Polynomial Inequalities and Combinatorial Interpretations

Explore polynomial inequalities and their combinatorial interpretations in this 50-minute seminar by Igor Pak, part of the Colloque des sciences mathématiques du Québec (CSMQ). Delve into the world of combinatorics, where many inequalities can be proven through explicit injection, resulting in elegant and insightful proofs. Discover how these proofs provide combinatorial interpretations for the differences between two sides of an inequality. Examine scenarios where the naive approach fails and learn techniques to prove the impossibility of such methods. The seminar is divided into two parts: the first half offers a comprehensive overview of known concepts with numerous examples, while the second half focuses on proving negative results for algebraic inequalities and their implications. Gain insights from Pak's collaborative work with Christian Ikenmeyer in this mathematical exploration presented at the Centre de recherches mathématiques (CRM) on September 13, 2024.