Special Year Seminar II

Suppose given a class of finite combinatorial structures, such as graphs or total orders. Nate Harman and I recently introduced a notion of measure in this context: this is a rule assigning a number to each structure such that some axioms are satisfied.  The purpose of this concept is that measures allow us to construct interesting new tensor categories. However, understanding measures seems to be a difficult combinatorial problem. I will explain some of what is known, and some of the major open problems.