Explore a groundbreaking algorithm for learning mixtures of linear regressions in subexponential time using Fourier moments in this 25-minute conference talk. Delve into solving multiple linear and Gaussian systems, examine mixture-of-experts and mixture models, and analyze previous results in the field. Investigate the potential barrier at exp(k) and discover the innovative approach that overcomes it. Learn about techniques for identifying individual components, understanding the minimum variance of Gaussian mixtures, and grasping the significance of exp(VR) in the algorithm's complexity. Gain insights into methods for learning all components simultaneously and consider open questions for future research in this cutting-edge area of machine learning and statistical analysis.