Ramanujan Graphs: Generating Functions and Expander Graphs

This lecture covers the importance of Ramanujan graphs, focusing on mathematical patterns, generating functions, and the concept of non-backtracking walks. It explores the building blocks of cycles and ways of combining nodes, as well as the behavior of graphs on expander graphs. The instructor discusses the relationship between Ramanujan graphs and certain NP-hard problems, highlighting their solvability on expander graphs. The lecture also delves into the concept of belief negotiation and coding theory, emphasizing the significance of expanders as worst-case scenarios for embedding. Additionally, it touches on the continuous and discrete distance properties of graphs.