Explore a 52-minute lecture from the Erwin Schrödinger International Institute's Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that delves into the manifold structure of data spaces in popular datasets. Gain insights into dimensionality reduction techniques through both Deep Learning and Geometric Deep Learning perspectives, drawing from fundamental concepts in geometry and physics. Learn how these mathematical principles can be applied to understand and analyze complex data structures in modern machine learning applications.