Braids and Combinatorics -
Combinatorics is, in principle, the subject devoted to counting certain kinds of mathematical objects.  Several objects appear regularly in this story: subsets, partitions, permutations, and the like.  I’ll begin with an introduction to these objects and how combinatorialists count them.  With that in hand, I’ll discuss “braided” analogues of these constructions — these have a much more geometric flavor, but still retain some of the original combinatorial aspects.  This allows us to upgrade the familiar notions of finite sets and functions between them to a world of braided sets and functions.