Explore the intricacies of high-dimensional learning in this 57-minute seminar by Joan Bruna Estrach from New York University. Delve into the experimental revolution of deep learning and its challenges, examining geometric function classes and harmonic analysis on the sphere. Investigate invariant kernels, optimization aspects, and overparametrisation while considering algorithm-specific hardness. Analyze the computational hardness of shallow learning, the shortest vector problem, and continuous learning with errors. Discover algorithmic upper bounds, the LLL algorithm, and random subset problems. Expand your understanding beyond generalized linear models in this comprehensive exploration of data structure's role in high-dimensional machine learning.