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Explore advanced concepts in high-dimensional expanders through this fourth 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 and mathematics, building upon the foundational concepts of expander graphs that have been instrumental across multiple computational domains. Gain insights into the latest developments in this relatively new area of mathematical research that bridges combinatorics, complexity theory, and information science. This lecture forms part of a comprehensive workshop series organized by leading experts from The Weizmann Institute, UC Berkeley, and TIFR Mumbai, designed to explore cutting-edge research at the intersection of high-dimensional expanders and coding theory.
