Ordered groups and braids

The braid groups B_n continue to surprise us, although they were introduced by Emil Artin 75 years ago. They have played a big role in topology, analysis, group theory and mathematical physics. For example, Vaughan Jones' discovery of new representations of B_n fifteen years ago led to a revolution in the theory of knots. One of the most astonishing recent discoveries is that the braid groups are actually right-orderable: there is a strict total ordering of all braids which is preserved under multiplication on the right. This was proved by Dehornoy, using techniques motivated by set theory and large cardinals. Since then, others (including myself) have found a natural geometric way of understanding this ordering, using techniques which are very different from the usual arguments in ordered group theory. I will discuss this ordering and some of its consequences, and a website which can decide the ordering.

Refreshments will be served in Math Annex Room 1115, 3:15 p.m.