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Explore advanced concepts in high-dimensional expanders through this sixth lecture delivered by Max Hopkins at the International Centre for Theoretical Sciences. Delve into the mathematical foundations and theoretical computer science applications of high-dimensional expanders, which represent a generalization of expander graphs to higher dimensions including hypergraphs and simplicial complexes. Learn about the intersection between high-dimensional expansion theory and error-correcting codes, two rapidly evolving fields that have witnessed significant breakthroughs in recent years. Examine how these mathematical structures play crucial roles in diverse areas of computer science, from communication systems that operate in noisy environments to quantum LDPC codes and capacity-achieving results. Understand the theoretical underpinnings that connect combinatorics, complexity theory, and information theory in the context of high-dimensional expansion. This lecture forms part of a comprehensive workshop series organized by leading researchers Irit Dinur, Venkat Guruswami, and Prahladh Harsha, designed to advance understanding of cutting-edge developments in both high-dimensional expanders and error-correcting codes for graduate students, postdoctoral researchers, and professionals working in computer science, mathematics, and electrical engineering.
