Lucas Sabalka, Binghamton University

Abstract:
One class of groups of great importance is Artin's classical and much studied braid groups. These groups may be defined topologically, in terms of configurations of points on a disk. A natural generalization of classical braid groups is to replace the disk with other spaces. This leads us to consider braid groups on graphs. In this talk, we will discuss the definition of graph braid groups and give a survey of some known results. In particular, we will discuss the relationship between graph braid groups and right- angled Artin groups, and possibly the isomorphism problem for certain tree braid groups.