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Explore the cutting-edge intersection of coding theory and computational complexity in this comprehensive two-part seminar that addresses the fundamental challenge of local list decoding. Delve into the question of whether data can be encoded for recovery when most information becomes corrupted and only a sub-constant fraction of the database remains accessible. Discover the first construction of high-rate locally list decodable codes that approach information theoretic limits for error tolerance and efficiency, built using novel local algorithmic machinery for high dimensional expanders. Learn about the powerful role of local list decoding in interactive proofs, hardness amplification, and pseudorandomness generation. Examine three major applications including constant rate codes with sub-polynomial time local list decoding, constant rate codes with highly parallel list decoding capabilities, and input-preserving hardness amplification leading to near-linear time pseudorandom generators. Gain insights into a simplified construction and decoding algorithm based on subspace hypergraph systems, presented as part of collaborative research with leading experts in the field.
