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Explore the applications of Shannon entropy in combinatorics and computer science through this 1-hour 21-minute colloquium talk. Delve into examples of combinatorial inequalities justified using information-based considerations and formalized with entropy. Examine the field of randomized two-party communication complexity, focusing on entropy-derived lower bounds for the Set Disjointness problem. Investigate Von Neumann entropy as the quantum-mechanical counterpart to Shannon entropy and its role in studying quantum communication complexity. Designed for a general scientific audience, no prior knowledge of computer science, information theory, or quantum mechanics is required.
