limited to arithmetic geometry, Galois representations, etc. The emphasis includes not only deep theoretical developments, but also applications of a more concrete/computational nature. Minicourses presenting a broad overview of these topics, delivered by top international experts, will be complemented by invited talks highlighting recent progress.