Combinatorial Inequalities and Combinatorial Interpretations: Part II

In the second talk, I will concentrate on polynomial inequalities and whether the defect (the difference of two sides) has a combinatorial interpretation.  For example, does the inequality  x2+y2≥2xy

  have a combinatorial proof and what does that mean?  There is a surprisingly clean answer of the most general questions of this kind which can be presented in purely algebraic terms.