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The research school "High Dimensional Approximation and Deep Learning" will be held in Nantes from May 16 to 20, 2022. This school addresses the mathematical foundations of high-dimensional approximation and statistical learning, with particular attention to nonlinear approximation, model reduction, tensors and neural networks. The research school is intended for master and PhD students, young researchers and confirmed researchers interested in these themes. The school will feature four courses given by experts in the mathematics of approximation and learning, and invited lectures.