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Explore the mathematical foundations of network connectivity in this Harvard CMSA lecture where Irit Dinur from the Institute for Advanced Study delves into expander graphs and their evolution into high dimensional expanders (HDXs). Learn how expander graphs serve as ideal models for robustly connected networks - from social systems to transportation infrastructure - where small groups of nodes maintain strong connections throughout the entire structure. Discover the historical development of expander graphs and their crucial applications in error-correcting codes, pseudorandomness, and probabilistically checkable proofs (PCPs). Examine the emerging field of high dimensional expanders (HDXs), understanding their unique local-to-global properties and potential applications that are revolutionizing theoretical computer science. Gain insights into how these mathematical structures ensure efficient information flow and maintain connectivity across complex network systems.
