Pseudorandomness: Theory and Applications

This lecture covers the concept of pseudorandomness, focusing on the theory and applications. It discusses the importance of pseudorandomness in AI, the challenges of testing properties with exponentially small probabilities, and the idea of pseudo-random graphs. The lecture also delves into the theory of dynamical systems, looking at manifolds and random walks on surfaces. It explores the transition matrix in random walks, Laplacian matrices, and the properties of adjacency matrices. Additionally, it explains the relationship between eigenvalues and eigenvectors in adjacency and Laplacian matrices, emphasizing the significance of pseudorandomness in various applications.