Topology Seminar: Briaid orderings and knot genus

The braid group has a left-invariant total ordering, called the Dehornoy ordering. In this talk, I will introduce the Dehornoy floor of braids, which measures a complexity of braids by using the Dehornoy ordering. I will give a new lower bound of knot genus by using the Dehornoy floor and also discuss other applications of the Dehornoy floor to knot theory.