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Delve into the world of combinatorial inequalities and interpretations in this advanced seminar talk by Igor Pak from the Institute for Advanced Study. Explore the intriguing question of whether polynomial inequalities and their defects have combinatorial interpretations. Examine specific examples, such as the inequality x^2 + y^2 ≥ 2xy, and uncover the meaning behind their potential combinatorial proofs. Discover a surprisingly clean answer to general questions in this field, presented in purely algebraic terms. Learn about the joint work with Christian Ikenmeyer, as presented at FOCS 2022, and gain insights into this fascinating area of combinatorial mathematics.
