Combinatorial Inequalities and Combinatorial Interpretations: Part I

In the first talk, I will give a broad survey of classical inequalities that arise in enumerative and algebraic combinatorics.  I will discuss how these inequalities lead to questions about combinatorial interpretations, and how these questions influence the area in return.  I will conclude with a complexity theoretic setup which allows one to formulate negative results.  This talk is aimed at the general audience and absolutely no prior knowledge of computational complexity is assumed.