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Explore the fascinating intersection of extremal combinatorics, additive number theory, and coding theory through this 56-minute conference talk by Noga Alon from Princeton University, presented at the PCMI Park City Mathematics Institute. Discover how viewing binary vectors as characteristic vectors of edge-sets of graphs transforms fundamental combinatorial questions in coding theory into compelling extremal problems about families of graphs. Learn about the key results, open problems, and research directions in this emerging field, while examining the sophisticated mathematical methods that combine combinatorial and probabilistic tools with techniques from information theory, number theory, and the theory of combinatorial designs to tackle these challenging questions.
