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Explore the mathematical foundations of chain complexes and their applications to error-correcting codes in this third lecture by Pavel Panteleev from the International Centre for Theoretical Sciences. Delve into advanced concepts at the intersection of algebraic topology and coding theory as part of the ICTS Workshop on High Dimensional Expanders (HDXs) and Codes. Learn how chain complexes provide a powerful framework for understanding the structure of codes and their properties, building upon previous lectures in this series. Examine the theoretical underpinnings that connect topological methods with practical coding applications, essential for researchers working in quantum LDPC codes and related areas. This lecture forms part of a comprehensive two-week program featuring leading experts in mathematics, theoretical computer science, and electrical engineering, designed to advance understanding of the rapidly evolving fields of high dimensional expansion and error-correcting codes.
