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Explore Kneser's theorem and its applications to error-correcting codes and ℓ-divisible set families in this 32-minute conference talk delivered at the ICTS Workshop on High Dimensional Expanders and Codes. Delve into the mathematical foundations connecting combinatorial structures with coding theory, examining how Kneser's classical result extends to modern applications in error-correcting codes. Learn about the relationship between set families with divisibility properties and their implications for code construction and analysis. Discover the intersection of combinatorics, algebra, and coding theory through rigorous mathematical exposition that bridges classical theorems with contemporary research in high-dimensional expansion and error correction. Gain insights into advanced techniques for analyzing combinatorial properties of codes and their connections to geometric and algebraic structures, presented as part of a comprehensive workshop exploring the cutting-edge developments in both high dimensional expanders and error-correcting codes.
