Optimal Transport and High Dimensional Probability

Explore advanced mathematical concepts through this mini course covering optimal transport theory, high-dimensional probability, and geometric aspects of deep learning. Delve into Wasserstein spaces and their applications in probability theory with Yair Shenfeld's comprehensive introduction to optimal transport. Master Otto's calculus on Wasserstein spaces and understand Langevin dynamics through the lens of calculus on metric spaces with Sinho Chewi's lectures on gradient flows. Investigate the computational aspects of solving systems of real quadratic equations and learn about approximately Hadamard matrices and random frames through Mark Rudelson's presentations. Examine the geometric structure underlying deep linear networks with Govind Menon's analysis of neural network architectures from a mathematical perspective. Gain insights into the intersection of optimal transport theory, high-dimensional probability, and modern machine learning through this intensive mathematical exploration spanning multiple interconnected topics in contemporary mathematical research.