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Explore advanced concepts in high-dimensional expanders through this lecture delivered by Madhur Tulsiani 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 how these structures connect to error-correcting codes and their role in modern communication systems that operate in the presence of noise. Examine the intersection between high-dimensional expansion theory and coding theory, two rapidly evolving fields that have experienced significant breakthroughs in recent years including new list-decodable codes, locally decodable/testable codes, polar codes, and quantum LDPC codes. Gain insights into how expander graphs have influenced diverse areas of computer science and how their higher-dimensional counterparts are shaping current research in mathematics and theoretical computer science. This lecture forms part of a comprehensive workshop series exploring the cutting-edge developments in both high-dimensional expanders and error-correcting codes, designed for graduate students and researchers in computer science, mathematics, and electrical engineering.
