Algebraic combinatorics seminar - Max Bennett

How to Count Positive Braids (or These Aren't The Droids You're Looking For)

Abstract:

Braids can be thought of in many different ways, most commonly as a geometric object or as a group. In this talk I will review a certain class of braids (positive braids) that is not a group, but a monoid. The braid monoid admits many combinatorial properties, and turns out to be a relatively easy thing to count. I will go through a few of these properties and derive a generating function with respect to length. Also come to learn about the role that the jedi force has on learning about braids.