From Braid Groups to Artin Groups - Lecture 1

Explore the fascinating world of Artin groups in this comprehensive lecture for a general mathematical audience. Delve into a broad class of groups that encompass well-known examples like braid groups, free groups, and free abelian groups, as well as more enigmatic structures. Begin with an examination of braid groups before progressing to various algebraic and geometric characterizations of Artin groups. Survey the current state of knowledge in this field, including both established facts and open questions. Gain insight into new approaches being developed to tackle the most challenging problems in Artin group theory. This Aisenstadt Chair Lecture, presented as part of the Workshop on Cube Complexes and Combinatorial Geometry, offers a captivating introduction to this important area of mathematics.