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Explore the third lecture in a series on high-dimensional expanders delivered by Max Hopkins at the International Centre for Theoretical Sciences. Delve into advanced concepts of high-dimensional expansion theory, which generalizes traditional expander graphs to higher dimensions through hypergraphs and simplicial complexes. Learn about the mathematical foundations and theoretical computer science applications of these structures, which have become increasingly important in recent years across various fields including coding theory and complexity theory. Understand how high-dimensional expanders connect to error-correcting codes and their role in modern communication systems. This lecture forms part of a comprehensive workshop series exploring the intersection of high-dimensional expanders and coding theory, featuring cutting-edge research and recent breakthroughs in list-decodable codes, locally testable codes, and quantum LDPC codes. Gain insights into the mathematical techniques and theoretical frameworks that underpin these advanced topics in computational mathematics and theoretical computer science.
